# Patent

## Title
Method for measurement-based connection admission control (MBAC) in a packet data network

## Abstract

A method for measurement-based connection admission control in a packet data network where traffic flow of arriving data packets is forwarded via a switch with a delay depending on the priority of a queue associated to the data packets of a respective connection and the amount of prevailing traffic. The method comprises providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements; approximating the envelope to a piecewise linear traffic constraint curve (A(Ik)); modifying the piecewise linear traffic constraint curve such that the curve assumes a concave shape; and checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and granting the requested new connection, if the predetermined delay bounds are not violated.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation of International Application PCT/EP99/04236 having an international filing date of Jun. 18, 1999 and from which priority is claimed under all applicable sections of Title 35 of the United States Code including, but not limited to, Sections 120, 363 and 365(c).


FIELD OF THE INVENTION
The present invention relates to a method for measurement-based connection admission control (MBAC) in a packet data network. Particularly, the present invention relates to such a MBAC method in a packet data network, in which plural connections are established via a switch such as, for example, an ATM switch adopting a static priority queuing model.
BACKGROUND OF THE INVENTION
A great advantage of packet and cell switched networks, like ATM is efficiency. Most traffic in a network is bursty in nature, because most traffic sources like people surfing on the web (i.e. the Internet) or talking to the phone have idle or almost idle periods. When the burstiness is combined with statistical discovery that bursts unlikely occur coincidentally, obviously there is some new efficiency available. We can take advantage of this efficiency with statistical multiplexing, which means having transfer capacity much smaller than the total sum of the peak capacity consumption of users. The term statistical multiplexing gain is used to denote the factor of the efficiency achieved.
The reverse of this efficiency is uncertainty. By providing a capacity less than the sum of peak consumption of users, we always take a statistical risk of congestion. The less capacity we provide, the more likely the offered traffic momentarily exceeds the offered capacity. To prevent the loss of data during rush means to store excess packets into a buffer for a moment. At this point, usually two questions arise: is the buffer large enough to keep the packet loss low enough or is the waiting time of packets in the buffer too long for users? We can think of this also as a kind of intuitive definition of quality of service (QoS). From users' point of view QoS is defined in terms of transfer delay, delay variation and proportional to lost data to send data.
The core idea of the ATM is achieving a combination of these two matters: efficiency and quality of service. With a time-division based system one could have guaranteed QoS for different bandwidth requirements but remarkable loss of efficiency would have been caused by allocation of resources according to absolute peak consumption. Unfortunately, carrying out this promising combination of quality and efficiency has proven much more difficult than the early visionaries of ATM thought.
In ATM the functional entity which has responsibility for determining whether there are enough resources for a new connection is commonly named as connection admission control (CAC). The limited resources are bandwidth and buffer space as in the case of any packet switched network. In specifications, it is not detailed how the determination of resource availability should be done. It is up to the manufacturer.
In general, connection admission control methods are divided into two groups:

    
    
        preventive CACs which determine the current usage of resources using traffic descriptor parameters of ongoing connections, announced by users at connection request, and
        measurement-based CACs (MBACs) which measure the current use of resources.
    
    


Because this application focuses on ATM (Asynchronous Transmission Mode) networks as an example of packet data networks, in the following the traffic classification and QoS definitions used in connection with ATM are briefly introduced for subsequent better understanding.
In an ATM network a traffic contract between a user and the network consists of QoS parameters on one hand and connection traffic description on the other hand. The latter one, in turn, comprises a source traffic description, a CDVT (cell delay variation tolerance) parameter and a conformance definition.
The end system, i.e. the network, announces the end-to-end QoS requirements of a new connection in terms of QoS parameters. The QoS parameters are maximum Cell Transfer Delay (maxCTD), peak-to-peak Cell Delay Variation (CDV) and Cell Loss Ratio (CLR). The maxCTD is defined so that the fraction of the cells violating maxCTD, that is, the fraction of the cells delivered late, is equal to or less than the CLR. The relationship between the maxCTD and CDV is clear: CDV is the difference between maxCDV and the minimum possible transfer delay.
Source traffic descriptor consists of traffic parameters describing the behavior of the traffic source of the end system. Four traffic parameters have been defined: Peak Cell Rate (PCR), Sustainable Cell Rate (SCR), Maximum Burst Size (MBS) and Minimum Cell Rate (MCR). Note that PCR, SCR are announced as cells per second whereas MBS is announced in cells.
The CDVT part consist of a single Cell Delay Variation Tolerance (CDVT) parameter. The end system either gives a value for CDVT or accepts the value suggested by the network. The existence of the CDVT value is dictated by the practice, because ATM layer does not work as an ideal transportation medium. In theory, connections having PCR value defined are not allowed to send cells closer to each other than T=1/PCR and therefore the switch could assume that the PCR is the absolute peak rate of the connection. In practice, the ATM layer is not able to transport given cells immediately, because there is a variable transmission delay due to insertion of maintenance cells and an overhead of lower transportation protocol, for example, SDH. As a result, the cell intervals at the user-network interface (UNI) are not constant any more, because some cells arrive closer to each other as clumps or clusters, respectively.
In such a situation of cells arriving in clumps or clusters, one can observe the fluctuating transmission delay with a minimum of dmin and a maximum of dmax. In this case, where the user application is sending at peak rate with interarrival times of T=1/PCR, the cell stream at the ATM link can be described with GCRA(T,CDVT) where CDVT=dmax−dmin. (Note that GCRA denotes a so-called Generic Cell rate algorithm.)
In general, the conformance definitions of the connections in ATM are based on the GCRA algorithm. The number of GCRA leaky buckets and the set of traffic parameters used depend on the service category. Moreover, in certain cases, the end systems are allowed to send more traffic than judged conformant by the GCRA by setting a special Cell Loss Priority (CLP) bit in the header of the offending cells. In the case of congestion in the network, these tagged cells are the first ones subject to discarding.
Furthermore, to serve a wide range of communication needs, ATM provides four service categories. In each category, QoS definition, source traffic description and conformance definition is different due to different characteristics of the services.
Constant bit rate (CBR) service with very small CDV and CLR requirements is intended to emulate circuit-switched connections. In addition to CDV and CLR, also maxCTD is defined for a CBR connection. The source traffic descriptor consist of only PCR parameter, and the conformance definition of the connection is defined by GCRA(1/PCR,CDVT). The CBR service is suitable for real-time applications producing almost constant rate traffic.
There are two types of variable bit rate (VBR) services: real-time (rt-VBR) and non-real-time (nrt-VBR) services. With both type of connections, source traffic descriptor consist of PCR, SCR and MBS parameters, where PCR>SCR. The conformance definition of both rt-VBR and nrt-VBR is defined with two leaky buckets, also called dual leaky bucket: GCRA (1/PCR, CDVT) and GCRA (1/SCR, τ+CDVT), where τ=(MBS−1)(1/SCR−1/PCR). The difference between these two services is in the QoS definition. For rt-VBR, all three QoS parameters, maxCTD, CDV and CLR, are defined, whereas for nrt-VBR, only CLR is defined. VBR services are intended for bursty traffic sources having high peak-to-mean rate ratio. Due to two bit rate parameters, PCR and SCR, the network may take advantage of statistical multiplexing. The rt-VBR is naturally intended for applications having real-time requirements.
Unspecified bit rate service (UBR) has been specified for traditional adaptive data services not requiring any QoS guarantees. Internet-like best effort service enables quite a good utilization of free capacity and therefore compensation of low utilization caused by imperfect CAC of other service classes. Possible congestion control is assumed to be a part of higher protocol layers, like TCP. For UBR connections, no QoS parameters are defined. However, the end system must announce the PCR parameter of the source traffic descriptor, because ATM networks may optionally perform CAC check for UBR connections.
To provide a rapid access to the continuously changing amount of unused bandwidth, an available bit rate (ABR) service has been defined. A traffic source using ABR connection adjusts its transmission rate according to the feedback sent by the switches along the connection. Specifications of the ATM forum define two kinds of feedback methods. First, a switch may control source implicitly by announcing about congestion with a congestion indicator bit in either resource management cells or data cells. Second, a switch may control the source explicitly by telling it the share of the available bit rate at which the source is allowed to send. In the traffic contract, no QoS parameters are defined. The traffic source descriptor consists of PCR and minimum cell rate (MCR) parameters, where the MCR denotes the minimum bandwidth the connection needs. Standard GCRA conformance definition is not applied since the conformance depends on the feedback method used. Implementation of the ABR service efficiently may be hard, as it requires a lot from CAC. In addition, the need for the ABR service may be arguable as far as IP and especially TCP are run over ATM.
Now, returning to the two different types of CAC methods mentioned above, these are briefly compared with each other.
The motivation for developing MBAC has originated from a few essential drawbacks in ATM traffic model:

    
    
        First, it is difficult for the user to characterize his traffic in advance and because the network polices the traffic contract, the user prefers overestimation.
        Second, deterministic traffic model based on leaky buckets is easy to police, but traffic flows with rate variations over multiple time scales are not adequately characterized by two leaky buckets which give only the worst-case upper bound leaving a large fraction of potential statistical multiplexing gain unreachable.
        Third, as a result, preventive CAC making decision on the basis of only traffic parameters combines the effect of both of these inefficiencies.
    
    


In other words, the main objective of MBAC is efficiency.
Users may describe their sources with very conservative parameters, because the resource demand of connections is determined by parameters only when connections are established—later their real resource need is measured.
Since MBAC determines availability of resources for a new connection on the basis of the measured behavior of existing connections, it is possible to achieve high utilization even with overly conservatively specified traffic descriptors.
MBAC also tolerates burst scale external dependencies of sources, unlike preventive CAC methods, which would allow too many connections.
Characteristics of real traffic such as long-range dependence make modeling of traffic very hard and models complex, and therefore reliable analytical evaluation of the performance of preventive algorithms is hard, especially with those taking large buffers into account.
Moreover, the performance of preventive algorithms in terms of utilization is not very easily compared, because results depend on the traffic model used. Therefore it is difficult to avoid simulations and empirical studies even with preventive algorithms.
One fundamental difference between preventive and measurement-based CAC must be understood:

    
    
        MBAC offers only a predicted, not guaranteed QoS, whereas preventive CAC suppose worst-case traffic in calculations to guarantee QoS. This is due to the fact that MBAC relies only on measurements and because the behavior of sources varies over time, there is no guarantee that an estimate based on current and past measurements holds in future. If a mistaken estimation is made, MBAC is able to adapt to the new situation but this takes some time depending on the system dynamics.
    
