# Patent

## Title
Method for connection acceptance and rapid determination of optimal multi-media content delivery over network

## Abstract

A method of bandwidth allocation for delivery of stored digital content from at least one server device to at least one client device by way of a network is disclosed. The method begins by prescribing a control variable which represents a target flow rate from the server device to each client device. Next, time-varying constraints on the flow rate of the content are determined. A cost function of the control variable for each client is determined. The cost function corresponds to a maximized value of the control variable. Finally, bandwidth is prescribed to each client based upon the value of the control variable maximized by the cost function. In this respect, the method achieves optimal allocation of bandwidth between the server and the respective clients.

## Background
RELATED APPLICATIONS
The present application is a continuation-in-part of U.S. patent application Ser. No. 09/344,688 filed on Jun. 25, 1999 which claimed priority to U.S. Provisional Patent Application No. 60/108,777 filed on Nov. 17, 1998.


BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to the field of delivery of multimedia content over a variety of networks. More specifically, it pertains to multimedia servers which service many clients simultaneously for the delivery of multimedia content which is used and played back at each client. It addresses methods for determining optimal delivery rates to each client and methods for determining whether new clients may be accepted without diminishing the quality of service to existing clients.
2. Status of the Prior Art
In the history of multimedia program delivery, some in the industry have long advocated the use of large client-side buffers and faster-than-real-time content delivery over a network as offering the best of all worlds: a jitter-free viewing experience and a cost-effective utilization of the network resources at hand. Few systems, however, go very far in addressing how to schedule clients or a method for accepting new clients. Real-time systems, often known as streaming systems, can schedule new clients in a very simple manner—if sufficient bandwidth remains for the added real-time stream, then the client may be accepted. However, such systems do not maximize the number of simultaneous clients. On the other hand, faster than real-time delivery, sometimes known as store-and-forward systems, opens up the possibility for more flexible scheduling procedures to control and optimize the number of simultaneous clients while ensuring a high level of quality of service.
The methods for such call acceptance and flow modulation that have been proposed in the prior art have been largely ad-hoc and also incomplete. These have been ad-hoc in the sense that there has been no guiding rationale for their selection from among many possible and potentially superior alternatives. The methods have also been incomplete insofar as they did not address the question of whether any given incoming request for service should be accepted or denied. Video-on-demand systems, or more generally, any system in which a multimedia server is designed to serve multiple clients over a network to deliver bounded content, can benefit from the use of such flow modulation techniques and call acceptance procedures.
Optimal Content Flow Modulation
One time-honored way of designing methods of the class required here is to re-cast the problem to be solved as an optimization problem, in which one seeks to maximize a designated value function moment-by-moment, subject to a set of real-world operational constraints which will typically vary over time. Accordingly, given a set of clients and associated sessions, an optimal delivery procedure continuously establishes content flow rates from the content server to each of its clients so as to maximize aggregate value according to the governing value function.
This approach holds several advantages: 1) optimization problems are well understood, and are tractable by a large and diverse collection of computational methods; 2) if it exists, a global solution that is obtained is arguably optimal by construction, and thus superior or equal to all other.
The present invention teaches the method of optimizing two particular value functions:

    
    
        1) total data delivered (maximize throughput).
        2) total delivery charges (maximize charges).
    
    