    


There is also one conceptual difference between preventive CAC and MBAC. The term CAC and most, if not all, preventive CAC methods originate from the broadband ISDN and ATM world, where tight QoS objectives are assumed. Due to the predictive nature of MBAC, many MBAC proposals are of a very general type and intended to serve any packet switched network, like Internet. Th present application is not concerned with this, because the aim of MBAC, achieving high utilization without violating QoS, is very general and common to all packet switching networks that provide QoS guarantees. For ATM as an example, we should choose a MBAC scheme that is able to preserve even quite strict QoS objectives, but it does not preclude us from investigating different schemes, even those intended for IP networks.
Naturally measurements constitute an essential part of any MBAC system. It is therefore considered first, what it is actually possible to measure.
Remember that a switch can be thought of as a collection of multiplexers. Cells arrive into the multiplexer according to some arrival process (at a plurality of input terminals) and leave the multiplexer through shared output link (at least one output terminal). Coincident cells are buffered until they are drawn from buffer to be sent forward. In this model, there are the following basic quantities that can be measured:

    1. The number of cells arriving at the multiplexer (before buffering)
    2. The number of cells leaving the multiplexer (after buffering)
    3. The delay experienced by cells.


The delay itself is a useful quantity, but it is to be noticed that there is no cell rate mentioned. This is due to the fact that the arrival rate, as well as utilization, cannot be measured directly but must be calculated as an average over some interval:

    
    
        The rate of incoming cells can be calculated counting the number of arrived cells during some interval.
        The rate of outgoing cells can be calculated similarly.
        Utilization is related to rate, because utilization can be calculated as the ratio of the rate of outgoing cells to the maximum link rate.
        Cell loss ratio is defined as the ratio of lost cells to arrived cells, where the number of lost cells is calculated as a difference between the number of arrived and departed cells.
    
    


It seems that the three listed measurements are able to fulfill most of the measurement needs.
Among recently introduced MBAC methods, the so-called “Qiu's MBAC” has found considerable attention. This MBAC method has been developed by J. Qui and E. Knightly and presented by these in the article: “Measurement-Based Admission Control Algorithm with Aggregate Traffic Envelopes”, in: Proceedings of the 10th IEEE ITWDC, Ischia, Italy, September 1998.
However, the rather theoretical approach presented in that paper is not perfect in order to be applied to practically existing switch means in packet data networks such as ATM switches.
Namely, having regard to such existing and/or currently used switch means, from implementation point of view, the wide range of delay bound requirements is not the only inconvenient consequence of the existence of several service categories.
Another one is the fact that all service categories must be carried through the same physical interface (i.e. switch means) while simultaneously still conforming QoS requirements of each category.
For example, some basic technologies used to implement service categories in ATM switches are presented herein above.
The basic concept of packet and cell multiplexing is scheduling. Scheduling is considered as a discipline according to which the next cell to be carried by output interface (output terminal) is chosen from a buffer that is always needed to accommodate arrivals of cells.
Whenever the buffer has more than one cell, it is up to the scheduler to choose the next cell to be served.
The cell buffer of a switching unit and/or switch means may be organized in many ways. Although the buffer often physically consists of one shared memory, the cells in the buffer memory are logically arranged into one or more queues.
From theoretical point of view, the scheduler could search and choose the most important cell from the queue but in practice the implementation of any such search algorithm is hard and therefore one usually have as many FIFO queues as needed.
Subsequently, the question arises: how should the FIFO queues be organized and how should the scheduler choose the next queue to be served? Assigning one queue for each connection and serving the queues in round robin fashion would provide fairness among connections, because bursts of one connection would not be able to cause additional delay for other connections. In addition, the service rate of the round robin scheduler should be weighted according to agreed traffic rate of each connection.
However, a weighted round robin scheduler cannot provide statistical multiplexing unless it is able to take advantage of silent periods of any connection to carry bursts of other connections. This in turn complicates the realization of the scheduler.
As a conclusion, per connection queuing sets hard requirements for scheduling discipline as it needs to preserve QoS of connections and still achieve good throughput.
Therefore, a first step of implementation of different service categories in an ATM switch resides in the use of shared static priority queues.
In this scenario, the switch means or switching unit has P static priority queues for each input and/or output, and possibly for each internal transport interface, and the scheduler always serves the queue of the highest priority having cells. Naturally the cells of the highest priority experience the shortest delay. One priority class is usually assigned to one or more service categories.
A wide variety of more sophisticated scheduling disciplines than the static priority, such as the rate-controlled static priority, has been developed. However the static priority implementation, as it is a widely known and used, is far more easy to implement even in large high bit rate systems.
Quite a complete worst-case delay analysis of such (static) priority queues is known from document “Exact Admission Control for Networks with a Bounded Delay Service” by J. Liebeherr, D. Wrege and D. Ferrari, in IEEE/ACM Transactions on Networking, Vol. 4, No. 6, pp. 885–901, 1996.
This document presents equations for theoretical maximum delays in static priority queue systems, assuming the arrival characteristics, i.e. exact arrival constraints, of all connections are known. However, this document is fully silent about how these arrival constraints are obtained, for example by measurements or by other means.
Still further, delay calculations of priority queues are more complicated than in the case of FIFO queues. The delay of the highest priority queue, usually denoted as a priority 1, is the only exception since its delay is the same as with FIFO queue. The service rate of lower priority queues is always determined by workload of higher priority queues.
Therefore one of the requirements of the Qiu's MBAC method mentioned later, i.e. the minimum service rate of the queue, cannot be fulfilled, so that Qiu's MBAC method can not be applied to such static priority queues.
Summing up, current MBAC methods, such as the Qiu MBAC method, proposed in the literature are still immature, and not ready-to-use as an all-purpose algorithm in practical situations. Generally, problems are related to difficult tuning of measurement and estimation parameters.
From the point of view of the ATM technology as an example technology of particular interest for packet data networks, current MBAC proposals proved to have a great number of deficiencies.
Firstly, most proposals assume a simplified switching model consisting of a simple cell multiplexer (switch). In reality, however, the complex traffic model of ATM makes the hardware implementation of switches complicated and for example a static priority queue system cannot be reduced to a collection of multiplexers with constant service rates.
Secondly, real-time services have tight delay variation and cell loss requirements which most MBAC methods are not designed to deal with.
Thirdly, virtual paths complicate admission control, because both VPC (Virtual Path Connection) conformance checks and VPC end point admission control need different admission control checks than normal VCC (Virtual Channel Connection) or VPC cross connections.
SUMMARY OF THE INVENTION
Hence, it is an object of the present invention, to provide a method for measurement-based connection admission control in a packet data network, which method is free from above mentioned drawbacks and applicable under practical situations.
According to a first aspect of the present invention, this object is achieved by a method for measurement-based connection admission control in a packet data network, wherein, in said network, a traffic flow is constituted by a plurality of connections, said connections being established between plural input terminals and at least one output terminal via a switch means having a plurality of P static priority queues of respective priority p (1<=p<=P), and the traffic flow of arriving data packets is forwarded via said switch with a delay, the delay depending on the priority of a queue associated to the data packets of a respective connection and the amount of prevailing traffic; the method comprising the steps of: providing an estimated maximal rate envelope of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve; modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and granting the requested new connection, if said predetermined delay bounds are not violated.
According to a second aspect of the present invention, there is proposed a method for measurement-based connection admission control in a packet data network, wherein, in said network, a traffic flow is constituted by a plurality of connections, said connections being established between plural input terminals and at least one output terminal via a switch means having a plurality of queues with non-constant service rates, and the traffic flow of arriving data packets is forwarded via said switch; the method comprising the steps of: providing an estimated maximal rate envelope of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve; modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether the sum of the arrival constraint of a new connection requesting to be admitted and the approximated piecewise linear traffic constraint curve of ongoing traffic does not exceed said modified concave shaped piecewise linear traffic constraint curve, and granting the requested new connection, if the sum does not exceed said modified concave shaped piecewise linear traffic constraint curve.
Favorable refinements of the present invention are defined in the dependent claims.
Accordingly, the present invention advantageously removes the above mentioned drawbacks. In particular, with the present invention it is possible to guarantee delays much shorter than the shortest measurement interval, unlike the original Qiu's MBAC method. The method according to the present invention can still provide some utilization gain in comparison to preventive CAC methods. Moreover, the proposed invention provides a MBAC method suitable to be applied to static priority queue model of packet data switch means such as ATM switches, which is one of basic mechanisms used to implement service categories of ATM. Importantly, the thus proposed “priority queue” MBAC method is fast, since it is only slightly more complicated than the original admission decision algorithm by Qiu. Also, it is advantageously proposed to perform a VPC conformance check.



BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be more readily understood with reference to the accompanying drawings, in which:
FIG. 1 shows an example of measuring a peak R3 rate occurring during a time window T according to the Qiu MBAC method;
FIG. 2 illustrates the measuring of maximal rate envelope Rk over a measurement window of T=8 according to the Qiu MBAC method;
FIG. 3 visualizes that the maximal rate Rk does not contain an information concerning a number of lost cells, because a number of periods during which a service rate is exceeded is unknown according to the Qiu MBAC method;
FIG. 4 illustrates an interpretation of delay τ according to the present invention (FIG. 4A), and an interpretation of delay violation check according to the present invention;
FIG. 5 shows the delay τ in connection with piecewise linear traffic constraints according to the present invention,
FIG. 6 illustrates the steps of piecewise linear approximation and subsequent modification to obtain a concave shaped traffic constraint curve;
FIG. 7 shows VC (Virtual Channel) and VP (Virtual Path) cross connections in a switch means such as an ATM switch; and
FIG. 8 shows a graph supporting the understanding of the VPC conformance check according to the present invention.



DETAILED DESCRIPTION OF THE INVENTION
According to the present invention as will be described herein below in greater detail, the present invention starts from Qiu's MBAC method which provides an estimated maximal rate envelope based on traffic measurements. By using this envelope one can form a piecewise linear approximated traffic constraint curve. This curve can easily be made concave, as illustrated below in FIG. 6.
Moreover, the document “Exact Admission Control for Networks with a Bounded Delay Service” by J. Liebeherr, D. Wrege and D. Ferrari, in IEEE/ACM Transactions on Networking, Vol. 4, No. 6, pp. 885–901, 1996, presents how worst-case delays for static priority queues are calculated if the traffic of each queue is limited by concave constraint.
The present inventor has discovered that this approach can be reformulated in terms of the proposed delay equations so that it is only checked, if a given (predetermined) delay bound is violated. Further, the present inventor has proved that the delay violation check with piecewise linear constraints needs to be performed only at those points denoted by numbers 1,2, . . . in the figure above. As a result, a very fast and simple delay test for each queues can be provided.
Thus, according to the first aspect of the present invention, the method consists mainly of the steps of providing an estimated maximal rate envelope of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve; modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and granting the requested new connection, if said predetermined delay bounds are not violated.
This check is effected since whenever additional traffic arises and is handled by adding to a priority queue of priority p, the delay of that queue will increase as well as the delay of all queues having a lower priority (i.e. denoted by a higher priority number, priority number 1 being the highest priority), because the available service time for all lower priority queues decreases.
Also, according to a second aspect of the present invention, the method consists mainly of the steps of providing an estimated maximal rate envelope of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve; modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether the sum of the arrival constraint of a new connection requesting to be admitted and the approximated piecewise linear traffic constraint curve of ongoing traffic does not exceed said modified concave shaped piecewise linear traffic constraint curve, and granting the requested new connection, if the sum does not exceed said modified concave shaped piecewise linear traffic constraint curve.
Thereby, an object of having an MBAC method which is capable of making an admission decision regarding the acceptance of virtual channel connections VCC's carried inside virtual path connections VPC's of variable bit rate (VBR), or an admission decision regarding an acceptance of connections to any single FIFO packet queue having a non-linear, but still concave service curve, like the traffic constraint of VPC illustrated in FIG. 9, is achieved by the VPC conformance check method according to the second aspect of the present invention. This VPC conformance check is performed by ensuring that the sum of the arrival constraint of a new connection and an approximated, piecewise linear traffic constraint of an ongoing connections does not exceed a VPC traffic constraint curve, or service curve of a queue in case of a general packet queue. Thus, this method can perform an admission check for queues having non-constant service rates (i.e. for VBR connections).
For still better understanding, a brief introduction in the Qiu's MBAC method is given.
The key idea of this algorithm is to measure maximal rates of the arrival process of the aggregated traffic flow at different time scales and predict the behavior of the flow in the future using these measurements. The algorithm is able to provide an estimate of the packet loss probability and take large buffers into account.
In the most recent approach presented by Qiu and Knightly, the principles of extreme value theory are applied for the cell loss estimation. Therefore we mainly refer to this most recent approach, in which the algorithm is introduced in the form of theorems and proofs. Here we take a slightly different approach to explain the algorithm, because a good understanding is important.
In the Qiu's algorithm, the measurement method characterizing the current aggregate flow is called measuring of maximal rate envelope. The basic idea is to find a set of peak rates over numerous intervals of different lengths during some measurement window T. The resulting maximal rate envelope describes the flow's maximal rate as a function of interval length.
Next we describe the maximal rate envelope formally. Let A[s, s+I] be the number of arrivals in the interval [s, s+I]. Cell rate over this interval is