The first value function does not distinguish one customer from another and will deliver as much data as possible from server to clients irrespective of the characteristics of the latter. The second value function favors the service of high paying customers. It can easily be seen that the first function is a special case of the second one whereby all clients are charged equally.
As will be seen in this disclosure, optimizing for these functions and identifying the necessary constraints requires a new and unique perspective that is specifically designed for the multimedia environment. Moreover, the disclosed methods are specifically designed to account for and accommodate real-world scenarios of today's networks. Consequently many variations of the method are presented to accommodate various scenarios.
SUMMARY OF THE INVENTION
Call/Connection Acceptance Control (CAC)
A CAC procedure is responsible for deciding whether a candidate for service can be accommodated without jeopardizing sessions already in progress at the present time or at some time in the future; failing that it must decide whether a service request should be queued for a time or rejected.
Flow Modulation
Flow modulation methods are those portions of the system which manage the communication and data flow between the server and the clients. Collectively, these methods provide the multimedia data to the client and provide the server with the information about the state of the transmission, playback, user status and network status. These parameters are further used by the present invention in the CAC procedures. In fact, as will be shown, the proposed CAC procedures are tightly integrated with the flow modulation methods.
Adaptation to Variations in Network Capacity
Operational constraints may change over time. For instance, one might elect to vary the total bandwidth available for multimedia content delivery according to the time of day. Alternatively, exogenous data flows on the network may cause unexpected disturbances by usurping available bandwidth and impeding the delivery of data along established session channels. The content delivery strategy of the present invention includes the ability to adapt to scheduled as well as unexpected disturbances so as to minimize unwanted disruptions of services.
Burst Transmissions Provide the Opportunity to Adapt
The present invention, due to it's faster-than-realtime transmissions (also know as burst transmissions), which are realized by use of high-bandwidth networks and large client cache or intermediate storage, provides an opportunity to adapt to changing network conditions. In contrast real-time (streaming) systems are essentially designed for worst-case scenarios: each client must be assumed to constantly use the complete real-time playback bandwidth. Such a system is unable to adapt to any derivation from this scenario. For example, take the simple case where the total server bandwidth is 100% utilized by all clients playing back the streaming video. Should any network condition change, such as a temporary decrease in available bandwidth over the network, then one or more clients' playback is interrupted, and the system can not recover from such a condition until the bandwidth is regained. Even worse if a single client presses pause either that unused bandwidth must remain reserved and no more clients can be accepted, or that paused client is pushed out in order to service the new client. In essence little or no CAC procedure may be implemented.
In contrast the present invention burst transmits portions of a program and immediately ‘gets ahead of itself’, thus allowing headroom for a myriad of methods to intelligently handle new clients, client interactivity and possible network fluctuations.
Methods are taught for optimally determining the flow rate to each client. Methods are also taught for accepting or rejecting new clients; these call-acceptance methods are tightly coupled with said flow rate modulation methods. A series of constraint expressions are presented which govern the methods for determining the flow rates and acceptance of new clients. Linear programming techniques are used to optimally solve these expressions. Various embodiments are presented including scenarios for multiple-rate tariffs, and time-of-day bandwidth variations.



BRIEF DESCRIPTION OF THE DRAWINGS
These as well as other features of the present invention will become more apparent upon reference to the drawings wherein:
FIG. 1 depicts the flow of control and/or data between the different stations of a content delivery session;
FIG. 2 illustrates the Entity Data Model;
FIG. 3 geometrically illustrates the linear programming problem statement;
FIG. 4a geometrically illustrates an expansion of the flow optimization problem statement;
FIG. 4b geometrically illustrates the method for rapid determination of flow rates to maximize flow;
FIG. 5 illustrates a method for implementing flow modulation to maximize flow;
FIG. 6 illustrates a method for implementing flow modulation for maximized charges;
FIG. 7 illustrates typical content flow;
FIG. 8 illustrates typical server swing capacity;
FIG. 9 illustrates a method for call-acceptance and control (CAC);
FIG. 10 illustrates planned constraints on maximum flow;
FIG. 11 illustrates a method for call-acceptance and control (CAC) with scheduled flow changes;
FIG. 12 illustrates stratification of services;
FIG. 13 illustrates a method for call-acceptance and control (CAC) for maximal charge;
FIG. 14 is a system block diagram for a system implementing the present optimization of client bandwidth;
FIG. 15 is a flowchart showing an algebraic method for calculating the optimization of client bandwidth;
FIG. 16 is a flowchart showing an algebraic method for calculating the optimization of client costs; and
FIG. 17 illustrates optimized viewing of a live event.