  
    
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This can be understood also as an average cell rate over the period I. Peak cell rate over intervals of length I inside the past measurement window T is given by




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Peak rate R can be understood as the largest average rate over time period of I observed during the measurement window T when time variable s gets all possible values. The set of peak rates over intervals of different length can be constructed simply by using different values Ik in place of interval I. Qiu and Knightly defined Ik to be simply a multiple of τ which is the smallest time period over which the number of arrivals A[s, s+τ] is measured:

Ik=kτ, k=1, . . . , T.

In practice, τ is larger than cell transmission time. Note that in the context of this MBAC T is not expressed in seconds but it is a pure integer. The length of the measurement window is obtained by multiplying T with the smallest time period τ:

Measurement window (in seconds)=Tτ

Clearly, the linear function I(k) makes the size of maximal rate envelope vector huge when either τ is very small or T is very large.
FIG. 1 shows an example of measuring peak rate R3, when Ik=I3=3τ and measurement window T=11.
Now we are ready to define the maximal rate envelope R, which is a set of peak rates over intervals Ik=kτ, k=1, . . . ,T inside measurement window Tn:

Rn={R1n, R2n, . . . , RTn},

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FIG. 2 shows an example of measuring maximal rate envelope. The index n=0,1, . . . , N−1 in the equation above denotes that actually N maximal rate envelopes are measured over N past measurement windows for estimation methods.
Maximal rate envelope can also be defined such that the intervals Ik are not restricted to be inside measurement window T but only begin inside T:




  
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In this way, absolute maximal peak rates over longer intervals are found in contrast to original definition, where the longest interval is not slid at all, because it is equal to Tτ, length of measurement window. This may increase the accuracy a little.
The idea of describing the behavior of the traffic flow by its maximal rates over numerous intervals of different length is quite unique among previously known MBAC proposals.
Several benefits of this approach have been attributed thereto. First, a traffic flow's rate and its maximal rate as well are meaningful only if they are associated with an interval length. Second, by characterizing the aggregate traffic flow by its maximal rates instead of mean rates one describes extreme rates of the flow which are most likely to cause buffer overflow. Finally, the variation of maximal rate tends to be less than the variance of traffic flow itself making estimation based on maximal rates more stable. This is due to asymptotic decrease of the variance of maximal rate when the length of observation period is increased.
It is important to observe how the maximal rate envelope describes the behavior of traffic flow over different time scales. This is in contrast to most measurement methods sampling rate over just one interval. The characterization over different time scales is important, since even the same kind of traffic may have very different characteristics.
Although maximal rate envelope describes recent extreme behavior of the traffic, it is incorrect to assume the envelope will bound the future traffic as well. The estimation in this MBAC is based on the behavior of N past maximal rate envelopes.
The theoretical background of the estimation is now explained. Two steps are taken to estimate the future traffic. First, the next maximal rate envelope in future is estimated by determining estimates of mean and variance for each maximal rate Rk. Second, to estimate the bandwidth demand of the aggregated flow in respect of target CLR, distributions of each maximal rate Rk are approximated.
A method to get an estimate of future maximal rate envelope is to calculate empirical mean and variance of each envelope element Rk using N past measured sample values:




  
    
      σ
      k
      2
    
    =
    
      
        1
        
          N
          -
          1
        
      
      ⁢
      
        
          ∑
          
            n
            =
            0
          
          
            N
            -
            1
          
        
        ⁢
        
          
            (
            
              
                R
                k
                n
              
              -
              
                
                  R
                  _
                
                k
              
            
            )
          
          2
        
      
    
  
  ,




where {overscore (R)}k is the mean of the Rkn's in past N windows:





  
    
      R
      _
    
    k
  
  =
  
    
      1
      N
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        
          N
          -
          1
        
      
      ⁢
      
        
          R
          k
          n
        
        .
      
    
  




Although these two basic statistical parameters alone do not predict the future behavior of aggregate flow reliably, together with the knowledge of the nature of the random variables Rk they give means for estimating distributions of Rk's.
As mentioned above, maximal rate envelope describes variations of aggregate flow at time scales up to Tτ. However, a single maximal rate envelope does not recognize current long time scale dynamics or trend—for example, whether there is currently more flow arrivals than flow departures or vice versa.
To estimate the effect of long time scale dynamics, a method based on conditional prediction technique has been presented by Qiu. Conditional prediction is used for predicting conditionally next value of mean rate, {circumflex over (m)}−1, and its variance based on the past measured values mN−1, mN−2, . . . , m0. Moreover, a normalized envelope is defined as the peak-to-mean ratio rkn=Rkn/mn, where mn is the mean rate over measurement window Tn during which the peak rate Rkn is measured. The mean of normalized envelopes is defined as




  
    
      r
      _
    
    k
  
  =
  
    
      1
      N
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        
          N
          -
          1
        
      
      ⁢
      
        r
        k
        n
      
    
  




and the variance as





  
    σ
    k
    2
  
  =
  
    
      1
      
        N
        -
        1
      
    
    ⁢
    
      
        ∑
        
          n
          =
          1
        
        N
      
      ⁢
      
        
          
            (
            
              
                r
                k
                n
              
              -
              
                
                  r
                  _
                
                k
              
            
            )
          
          2
        
        .
      
    
  




Finally, the predicted mean {circumflex over (m)}−1 and the mean of normalized envelopes {overscore (r)}k are combined to get predicted value of mean:

{overscore ({circumflex over (R)}k={overscore (r)}k·{circumflex over (m)}−1,

{circumflex over (σ)}k2≦({overscore (r)}k2+σk2)·({circumflex over (m)}−12+Σ22′2),

where Σ22′2 is the predicted variance of {circumflex over (m)}−1. Now, the first term of {overscore ({circumflex over (R)}k reflects the burstiness over intervals of length of Ik in each measurement window and the second term, predicted mean rate, describes the dynamics at time scales longer than Tτ. In an actual admission control algorithm (mentioned later), these predicted values {overscore ({circumflex over (R)}k and {circumflex over (σ)}k2 are used instead of simple mean {overscore (R)}k and variance σk2. The difference in performance between using predicted and not predicted estimates is presented further below.

For an admission control algorithm, an estimate of the bandwidth demand of the aggregated flow for a given target CLR is needed. This is due to the fact that in statistical multiplexing, the bandwidth demand of the aggregated flow depends on the target CLR and delay constraint. The effect of buffers causing delay is taken into account in the admission control algorithm.
Because the empirical mean and variance of the maximal rate Rk inside interval of length Tτ are known, a natural way to approach the solution is to assume the distribution of the random variable is known as well, and then write the estimated limit for maximal rate {tilde over (R)}k in terms of the mean, standard deviation and confidence coefficient α:

{tilde over (R)}k={overscore (R)}k+ασk.

If the (cumulative) distribution function (cdf) of Rk is Fk(•), then the probability that the random variable, maximal rate Rk, will not exceed the value of {tilde over (R)}k in the time interval Tτ can be written as




  
    
      Φ
      k
    
    ⁢
    
      (
      α
      )
    
  
  =
  
    
      P
      ⁢
      
        {
        
          
            R
            k
          
          ≤
          
            
              R
              ~
            
            k
          
        
        }
      
    
    =
    
      
        P
        ⁢
        
          {
          
            
              R
              k
            
            ≤
            
              
                
                  R
                  _
                
                k
              
              +
              
                ασ
                k
              
            
          
          }
        
      
      =
      
        
          
            ∫
            
              -
              ∞
            
            
              
                
                  R
                  _
                
                k
              
              +
              
                ασ
                k
              
            
          
          ⁢
          
            
              [
              
                
                  
                    d
                    
                      
                    
                  
                  
                    d
                    x
                  
                
                ⁢
                
                  
                    F
                    k
                  
                  ⁢
                  
                    (
                    x
                    )
                  
                
              
              ]
            
            ⁢
            
              d
              x
            
          
        
        =
        
          
            ∫
            
              -
              ∞
            
            
              
                
                  R
                  _
                
                k
              
              +
              
                ασ
                k
              
            
          
          ⁢
          
            
              d
              
                F
                k
              
            
            .
          
        
      
    
  




The motivation for writing bandwidth demand as {tilde over (R)}k={overscore (R)}k+ασk is governed by the fact that with the Gumbel distribution, as well as with the normal distribution, the probability P{Rk≦{overscore (R)}k+ασk} remains the same if we normalize the distribution Fk(•) so that the mean is zero and variance is one. Therefore α corresponding to certain probability can be found using normalized distribution without need to find empirical parameters of distribution every time, supposing the distribution Fk(•) itself is known.
Subsequently, the question is how to find a distribution approximating the cdf Fk(•) well enough? If the number of past samples N was huge and measured Rk's were independent of each other, Gaussian distribution would be a natural and safe choice. In this case, however, N is not large enough. Further, the approximation of Gaussian cdf is not accurate with tail probabilities. Gaussian approximation has been used in the first version of the Qiu's MBAC method, anyway.
A good idea introduced by Knightly and Qiu is to take advantage of the extreme value theory. In fact, Rk is not a plain random variable of traffic rate but it is a maximum of several observed values. The extreme value theory in turn describes the behavior of extreme values like minimum and maximum values.
From the collection of distributions describing different asymptotic distributions of the probability P{max{X1, X2, . . . , Xn}≦x} when n→∞, Knightly and Qiu have chosen the Gumbel distribution to approximate the cdf of Rk. Naturally, the asymptotic distribution depends on the distribution of the underlying random variable whose cdf in the case of data traffic rate is generally not known. In Knightly's and Qiu's publication, no comparison with data traffic has been made between candidate distributions, so the choice of the Gumbel distribution has not been justified thoroughly. On the other hand, in some document the Gumbel distribution is proven to describe the asymptotic distribution of the maximum with most of the well-known distributions. Moreover, the simulation results of Knightly and Qiu give reason to believe the choice of the Gumbel distribution works.
The cdf of the Gumbel distribution is given by




  
    G
    ⁢
    
      (
      x
      )
    
  
  =
  
    
      exp
      ⁡
      
        [
        
          -
          
            exp
            ⁢
            
              (
              
                -
                
                  
                    x
                    -
                    λ
                  
                  δ
                
              
              )
            
          
        
        ]
      
    
    .
  