DETAILED DESCRIPTION OF THE INVENTION
Data & Control Flows (FIG. 1)
FIG. 1 depicts the flow of control and/or data between the different stations of a content delivery session. As shown a client attempts a connection 100 and manifests itself to the Content Selection subsystem by means of a low bandwidth control channel (not shown). Next the client is authenticated and a selection is made 110, typically with the aid of browser software. If the client is not authenticated, it is dismissed from the system 120. If the client has been authenticated and a program selected for viewing then the rate of service is set at this point 130, perhaps according to the selection that was made, or some contractual stipulation. The client is now placed on the service queue of the CAC subsystem 140. A client that is made to wait too long will eventually balk 150. Assuming this does not occur, the CAC subsystem 140 will eventually allocate a channel to the client and open a session 160. Control now devolves upon the Content Flow Modulator (not shown) which starts the flow of content from server to client 170. Subsequent capacity changes, whether predictable or not, may force an abrupt termination of a session in progress 180. Otherwise the session runs to completion 190.
Entity Data Model (FIG. 2, listing, table)
The entities entering into our discussion are depicted in FIG. 2. Client 200 maintains certain data associated with this entity; as shown but not labeled, which includes without limitation, status, id and costOfService. The other entities also each include unlabeled but depicted data. The diagram further depicts the relationship between each entity. As shown, client 200 is assigned a session 240. Client 200 employs a channel 210. Client 200 selects contentSelection 230. Session 240 delivers content through channel 210. Server 220 modulates channel 210. Server 200 contains contentSelection 210. Server 220 accepts, defers or denies client 200 and contentSelection 230 is associated with session 240.
Furthermore FIG. 2 depicts the various one-to-many relationships. Each client 200 employs one channel 210. Client 200 may or may not receive one of channel 210, as depicted by the 0/1 notation. Similarly, client 200 may or may not receive a session 240. However, whenever client 200 does receive a session 240, it will always receive a channel 210 since channel 210 and session 240 are allocated as a pair. One or more (N) of client 200 may select one of contentSelection 230. And server 220 contains one or more (N) of contentSelection 230. Each one of contentSelection 230 is associated with 0-N of session 240. Each session 240 delivers content through one of channel 210. And server 220 modulates one or more (N) of channel 210.
A more detailed list of each entity of FIG. 2, and each one's associated description, data elements and function calls is listed below. This listing closely resembles that of object-oriented programming. As such, ‘methods’ represent the ability to obtain or modify data, while ‘attributes’ represent data which is directly associated with that particular entity. The listing also includes information relating to one embodiment wherein software programming specifics are disclosed, such as a variable type (double, int and so forth) and more. The present invention is not limited to such an embodiment and other implementations are possible without deviating from the scope and intent of the present invention. The listing, however detailed, is merely illustrative of the data and functions which are used in the equations and methods described herein.
Consequently, data and functions from this listing, associated with the various entities, will be used in forthcoming equations, flowcharts and methods. The reader is directed to this listing as reference when reading such equations and examining such drawings.
—start of entity data model detailed listing—
Model: Untitled 1 (public)
Contains:
client, session, channel, server, contentSelection.
Component: Client (Public Class/Interface)
Comment:
A client entity stands for a client presently requesting or receiving service.
Methods:


    
    
        public static lookup (id: in int): client
        public GetId ( ): const int&
        public SetId (val: in int&)
        public GetCostOfService ( ): const double&
        public SetCostOfService (val: in double&)

Attributes:

        private status: client <int>
        Specifies whether or not a client has been allocated a channel and session.
        private id: int
        Integer-valued identifier that is unique to the client (primary key). Can be obtained from a monotonically increasing counter.
        private costOfService: double
        Dollar charge per Mbyte. This value is the same for all customers under flow optimization. Under cost/charge optimization may be an integer value reflective of the rank; the higher the rank the higher the charge.