Parameters λ and δ are related to mean {overscore (R)}k and variance σk2 as follows:




  {
  
    
      
        
          
            
              δ
              2
            
            =
            
              6
              ⁢
              
                
                  σ
                  k
                  2
                
                /
                π
              
            
          
          ,
        
      
    
    
      
        
          λ
          =
          
            
              
                R
                _
              
              k
            
            +
            
              0
              ,
              57772
              ⁢
              
                δ
                .
              
            
          
        
      
    
  
   




However, because it is possible to use a normalized distribution instead an empirical one, it is easier to calculate parameters for normalized distribution and use them from this point onward:




  {
  
    
      
        
          
            
              δ
              0
            
            =
            
              
                6
              
              /
              π
            
          
          ,
        
      
    
    
      
        
          
            λ
            0
          
          =
          
            0
            ,
            57772
            ⁢
            
              
                δ
                0
              
              .
            
          
        
      
    
  
   




Now, using the normalized distribution, the probability that the random variable, maximal rate Rk, will not exceed {tilde over (R)}k in time interval Tτ is




  
    Φ
    ⁢
    
      (
      α
      )
    
  
  =
  
    
      exp
      ⁡
      
        [
        
          -
          
            exp
            ⁢
            
              (
              
                -
                
                  
                    α
                    -
                    
                      λ
                      0
                    
                  
                  
                    δ
                    0
                  
                
              
              )
            
          
        
        ]
      
    
    .
  




This is also the probability that no cell loss will occur, assuming buffers are able to accommodate bursts exceeding the average rate Rk during interval Ik. However, the complementary probability 1−Φ(α) does not tell directly an estimate for CLR, since it indicates only the probability that the actual maximal rate Rk will exceed the estimated limit {tilde over (R)}k, but not how large the exceeding, Rk−{tilde over (R)}k, is. Even if the expected exceeding E[(Rk−{tilde over (R)}k)+] was known, it would indicate only the average of the maximal exceeding in interval Tτ but not how many smaller exceedings there occur.
Given a queuing system able to serve at maximum rate of {tilde over (R)}k over interval Ik, then an lower bound of number of cells lost in the interval Ik is (Rk−{tilde over (R)}k)+·Ik. Now, if the maximal rate Rk>{tilde over (R)}k in the measurement window Tτ is known, we cannot determine the number of cells lost Lk, because there may exist other periods of length Ik over which the rate is between rates {tilde over (R)}k and Rk. FIG. 3 illustrates the problem. According to Knightly and Qiu, the average upper bound of the number of cells lost E[Lk] in measurement window Tτ is determined by assuming the average exceeding

E[(Rk−{tilde over (R)}k)+]

holds over every interval Ik in the measurement window Tτ and the service queue is served at least at the rate {tilde over (R)}k={overscore (R)}k+ασk:

E[Lk]≦E[(Rk−{tilde over (R)}k)+]·Tτ,

where





  
    
      
        
          E
          ⁡
          
            [
            
              
                (
                
                  
                    R
                    k
                  
                  -
                  
                    
                      R
                      ~
                    
                    k
                  
                
                )
              
              +
            
            ]
          
        
        =
        
        ⁢
        
          
            ∫
            
              
                R
                ~
              
              k
            
            ∞
          
          ⁢
          
            
              (
              
                r
                -
                
                  
                    R
                    ~
                  
                  k
                
              
              )
            
            ⁢
            
              d
              
                F
                k
              
            
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            
              σ
              k
            
            ⁢
            
              
                ∫
                α
                ∞
              
              ⁢
              
                
                  
                    (
                    
                      x
                      -
                      α
                    
                    )
                  
                  ·
                  
                    [
                    
                      
                        
                          d
                          
                            
                          
                        
                        
                          d
                          x
                        
                      
                      ⁢
                      
                        exp
                        ⁡
                        
                          (
                          
                            -
                            
                              exp
                              ⁡
                              
                                (
                                
                                  -
                                  
                                    
                                      α
                                      -
                                      
                                        λ
                                        0
                                      
                                    
                                    
                                      δ
                                      0
                                    
                                  
                                
                                )
                              
                            
                          
                          )
                        
                      
                    
                    ]
                  
                
                ⁢
                
                  d
                  x
                
              
            
          
          ≈
        
      
    
  
  
    
      
        
        ⁢
        
          
            σ
            k
          
          ⁢
          
            δ
            0
          
          ⁢
          
            
              e
              
                -
                
                  
                    α
                    -
                    
                      λ
                      0
                    
                  
                  
                    δ
                    0
                  
                
              
            
            .
          
        
      
    
  




Because the CLR is defined as the number of lost cells per the number of cells sent, CLR can be derived from E[Lk] just by dividing it by {overscore (R)}TTτ, where {overscore (R)}T is the average rate over intervals of Tτ, and finding the time scale which causes the greatest cell loss:




  CLR
  =
  
    
      
        E
        ⁡
        
          [
          
            L
            k
          
          ]
        
      
      
        
          
            R
            _
          
          T
        
        ⁢
        T
        ⁢
        
          
        
        ⁢
        τ
      
    
    ≤
    
      
        max
        
          
            k
            =
            1
          
          ,
          2
          ,
          
            
          
          ⁢
          ...
          ⁢
          
            
          
          ,
          
            
          
          ⁢
          T
        
      
      ⁢
      
        
          
            E
            ⁡
            
              [
              
                
                  (
                  
                    
                      R
                      k
                    
                    -
                    
                      
                        R
                        ~
                      
                      k
                    
                  
                  )
                
                +
              
              ]
            
          
          ⁢
          T
          ⁢
          
            
          
          ⁢
          τ
        
        
          
            
              R
              _
            
            T
          
          ⁢
          T
          ⁢
          
            
          
          ⁢
          τ
        
      
    
    ≈
    
      
        max
        
          
            k
            =
            1
          
          ,
          2
          ,
          
            
          
          ⁢
          ...
          ⁢
          
            
          
          ,
          T
        
      
      ⁢
      
        
          
            
              σ
              k
            
            ⁢
            
              δ
              0
            
            ⁢
            
              e
              
                -
                
                  
                    α
                    -
                    
                      λ
                      0
                    
                  
                  
                    δ
                    0
                  
                
              
            
          
          
            
              R
              _
            
            T
          
        
        .
      
    
  




Although not addressed by Qiu and Knightly, one should recognize the following supposition: the inequality above is an upper bound for the CLR only in the case where the queuing system has enough buffer capacity to accommodate worst possible burst structure with average rate {tilde over (R)}k inside interval Ik. Both an imaginary typical case and the worst possible case of the buffer need are now considered. The worst case appears when sources behave extremely by sending two bursts of size RkIk consecutively, assuming the maximal rate Rk+1 over longer interval Ik+1 allows a burst of size 2·RkIk. Although the maximal rate Rk does not exceed the service rate C={tilde over (R)}k, a buffer of a size bmax is needed to avoid cell loss. The buffer size is dependent on the maximal incoming rate Cin—max which is at most the sum of all incoming links Ci:




  
    b
    max
  
  =
  
    
      2
      ⁢
      
        
          I
          k
        
        ⁡
        
          [
          
            
              C
              
                C
                in_max
              
            
            ⁢
            
              (
              
                
                  C
                  in_max
                
                -
                C
              
              )
            
          
          ]
        
      
    
    =
    
      2
      ⁢
      
        
          
            I
            k
          
          ⁡
          
            [
            
              
                C
                
                  
                    ∑
                    i
                  
                  ⁢
                  
                    C
                    i
                  
                
              
              ⁢
              
                (
                
                  
                    
                      ∑
                      i
                    
                    ⁢
                    
                      C
                      i
                    
                  
                  -
                  C
                
                )
              
            
            ]
          
        
        .
      
    
  




It is believed that this is a finding not to be forgotten in the context of admission control and delay estimation, because the maximal rate Rk does not bound the traffic flow or give any other information about it at time scales remarkably shorter than Ik.
After introducing the basis for the cell loss estimation used in the context of this (Qiu's) method, we are finally ready to reveal the admission control algorithm.
The algorithm is presented using the two theorems introduced and proved in Qiu and Knightly. Before presenting the theorems, the connection setup information supposed by the method is explained because the algorithm is not designed for any particular network model like ATM.
A new flow is supposed to be bounded by similar maximal rate envelope rk as the estimated aggregated flow. However, leaky bucket based traffic parameters of ATM are easily mapped to maximal rate envelope. For example, with a CBR connection, the PCR parameter bounds the rate over every interval Ik, so the envelope is r={PCR, PCR, . . . , PCR}. For VBR sources, the maximal rate over intervals of length Ik is given by




  
    r
    k
  
  =
  
    
      1
      
        I
        k
      
    
    ⁢
    
      
        min
        ⁢
        
          (
          
            
              PCR
              ·
              
                I
                k
              
            
            ,
            
              MBS
              +
              
                SCR
                ·
                
                  (
                  
                    
                      I
                      k
                    
                    -
                    
                      MBS
                      PCR
                    
                  
                  )
                
              
            
          
          )
        
      
      .
    
  




In the admission control algorithm and/or method, the delay or cell loss requirements of a connection are not explicitly taken into account. Because the algorithm assumes a shared FIFO queue, maximal queue length (buffer size) and service rate determine absolute delay bound straightforwardly:

Delay bound=(buffer size)/(service rate).

In line with the shared queuing scenario, the queue under decision must have a predefined CLR target less than or equal to the CLR of any connection.
Admission Decision Theorem
Theorem 1: Consider a new flow bounded by rk, k=1, . . . , T requesting admission to a first-come-first-served server with capacity C, buffer size B, and a workload characterized by a maximal rate envelope with mean bounding rate {overscore (R)}k and variance σk2, k=1, . . . , T. With confidence level Φ(α), no packet loss will occur with admission of the new flow if



  
    
      
        
          max
          
            
              k
              =
              1
            
            ,
            2
            ,
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ,
            
              
            
            ⁢
            
              T
              -
              1
            
          
        
        ⁢
        
          {
          
            
              I
              k
            
            ⁢
            
              (
              
                
                  
                    R
                    _
                  
                  k
                
                +
                
                  r
                  k
                
                +
                
                  α
                  ⁢
                  
                    
                  
                  ⁢
                  
                    σ
                    k
                  
                
                -
                C
              
              )
            
          
          }
        
      
      ≤
      B
    
    ,
    
      
    
    ⁢
    and
  




  
    
      
        
          
            R
            
              _
              ^
            
          
          T
        
        +
        
          r
          k
        
        +
        
          α
          ⁢
          
            
          
          ⁢
          
            
              σ
              ^
            
            T
          
        
      
      ≤
      C
    
    ,
  



where





  
    R
    
      _
      ^
    
  
  T




is the mean rate over intervals of IT and {circumflex over (σ)} its deviation.

This theorem offers the actual admission decision. The first condition of the theorem checks that allocated buffer B is able to accommodate all bursts of length less or equal to IT−1 by estimating the buffer need over every interval Ik is less than B. The buffer need is approximated by first calculating the difference between estimated future maximal rate and service rate and then multiplying the difference by the length of the interval Ik in order to get the size of the burst in bits.
The second condition of the theorem 1 is referred to as the stability condition in Qiu's and Knightly's aforementioned publication, because it requires that the average rate over IT is less than the link rate. As a consequence, the busy period of the queue server is less than IT meaning that queue will not be occupied longer than IT. Note that if Rk is defined according to the equation introduced in connection with FIG. 2, then




  
    
      R
      
        _
        ^
      
    
    T
  
  ≠
  
    
      
        R
        _
      
      T
    
    ⁢
    
      
    
    ⁢
    and
    ⁢
    
      
    
    ⁢
    
      
        σ
        T
      
      ^
    
  
  ≠
  
    σ
    T
  




and therefore





  
    R
    
      _
      ^
    
  
  T




must be measured separately.

To bind the confidence level Φ(α) to the target CLR, another theorem is proposed:
Theorem 2: Consider an aggregate traffic flow that satisfies the schedulability condition of Theorem 1 and has mean bounding rate {overscore (R)}k and variance σk2 over intervals of length IT. For a link capacity C, buffer size B, and schedulability confidence level Φ(α), the packet loss probability is bounded by



  
    
      
        
          max
          
            
              k
              =
              1
            
            ,
            2
            ,
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ,
            
              
            
            ⁢
            T
          
        
        ⁢
        
          
            
              σ
              k
            
            ⁢
            
              Ψ
              ⁢
              
                (
                α
                )
              
            
            ⁢
            
              I
              k
            
          
          
            
              
                R
                _
              
              T
            
            ⁢
            
              I
              T
            
          
        
      
      ≤
      
        P
        loss
      
      ≤
      
        
          max
          
            
              k
              =
              1
            
            ,
            2
            ,
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ,
            
              
            
            ⁢
            T
          
        
        ⁢
        
          
            
              σ
              k
            
            ⁢
            
              Ψ
              ⁢
              
                (
                α
                )
              
            
          
          
            
              R
              _
            
            T
          
        
      
    
    ,
    
      
    
    ⁢
    where
  




  
    
      Ψ
      ⁡
      
        (
        α
        )
      
    
    =
    
      
        δ
        0
      
      ⁢
      
        e
        
          -
          
            
              
                α
                -
                
                  λ
                  0
                
              
              
                δ
                0
              
            
            .
          
        
      
    
  



For theorem 2, the upper bound of loss probability was actually derived earlier herein above in the context of estimation. To take the desired cell loss probability into account in the admission decision, the corresponding parameter α must be solved from the theorem 2 using the upper bound inequality.
Subsequently, some important issues about the feasibility of this MBAC are highlighted. We assess here the impact of the theoretical problems more than practical details because the latter ones are considered in later chapters. The estimation of future behavior of maximal rates relies strongly on the assumption that maximal rates of data traffic obey the Gumbel distribution. Naturally some experimental evidence about the distribution of Rk's with different kind of traffic would be welcome to assure that the estimation is able to give correct results even with very small target cell loss probabilities.
A serious theoretical approximation we are concerned about is the correctness of cell loss estimation with small buffer B corresponding delays much shorter than the shortest measurement interval I1. The buffer test in admission decision ensures that the difference between estimated maximal rate Rk and server rate C is so small that buffer B does not overflow over any interval Ik. However, as mentioned before, some buffers are needed unless the maximal traffic rate stays constant over whole Ik. The problem is emphasized over shortest interval I1, because there are not shorter intervals to reveal higher maximal rates inside I1. To predict delays which are, for example, one tenth of the shortest interval I1 or less, the traffic should be very smooth over whole I1 to avoid excess cell loss.
Actually, according to worst-case calculation B=bmax the smallest delay which can be guaranteed if maximal rate R1 does not exceed service rate C is




  
    d
    min
  
  =
  
    
      
        
          b
          max
        
        C
      
      ≈
      
        2
        ⁢
        
          I
          1
        
        ⁢
        
          
        
        ⁢
        as
        ⁢
        
          
        
        ⁢
        
          
            ∑
            i
          
          ⁢
          
            C
            i
          
        
      
    
    →
    
      ∞
      .
    
  




However, one must remember that the worst-case traffic scenario mentioned earlier before is very unlikely, as is the best case scenario assumed by the algorithm with very short delays, so in practice the truth lies probably somewhere between these two extremes. In addition, the upper bound of the cell loss estimate is based on the worst-case assumption that the maximal rate Rk holds over every Ik inside measurement window IT. It would not be a surprise if this assumption were able to partly compensate the optimistic assumption because the maximal rate over shorter interval is usually higher and it is unlikely that the maximal rate over shortest interval would hold over IT.
Selection of the shortest and the longest measurement intervals, I1 and IT, is an important theoretical and practical issue. From a practical point of view, both a very large T and a very short I1 increase computational complexity. From a theoretical point of view, the importance of a short I1 was already discussed, so a trade-off between complexity and accuracy exists.
The length of the measurement window IT is a complicated question with this MBAC. The maximal rates are searched inside IT but their mean and variance are calculated using measurements of N past windows. Therefore there are actually two measurement windows of lengths IT and N*IT.
Fortunately, the algorithm should be robust against the choice of IT. According to Knightly and Qiu, this is due to opposite behavior of the two admission tests, buffer occupancy test and stability test in function of IT. With a short IT, the stability test behaves conservatively because the variation of mean rates among N windows of length IT is large and therefore the variance of mean {overscore (R)}T is large. The mean of mean rates {overscore (R)}T over N past windows is not much affected by the choice of IT. In contrast, the buffer test becomes more conservative (or realistic) when IT is increased because larger windows obviously present larger maximal rates. For these reasons Qiu and Knightly argue that there exists an optimal choice of IT, and a wrong choice only compromises utilization, not quality of service. If the IT is not too optimal, then it should be possible to occasionally optimize IT, for example, by trying which test fails when service rate C is decreased under current workload.
As the choice of I1 is determined by limitations of implementation and as the choice of IT could probably be adjusted automatically, the only parameter without clear guidelines is N, the number of past windows to take into account in mean and variation calculations. Recalling Tse's stability analysis of measurements, it is easy to imagine that with too large an N the CAC could not react fast enough to changes in flow dynamics. Probably the use of conditional prediction makes the algorithm more robust against the choice of N. It is suggested to use N=8 or N=10. Without conditional prediction, the algorithm will probably allow too many connections in the transient state where initially an empty system is rapidly filling with connection, because the mean rate remains low, unless the variation becomes so large that it can compensate a too low mean rate.
None of Qiu's and/or Qiu's and Knightly's publications directly suggest how to handle very frequent connection requests. Before a new estimated rate envelope is ready, new connections accepted meanwhile are not taken into account in measured variables—this leads to overload.
The solution to this resides in the following: advertised rate envelopes of flows admitted after the last estimation are added to the requested flow's advertised envelope before using it in admission decision. This makes the algorithm a bit conservative under high load and also relieves the real-time requirement of the estimate updates. As a whole, this MBAC seems to be the most convincing one of those introduced in this work because it characterizes traffic over many time scales and because it should be quite robust against the choice of measurement time scale in contrast to previous methods.
Nevertheless, with the Qiu's method described up to here, the problems mentioned earlier in using it under practical packet data networks such as ATM networks still exist.
Note that in previous publications dealing with CAC and/or MBAC methods, algorithms are introduced for a simplified environment, like for one FIFO queue.
However, when the implementation of CAC and/or MBAC in an ATM switch is considered, a number of new problems are encountered, which are solved by the present invention.
To keep the discussion and explanation of the present invention at a practical level, we have chosen Qiu's maximal rate MBAC algorithm as a basis and this Qiu's MBAC method is adapted to ATM as an example of a packet switched network.
Recall what kind of multiplexing environment and what information is required for the employment of the maximal rate algorithm:

    1. A shared packet or cell queue with buffering capacity B (in bits) which is serviced using first-in-first-out (FIFO) scheduling discipline,
    2. Target cell loss ratio Ploss 
    3. Minimum service rate S
    4. Measured maximal rate envelope, R={R1, R2, . . . , Rk}, k=1,2, . . . , T, of the recent workload of the queue,
    5. Maximal rate envelope r={r1, r2, . . . , rk}, k=1,2, . . . , T bounding the connection requested.


Several conclusions can be drawn from these assumptions. Firstly, the algorithm in its basic form requires the switching system to consist of shared queues that are served with FIFO scheduling and cell arrivals of each queue to be counted by hardware. Secondly, the algorithm does not accept direct delay constraints for the queues. Instead, the buffer size and the minimum service rate of the queue determine the delay constraint:




  delay
  =
  
    
      
        buffer
        ⁢
        
          
        
        ⁢
        capacity
      
      
        minimum
        ⁢
        
          
        
        ⁢
        service
        ⁢
        
          
        
        ⁢
        rate
      
    
    .
  




Third, due to FIFO queuing the delay constraint of the queue must be chosen according to the connection having the tightest delay constraint. Consequently, in order to increase the utilization by extensive buffering of connections with looser delay constraints one must have several queues with different delay bounds.
An ATM network is supposed to be able to provide particular services with such a high QoS level that the Internet is not imagined to provide even far in the future. This is partly due to historical reasons: ATM was chosen to be an implementation technique of the B-ISDN, which in turn was designed to be the successor of the narrowband ISDN network providing digital service of very high quality.
From CAC's viewpoint, the real-time services of the ATM are the most demanding. ITU-T has defined the end-to-end cell delay variation (CDV) objective of QoS class 1 (QoS class 1 defines QoS objectives for Deterministic Bit Rate and Statistical Bit Rate 1 ATM transfer capabilities which correspond to CBR and VBR services of ATM forum) to be 3 ms with exceeding probability of 10−8 and the end-to-end CLR to be 10−7, or 10−8 if possible. Because one connection may traverse even dozens of switches, the delay variation due to queuing of real-time connections must be of the order of hundreds microseconds.
For the maximal rate MBAC (i.e. Qiu's MBAC) very tight delay constraints seem to be a problem. As mentioned before, the cell loss estimation is based on the assumption that the switch has some buffers to accommodate variations inside the measurement interval I1. While the variations inside intervals of Ik, k=2, . . . , T are mostly characterized by maximal rates over shorter intervals, the variations inside the shortest intervals I1 are not characterized at all. For this reason, when the buffer size B is very small in comparison to the number of cells arriving during I1, the probability that the buffer is not able to accommodate variations, increases.
To predict delays that are very short in comparison to the shortest measurement interval, a simple modification of the maximal rate algorithm (Qiu' MBAC) is presented. The improved algorithm is based on two components: traffic contract based peak rate of the queue and the estimated maximal rate envelope of the original algorithm, Rk={overscore (R)}k+ασk, k=1,2, . . . , T.
Because we are concentrating on packet networks such as ATM networks now, we can assume that for any input queue in the switch the deterministic traffic constraint function is defined by the PCR and CDVT parameters of the connections flowing through the queue. Further, if the shaping effect of the upstream queues inside the switch is known, that is, the change of cell delay variation, then our model is suitable for any constant rate FIFO queue in an ATM switch.
A combination of deterministic traffic constraint and estimated maximal rate envelope gives a traffic constraint function (no shown) of a shape that can be described as follows: the rectangular portions as a function of time intervals denote the estimated maximal rate envelope limiting the maximal number of arrivals over periods Ik. Inside interval I1 the maximum arrival rate is limited by PCR, the total peak rate of connections. A burst at the beginning, BPCR, is due to delay variations and it is determined by the leaky bucket (PCRi, CDVTi) of each connection i according to equation BPCR=ΣiPCRi·CDVTi.
With this function, the worst-case delays are obtained when assuming that

    i) Total peak rate PCR is larger than service rate S.
    ii) Estimated maximal rate Rk over any interval Ik is less than service rate S.


With these assumptions we can easily calculate the delays occurring with the function:

    
    
        Delay d0 is determined by queue service rate S and BPCR:
    
    






  
    d
    0
  
  =
  
    
      
        B
        ⁢
        
          
        
        ⁢
        P
        ⁢
        
          
        
        ⁢
        C
        ⁢
        
          
        
        ⁢
        R
      
      S
    
    .
  




Delay d1 is determined by BPCR, PCR, S and estimated maximal arrivals R1T1:




  
    d
    1
  
  =
  
    
      
        
          R
          1
        
        ⁢
        
          I
          1
        
      
      S
    
    -
    
      
        
          
            
              R
              1
            
            ⁢
            
              I
              1
            
          
          -
          
            B
            ⁢
            
              
            
            ⁢
            P
            ⁢
            
              
            
            ⁢
            C
            ⁢
            
              
            
            ⁢
            R
          
        
        
          P
          ⁢
          
            
          
          ⁢
          C
          ⁢
          
            
          
          ⁢
          R
        
      
      .
    
  




Delays d2 . . . dT are calculated identically:




  
    d
    i
  
  =
  
    
      (
      
        
          
            R
            i
          
          ⁢
          
            I
            i
          
        
        -
        
          
            R
            
              i
              -
              1
            
          
          ⁢
          
            I
            
              i
              -
              1
            
          
        
      
      )
    
    ⁢
    
      
        (
        
          
            1
            S
          
          -
          
            1
            
              P
              ⁢
              
                
              
              ⁢
              C
              ⁢
              
                
              
              ⁢
              R
            
          
        
        )
      
      .
    
  




For the cases other than assumed above we may conclude as follows:

    a) S>PCR: some delay occurs only at the beginning due to BPCR and therefore the only delay to check against delay constraint is d0.
    b) If Ri>S for some i=1, . . . , T: This kind of situation suggests there may be long busy periods and therefore small delay constraint is hard to preserve unless the traffic is totally smooth at short time scales. Therefore it is reasonable to exclude this kind of situation by requiring that S>Ri for all i.
    c) Ri>PCR for some i=1, . . . , T: This odd situation might occur due to variations of maximal rates or at least it might be difficult to show that the situation is impossible. However, it does not matter whether the situation is possible or not because the condition S>Ri ensures that the estimate never exceeds service rate, and therefore the condition S>PCR holds and according to a) only d0 is checked.


From the calculations and conclusions above we can draw the admission control algorithm where D denotes the maximum delay allowed:

    If new total PCR is less than service rate S then
    if d0<D then
    accept connection
    else
    
        deny connection
    
    
    else
    
        if S>Ri for every i and di<D for every i then
    
    
    accept connection
    else
    deny connection


Remember that the buffer size required for the queue under decision is B=D·S.
One must understand that the (modified) algorithm presented above is only the first step towards an improved MBAC controlling very small delays. The original (Qiu's) algorithm is able to give only an estimate of the maximal number of arrivals over shortest interval I1 and because the target CLR is already taken into account in estimation, we must ensure that no remarkable cell loss occurs due to traffic fluctuations at time scales shorter than I1. Because measurements do not directly provide any information about these short-range fluctuations, we chose a deterministic way to approximate short delays. To get more efficient CAC for real-time traffic one must estimate the effect of short-range fluctuations either with statistical means or with another measurement methodology.
Despite the worst-case approach, our improved algorithm is able to provide better utilization than the peak rate allocation




  S
  ≥
  
    
      ∑
      1
    
    ⁢
    
      PCR
      1
    
  




if the sources are not sending at their peak rates.

However, judging the maximum ratio of PCR/S allowed as a function of ratio R1/S, where R1 is the measurement-based estimate of maximum rate over R1, the algorithm does not perform very well. For example, with 1 ms delay constraint and completely smooth traffic with rate R1/S=0,5 the algorithm achieves utilization of only 0,5*1,25=0,625 although the utilization close to one would be possible due to smooth traffic. However, it is still 25 percent better than the peak rate allocation based only on traffic contracts.
In consequence, according to the present invention as claimed, a still further modified algorithm for static priority queues is proposed, starting from the maximal rate MBAC algorithm, i.e. Qiu's MABC method.
Particularly, delay calculations of priority queues are more complicated than those of FIFO queues. The delay of the highest priority queue, usually denoted as a priority 1, is the only exception since its delay is same as with FIFO queue. The service rate of lower priority queues is always determined by the workload of higher priority queues.
A fairly complete worst-case delay analysis of priority queues is presented in literature by Liebeherr et. al (mentioned before). Advantageously, the performance analysis of static priority queues as presented in literature by Liebeherr et. al (mentioned before) is used in a suitable modification conceived by the present inventor in connection with the proposed method according to the present invention.
Liebeherr et. al. give deterministic delay bounds of static priority queues both for concave and non-concave traffic constraint functions. For concave traffic constraints, the maximum delay of the queue of priority p is




  
    d
    max
    P
  
  =
  
    
      s
      min
      p
    
    +
    
      
        max
        
          t
          ≥
          0
        
      
      ⁢
      
        
          {
          
            min
            ⁢
            
              {
              
                
                  τ
                  |
                  
                    
                      S
                      ·
                      
                        (
                        
                          t
                          +
                          τ
                        
                        )
                      
                    
                    ≥
                    
                      
                        
                          ∑
                          j
                        
                        ⁢
                        
                          
                            A
                            j
                            p
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                      
                      +
                      
                        [
                        
                          
                            ∑
                            
                              q
                              =
                              1
                            
                            
                              p
                              -
                              1
                            
                          
                          ⁢
                          
                            
                              ∑
                              j
                            
                            ⁢
                            
                              
                                A
                                j
                                q
                              
                              ⁡
                              
                                (
                                
                                  
                                    (
                                    
                                      t
                                      +
                                      τ
                                    
                                    )
                                  
                                  -
                                
                                )
                              
                            
                          
                        
                        ]
                      
                      -
                      
                        s
                        min
                        P
                      
                      +
                      
                        
                          max
                          
                            r
                            >
                            p
                          
                        
                        ⁢
                        
                          s
                          max
                          r
                        
                      
                    
                  
                
                ,
                
                  τ
                  ≥
                  0
                
              
              }
            
          
          }
        
        .
      
    
  




Here Ajp(t) denotes the traffic constraint function of the connection j of priority p indicating the time required to serve cells arrived by the time t; sminp denotes the minimum service time of a packet of priority p and smaxr denotes the maximum service time of a packet of priority r. However, the service times of ATM cells are equal and negligible, so as the inventor found out in the course of his research, the equation may be simplified just by leaving out (neglecting) all three s terms.
Suppose we are given the constraints of aggregated traffic, Ap, instead of individual constraints Ajp such that



  
    
      A
      p
    
    =
    
      
        ∑
        j
      
      ⁢
      
        A
        j
        p
      
    
  




  and




  
    
      A
      
        1
        ,
        
          p
          -
          1
        
      
    
    =
    
      
        
          ∑
          
            q
            =
            1
          
        
        
          p
          -
          1
        
      
      ⁢
      
        
          ∑
          j
        
        ⁢
        
          
            A
            j
            q
          
          .
        
      
    
  



Further, due to negligible cell transmission times we may approximate A1,p−1(t+τ)−≈A1,p−1(t+τ). As a result, the maximum delay is




  
    d
    max
    p
  
  =
  
    
      max
      
        t
        ≥
        0
      
    
    ⁢
    
      {
      
        min
        ⁢
        
          
            {
            
              τ
              |
              
                
                  S
                  ·
                  
                    (
                    
                      t
                      +
                      τ
                    
                    )
                  
                
                ≥
                
                  
                    
                      A
                      p
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  +
                  
                    
                      A
                      
                        1
                        ,
                        
                          p
                          -
                          1
                        
                      
                    
                    ⁡
                    
                      (
                      
                        t
                        +
                        τ
                      
                      )
                    
                  
                
              
            
            }
          
          .
        
      
    
  




To interpret the equation above intuitively, consider the time t as the arrival time of a tagged cell of priority p. Then, the inner minimization indicates the first moment τ when the scheduler has had enough free cell slots between higher priority cells to serve all of the cells of priority p arrived by the time t, Ap(t), including the tagged cell. See FIG. 4A for visual interpretation of the delay τ. If the maximum delay is not interesting but only the knowledge that the predefined delay bound Dmaxp is not violated, then the following delay violation test gives a sufficient condition, assuming it holds for all t≧0:

S·(t+Dmax p)≧Ap(t)+A1,p−1(t+Dmaxp).

This condition follows directly from the delay equation. FIG. 4 illustrates the condition visually.
From a practical point of view, it is important that both the delay equation (illustrated in FIG. 4A) and the violation test above (illustrated in FIG. 4B) hold for all concave traffic constraints, like piece-wise linear constraints, because many traffic contracts and measurement methodologies provide piece-wise linear constraints.
Actually, the use of the equations in practice is much easier with piece-wise linear constraints because the maximum delay may occur only with certain values of t. To prove this claim, suppose the case of FIG. 5 where we are given piece-wise linear constraints Ap and A1,p−1 which are both linear over periods of k. Further, suppose we have found the delay τ for certain t, satisfying

S·(t+τ)=Ap(t)+A1,p−1(t+τ).

Then, consider how the value of τ changes if t is either increased or decreased:

    i) When t is increased, τ increases until t+τ=3k, because the function Ap grows faster around t than the difference S−A1,p−1 does around t+τ, that is,






  
    
      
        d
        
          
        
      
      
        d
        t
      
    
    ⁢
    
      
        A
        p
      
      ⁡
      
        (
        t
        )
      
    
  
  >
  
    
      
        
          d
          
            
          
        
        
          d
          t
        
      
      ⁡
      
        [
        
          
            S
            ⁡
            
              (
              
                t
                +
                τ
              
              )
            
          
          -
          
            
              A
              
                1
                ,
                
                  p
                  -
                  1
                
              
            
            ⁡
            
              (
              
                t
                +
                τ
              
              )
            
          
        
        ]
      
    
    .
  




Note that the difference S−A1,p−1 is used to serve priority p cells arrived by the time t.

    ii) After t+τ has passed the value of 3k, τ starts to decrease, because now the difference S−A1,p−1 grows faster than the function Ap does around t, that is,






  
    
      
        d
        
          
        
      
      
        d
        t
      
    
    ⁡
    
      [
      
        
          S
          ⁡
          
            (
            
              
                (
                
                  3
                  ⁢
                  k
                
                )
              
              +
            
            )
          
        
        -
        
          
            A
            
              1
              ,
              
                p
                -
                1
              
            
          
          ⁡
          
            (
            
              
                (
                
                  3
                  ⁢
                  k
                
                )
              
              +
            
            )
          
        
      
      ]
    
  
  >
  
    
      
        d
        
          
        
      
      
        d
        t
      
    
    ⁢
    
      
        
          A
          p
        
        ⁡
        
          (
          
            
              3
              ⁢
              k
            
            -
            τ
          
          )
        
      
      .
    
  




We can conclude that the increase or decrease rate of τ stays constant until either t or t+τ reaches next integer multiple of k because the rate of change of τ depends only on the derivative of Ap around t and the derivative of difference S−A1,p−1 around t+τ. Due to piecewise linearity, these derivatives stay constant until the next multiple of k is reached. As a result, the global maximum of τ may occur only either when t=n·k or t+τ=n·k, where n=1,2, . . . .
From the viewpoint of our delay violation test, this result is remarkable. If the delay bound Dmaxp is a multiple of k, the violation test needs to be performed only with values t=n·k. To prove that, we first consider the maximum delay such that τ>Dmaxp. Then the maximum is found either when tm=n·k or tm+τ=n·k. In the former case the condition

S·(t+Dmaxp)<Ap(t)+A1,p−1(t+Dmaxp)

holds at least when t=tm. In the latter case, when t is increased to the next multiple of k, so that t>tm, the endpoint of busy period, t+τ, must advance unless the service rate S is infinite at the moment tm+τ and therefore our condition check reveals the violation.

Let us sum up our priority queue algorithm:
Consider a static priority queue system with total service rate of S and with P queues having each an individual delay bound Dmaxp defined, where Dmaxp=i·k, iεN. In addition, traffic constraint Ap(t) of the current workload of each queue is given and these constraints are linear between values t=n·k, n=1,2, . . . , T. Also similar traffic constraints of total current workload of queues from priority 1 to p, A1,p−1, are given, where p=1,2, . . . , P.
Now, consider a new connection of priority q with an arrival constraint a(t) requesting admission, where a(t) is also linear between values t=n·k.
The admission is granted, if both the following condition holds
for all n=1,2, . . . , T:

(nk+Dmaxq)·S≧Aq(nk)+a(nk)+A1,q−1(nk+Dmaxq)

and the following condition holds

for all p=q+1, . . . , P and n=1,2, . . . , T:

(nk+Dmaxp)·S≧Ap(nk)+A1,p−1(nk+Dmaxp)+a(nk+Dmaxp).

Usually there are only a few different priorities, so the test is not much more complicated than the buffer test in Qiu's MBAC.
Since we have a simple admission control test for concave, piece-wise linear traffic functions, the next question is: how do we actually get such traffic constraint functions? Recall that a piecewise linearization of estimated maximal rate envelope Rk={overscore (R)}k+ασk, k=1,2, . . . , T, represents an approximated traffic constraint function of FIG. 6 and that due to probability of overflow of small buffers, the approximation is justified only if the delay bound Dmaxp is at least of the order of magnitude of the shortest measurement interval I1. However, because the maximum rate envelope decreases only near monotonically as a function of interval length, the traffic constraint function is not completely concave. Therefore a concave approximation must be done as illustrated in FIG. 6. Coding an iterative function that makes the traffic constraint concave is not too complicated a task and therefore not described herein in detail.
Concave approximation has some performance drawbacks. Firstly, especially with quasi-periodic traffic, like MPEG coded video, the concave constraint degrades performance. Secondly, every new estimated maximal rate envelope must be made concave before any CAC decision.
To avoid such performance problems of concave approximation, one could use the delay equation with non-concave traffic constraints, presented by Liebeherr et al., to develop another method.
However, maximum delay with non-concave constraints is more complicated and at least admission decisions as conceived by the present inventor and derived from the delay equation of Lieberherr et. al. resulted in a complicated decision with a complexity of O(n2) where n is the number of elements in maximal rate envelope.
Because the estimate update interval is typically of the order of seconds, under high load one estimate is likely to be used for several CAC/MBAC decisions and therefore concave approximation with simple O(n) admission check should be a more stable choice. Finally, note that computational complexity of the simple admission check equals that of the original algorithm's admission check which also has O(n) running time.
Another performance related issue is the estimation of the traffic constraint of aggregated traffic of priorities from 1 to p−1. The simplest solution is to sum the individual constraints:




  
    A
    
      1
      ,
      
        p
        -
        1
      
    
  
  =
  
    
      
        ∑
        
          q
          =
          1
        
      
      
        p
        -
        1
      
    
    ⁢
    
      
        A
        p
      
      .
    
  




However, this compromises utilization, since each constraint is estimated in respect of cell loss and it is very unlikely that all queues behave extremely at the same time. Better utilization is achieved by measuring and estimating maximal rates of aggregated traffic of priority queues from 1 to p−1 for all p=2, . . . , P−1, where P is the lowest priority queue having a delay bound defined.

Finally, note that one may use any other CAC method for real-time queues and apply the MBAC method only for non-real-time queue(s). Consider a case where CBR connections are directed to the highest and rt-VBR connections to the second highest priority queue. The third priority queue is used for nrt-VBR connections, and the fourth for UBR traffic. The MBAC is used only for CAC of nrt-VBR connections to achieve high link utilization. In this case, the only constraints needed are A1,2 and A3.
So far we have concentrated only on the allocation of physical resources, like the bandwidth of an output link, the service rate of a scheduler or the buffer space of an interface unit. Although these physical resources ultimately determine the quality of service experienced by cross-connected connections, there are also logical resources in an ATM switch to be controlled by CAC according to another aspect of the present invention In ATM, VC connections (VCC) are carried logically inside VP connections (VPC) by giving a VP identifier to VC connections. Every VPC has a traffic contract similar to a contract of VCC, including service category and traffic description. An ATM network node may perform either VP, VC or both VP and VC cross connections.
In VP cross connection, cells are forwarded to the proper output link according to VP identifiers. The VPC can be seen as a bunch of VCCs, but the switch is not aware of the number or the nature of those VCCs. It only needs to know the traffic descriptor of the VPC to make CAC decision and reserve resources. In FIG. 7, the VPC 2 illustrates the cross connection of a VPC. Note that in practice the VP identifiers are changed even in this case, because VC and VP identifiers are always link specific. However, from resource management's point of view, the change of identifiers has no meaning and therefore the identifiers of VPCs in FIG. 7 do not correspond to the real identifiers.
In VC cross connection, VPCs end up and they are broken down into VCCs. Individual VCCs need to change into other VPCs due to possibly different destinations links. In this case, the switch sets up cross connections separately for each VCC, meaning that each VCC is going to travel under a new VPC and the cells are forwarded to the proper output links depending of their new VPC. In VC cross connection, the switch needs to know the traffic descriptor of each VCC, because different VCCs consume different resources, like the bandwidth of different links. FIG. 7 illustrates also VC cross connection.
Note that in VC cross connection VPCs are terminated in the switch, like VPC 1, 3, 4 and 5 in FIG. 7. Terminated VPCs are also called VPC end points and we may consider them as logical resources, because the switch may but it does not have to reserve any resources for them. An empty VPC, like VPC 4, does not carry any cells and therefore in reality it does not consume any bandwidth or buffers.
However, even VPC end points have service category and traffic descriptor defining PCR, SCR etc, because the next switch may perform only VP cross connection and it has to know the traffic descriptor to determine sufficiency of physical resources. As a consequence, the aggregated flow of the VCCs switched into a VPC must not violate the traffic description of the VPC.
Clearly, there is kind of a dilemma: Should we reserve resources immediately for a new VPC end point, meaning that the CAC checks whether there is resources or not for the new VPC, or should we just accept the new VPC end point and not reserve any resources until a new VCC request arrives for it? And if we want to reserve some resources for a terminated VPC, how should it be done?
First of all, one needs to understand that the bandwidth of the outgoing link is actually the sole possible resource to be reserved for a VPC end point. This stems from the fact that the buffer need depends on the nature of VCCs to be switched inside the VPC and the fact that VCCs may traverse through different queues and internal interfaces inside a switch depending on the incoming link and the VPC.
Suppose we have somehow allocated bandwidth for terminated VPCs. Then, if a new VCC does not cause VPC traffic descriptor violation, it will be accepted with a great probability. Only the internal bottlenecks of the switch can restrict the access. One drawback of advance allocation is the overall utilization of the switch may stay at a very low level since the request for creation of new VPC end points or increase of the allocation for an old one could be rejected although there would be a plenty of real bandwidth for new traffic on the outgoing link. Note that advance resource allocation for VPCs must be done with some preventive CAC method that may provide either statistical or deterministic QoS guarantee.
In the case where no advance allocation for VPC end points have been made, it is possible to achieve high utilization of the switch. However, a drawback with this option is that some VCCs may be rejected although the target VPC would be half-empty, resulting low utilization in the next VP cross connecting switch unless that switch is using MBAC. On the other hand, it may be even dangerous to apply MBAC in a switch performing mostly VPC cross connections, because the connection holding times with VPCs may be very long and so the switch recovers very slowly from an overload situation caused by sudden increase in traffic of ongoing VPCs.
Neither no-allocation nor pre-allocation strategy provides optimal network utilization. For a network having a lot of long VP connections traversing through numerous switches, the high utilization of VPCs is the key to high overall network utilization, supposing the backbone switches use a preventive, parameter-based VPC admission control. In such an environment, some hybrid of the two alternatives in the border switches, like an automatic renegotiation of traffic parameters of VPCs according to changes of load or a partial advance allocation of resources for terminated VPCs could provide the best result.
A first step and still adequate solution is to perform the following admission check for new CBR-type VPC end points:




  
    capacity
    ⁢
    
      
    
    ⁢
    of
    ⁢
    
      
    
    ⁢
    the
    ⁢
    
      
    
    ⁢
    link
  
  ≥
  
    
      ∑
      i
    
    ⁢
    
      PCR
      i
    
  




and the following test for new VBR-type end points:





  
    capacity
    ⁢
    
      
    
    ⁢
    of
    ⁢
    
      
    
    ⁢
    the
    ⁢
    
      
    
    ⁢
    link
  
  ≥
  
    
      ∑
      i
    
    ⁢
    
      
    
    ⁢
    
      
        SCR
        i
      
      .
    
  




An overallocation of VBR-type end points provides better overall utilization of the switch and because it is very unlikely that all VPC end points are concurrently full, individual VPC end points rarely lose VC connections because of the shortage of physical resources.
Regardless of VPC admission control method and policy, a VC cross connecting switch must ensure that every terminated VPC conforms to its traffic contract, meaning that the traffic parameters of a VPC are not exceeded due to acceptance of a new VC connection. The conformance can be checked by using estimated maximal rate envelope, as illustrated in FIG. 8, where the estimated traffic constraint should be below the traffic contract-based constraint of VPC for every Ik. Note that the estimation requires per VPC measurements, meaning that the transmitted cells per VPC must be counted after buffering. Counting cells before buffering gives obviously inaccurate estimates because buffering reshapes the traffic.
Describing the admission test formally, the following condition must hold for all k=1,2, . . . , T:




  
    
      
        R
        k
      
      +
      
        r
        k
      
    
    <
    
      
        1
        
          I
          k
        
      
      ⁢
      
        min
        ⁡
        
          (
          
            
              PCR
              ·
              
                I
                k
              
            
            ,
            
              MBS
              +
              
                SCR
                ·
                
                  (
                  
                    
                      I
                      k
                    
                    -
                    
                      MBS
                      /
                      PCR
                    
                  
                  )
                
              
            
          
          )
        
      
    
  
  ,




where Rk={overscore (R)}k+ασk, k=1,2, . . . , T and rk is the maximal rate envelope of the new connection. In addition, a condition similar to the stability condition of Qiu's original algorithm can be checked as well to get a more reliable decision:





  
    
      
        
          
            R
            _
          
          ^
        
        T
      
      +
      
        r
        k
      
      +
      
        α
        ⁢
        
          
            σ
            ^
          
          T
        
      
    
    <
    SCR
  
  ,




where





  
    
      R
      _
    
    ^
  
  T




denotes the average traffic rate over intervals of T.

Although these VPC conformance tests provide high utilization, they may not be applicable in the ATM network performing strict policing. This is due to the inaccuracy of the approximated traffic constraint giving a peak rate that is actually a maximal mean rate over I1. Therefore momentary peak rates may violate the leaky bucket GCRA(PCR, CDVT) used by policing, although the estimated traffic constraint of FIG. 8 does not exceed PCR.
If a very strict conformance to traffic contract is required, then the short delay version of the MBAC introduced earlier or some preventive CAC method must be used, but in most cases it will result in lower utilization. On the other hand, one may question the need for absolutely strict conformance in the case where switches use some preventive CAC method for VPC admission control. Such CAC methods are based on traffic parameters and usually allocate resources assuming that sources send maximal traffic allowed by the traffic contract. In reality, it is unlikely that the every VPC end point on the same link is full of traffic and has non-conforming bursts concurrently. Further, our conformance test restricts the duration of such burst to be less than I1.
As has been described herein above, the present invention proposes a method for measurement-based connection admission control in a packet data network, wherein, in said network, a traffic flow is constituted by a plurality of connections, said connections being established between plural input terminals and at least one output terminal via a switch means having a plurality of P static priority queues of respective priority p (1<=p<=P), and the traffic flow of arriving data packets is forwarded via said switch with a delay, the delay depending on the priority of a queue associated to the data packets of a respective connection and the amount of prevailing traffic; the method comprising the steps of: providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve (A(Ik)); modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and granting the requested new connection, if said predetermined delay bounds are not violated.
Also, the present invention proposes a method for measurement-based connection admission control in a packet data network, wherein, in said network, a traffic flow is constituted by a plurality of connections, said connections being established between plural input terminals and at least one output terminal via a switch means having a plurality of queues with non-constant service rates, and the traffic flow of arriving data packets is forwarded via said switch; the method comprising the steps of: providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements; approximating said envelope to a piecewise linear traffic constraint curve (A(Ik)); modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and checking whether the sum of the arrival constraint of a new connection (rk) requesting to be admitted and the approximated piecewise linear traffic constraint curve (Rk) of ongoing traffic does not exceed said modified concave shaped piecewise linear traffic constraint curve, and granting the requested new connection, if the sum does not exceed said modified concave shaped piecewise linear traffic constraint curve.
It should be understood that the above description and accompanying figures are merely intended to illustrate the present invention by way of example only. The preferred embodiments of the present invention may thus vary within the scope of the attached claims.

## Claims

1. A method for measurement-based connection admission control in a packet data network,
wherein, in said network,
a traffic flow is constituted by
a plurality of connections,
said connections being established between
plural input terminals and at least one output terminal via a switch means having a plurality of P static priority queues of respective priority p (1<=p<=P) for each input/output, and



the traffic flow of arriving data packets is forwarded via said switch with a delay, the delay depending on the priority of a queue associated to the data packets of a respective connection and the amount of prevailing traffic;
the method comprising the steps of:
providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements;
approximating said envelope to a piecewise linear traffic constraint curve (A(Ik));
modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and
checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and
granting the requested new connection, if said predetermined delay bounds are not violated.

2. A method according to claim 1,
further comprising a step of
verifying whether a maximum delay of a queue of priority p is violated, wherein
the requested new connection is granted, if said predetermined delay bound and said maximum delay are not violated.

3. A method according to claim 2, wherein
said checking is performed at regular time intervals corresponding to integer multiples of measurement time intervals.

4. A method according to claim 2, wherein
said verifying is performed at regular time intervals corresponding to integer multiples of measurement time intervals.

5. A method according to claim 3, wherein
said checking is performed according to the following equations:


(nk+Dmaxq)·S≧Aq(nk)+a(nk)+A1,q−1(nk +Dmaxq),

for all n=1, 2, . . . T, and


(nk+Dmaxp)·S≧Ap(nk)+A1,p−1(nk+Dmaxp)+a(nk+Dmaxp),



for all p=q+1, . . . , P and n=1, 2, . . . , T

with S being a total service rate of the P queues each having an individual predetermined delay bound Dmaxp=i*k, iεN, k defining a measurement window of length k*τ, with τ being a smallest time period for measurements within a superposed measurement window T*τ, Ap(t), Aq(t) being the traffic constraint of the current workload of each queue of priority p and/or q, respectively, with the constraints being piecewise linear and concave between values t=n*k, n=1, 2, . . . , T, A1,p−1 representing the traffic constraints of current workload of queues from priority 1 to p, abd a new connection of priority q having an arrival constraint of a(t) requesting admission, with a(t) being also piecewise linear and concave between values t=n*k.

6. A method according to claim 1,
further comprising a step of
measuring at least one of the following traffic quantities:
the number of cells arriving to the switch means
the number of cells leaving the switch means,
the delay experienced by the cells between arrival at and departure from said switch means.

7. A method according to claim 6, wherein
said measurement step is effected per each queue at said switch means.

8. A method according to claim 6, wherein
said measurement step is effected per each connection at said switch means.

9. A method according to claim 1, wherein
said checking is performed at regular time intervals corresponding to integer multiples of measurement time intervals.

10. A method for measurement-based connection admission control in a packet data network,
wherein, in said network,
a traffic flow is constituted by
a plurality of connections,
said connections being established between
plural input terminals and at least one output terminal via a switch means having a plurality of queues with non-constant service rates, and



the traffic flow of arriving data packets is forwarded via said switch;
the method comprising the steps of:
providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements;
approximating said envelope to a piecewise linear traffic constraint curve (A(Ik));
modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and
checking whether the sum of
the arrival constraint of a new connection (rk) requesting to be admitted and
the approximated piecewise linear traffic constraint curve (Rk) of ongoing traffic

does not exceed said modified concave shaped piecewise linear traffic constraint curve, and
granting the requested new connection, if the sum does not exceed said modified concave shaped piecewise linear traffic constraint curve.

11. A method according to claim 10, wherein said checking is performed according to the following equations:
for all k=1,2, . . . , T:





  
    
      
        R
        k
      
      +
      
        r
        k
      
    
    <
    
      
        1
        
          I
          k
        
      
      ⁢
      
        min
        ⁡
        
          (
          
            
              PCR
              ·
              
                I
                k
              
            
            ,
            
              MBS
              +
              
                SCR
                ·
                
                  (
                  
                    
                      I
                      k
                    
                    -
                    
                      MBS
                      /
                      PCR
                    
                  
                  )
                
              
            
          
          )
        
      
    
  
  ,




where Rk={overscore (R)}k+ασk, k=1,2, . . . , T and rk is the maximal rate envelope of the new connection, and




  
    
      
        
          
            R
            _
          
          ^
        
        T
      
      +
      
        r
        k
      
      +
      
        α
        ⁢
        
          
            σ
            ^
          
          T
        
      
    
    <
    SCR
  
  ,




where




  
    
      R
      _
    
    ^
  
  T




denotes the average traffic rate over intervals of T.

12. A method according to claim 10, wherein said connections are virtual channel connections (VCC) within virtual path connections (VPC).

13. A method for measurement-based connection admission control in a packet data network,
wherein, in said network,
a traffic flow is constituted by
a plurality of connections,
said connections being established between
plural input terminals and at least one output terminal via a switch means having a plurality of P static priority queues of respective priority p (1<=p<=P) for each input/output, and




the traffic flow of arriving data packets is forwarded via said switch with a delay, the delay depending on the priority of a queue associated to the data packets of a respective connection and the amount of prevailing traffic; and
wherein, in said network,
a traffic flow is constituted by
a plurality of connections,
said connections being established between
plural input terminals and at least one output terminal via a switch means having a plurality of queues with non-constant service rates, and



the traffic flow of arriving data packets is forwarded via said switch;
the method comprising the steps of:
providing an estimated maximal rate envelope (Rk) of the traffic flow based on traffic measurements;
approximating said envelope to a piecewise linear traffic constraint curve (A(Ik));
modifying said piecewise linear traffic constraint curve such that said curve assumes a concave shape; and
checking whether a predetermined delay bound for the priority queue of a new connection requesting to be admitted, and the delay bounds for all queues having a lower priority than the requesting new one, are not violated, and
granting the requested new connection, if said predetermined delay bounds are not violated; and
checking whether the sum of
the arrival constraint of a new connection (rk) requesting to be admitted and
the approximated piecewise linear traffic constraint curve (Rk) of ongoing traffic

does not exceed said modified concave shaped piecewise linear traffic constraint curve, and
granting the requested new connection, if the sum does not exceed said modified concave shaped piecewise linear traffic constraint curve.