Has:

        public selected: contentSelection
        public assigned a: session
        public employs: channel

Component: Session (Public Class/Interface)

Comment:

        A session entity holds various state information about the service being received by an associated customer.
        public GetCurrentPosition ( ): const double&
        public SetCurrentPosition (val: in double&)
        public GetPayloadToGo ( ): const double&
        public SetPayloadToGo (val: in double&)
        public GetStatus ( ): const int&
        public SetStatus (val: in int&)
        public GetMinimumFlowRate ( ): const double&
        public SetMininumFlowRate (val: in double&)
        public GetFlowRateRange ( ): const double&
        public SetFlowRateRange (val: in double&)
        public GetMaxFlowRate ( ): const double&
        public SetMaxFlowRate (val: in double&)

Attributes:

        private playTimeToGo: double
        Indicates the minutes remaining in the viewing experience. Initialized to contentSelectiont.playTime (see below).
        private currentPosition: double
        Pointer into media content from which content is being delivered.
        private payloadToGo: double
        The amount of media content (in Mbytes) as yet undelivered by the server. Does not include any content presently stored in the client-side buffer.
        private status: int
        Indicates whether session is active or paused.
        private minimumFlowRate: double
        This is the minimum flow from server to client required to ensure uninterrupted service over the remaining playTime. Has a value of zero if playloadToGo is zero. Given by (payloadToGo*8)/(playTimeToGo*60)
        private flowRateRange: double
        Specifies the effective range over which the channel content flow serving a session is constrained without consideration for interactions with other flows.
        Equals maxFlowRate−minimumFlowRate
        private maxFlowRate: double
        Effective maximum bound on flow as expressed in formula (8) which must be re-evaluated periodically.

Has:

public delivers content through: channel

Component: Channel (Public Class/Interface)

Comment:

        A channel represents the network resources from server to client associated with an ongoing session, encompassing the client-side buffer if any, and its level.
        public GetBufferLevel ( ): const double&
        public SetBufferLevel (val: in double&)
        public GetFlowRate ( ): const double&
        public SetFlowRate (val: in double&)
        public GetMaxFlowRate ( ): const double&
        public SetMaxFlowRate (val: in double&)

Attributes:

        private bufferSize: double
        Capacity of the client-side buffer (or equivalent)
        private bufferLevel: double
        Current buffer level in MBytes of stored content.
        private flowRate: double
        Flow rate through channel specified by the relevant optimizing flow modulator.
        private maxFlowRate: double
        This value represents the maximum possible flow rate from the server to an individual client over its “channel”. This value reflects restrictions on flow that pertain to an individual client. It may be determined by factors such as the bandwidth of client's link to the network, or a limit imposed administratively to ensure balanced network utilization.

Component: Server (Public Class/Interface)

Comment:

        Entity representing the media server and its CAC and flow modulation activities.
        public GetFlowRate ( ): const double&
        public SetFlowRate (val: in double&)
        public GetMaxMinFlowRate[ ] ( ): const double&
        public SetMaxMinFlowRate[ ] (val: in double&)

Attributes:

        private maxFlowRate: double
        Maximum possible content flow that is allocated to the server by the network.
        private flowRate: double
        Aggregate content flow rate, summed over all sessions and their associated channels.
        private cac_SafetyMargin: double
        Tunable safety margin used by the CAC algorithm to protect sessions-in-progress from being affected by changes in available network bandwidth.
        private maxMinFlowRate[ ]:double
        Applies when N rate tariffs exist. This array holds the maximum floor level for each category of service. The value for the costliest category N is stored in maxMinFlowRate[N−1], and for the least costliest in maxMinFlowRate[0].
    
    


It is the relative magnitude of these ascending values that matters, not their absolute value. Thus the actual maximum floor flow rate for category k is given by server.maxFlowRate*(server.maxMinFlowRate[k−1]/server.maxMinFlowRate[N−1]). Similarly, the maximum floor flow rate for category N is server.maxFlowRate.
Has:


    
    
        public contains: contentSelection
        public modulates: channel

Component: ContentSelection (Public Class/Interface)

Comment:

        Entity represents a video/sound clip or other bounded unit of content. A continuous data feed does not qualify.

Attributes:

        private averagePlayRate: double
        The average rate at which media content is consumed by the client, as computed by dividing the (payload*8) by the (playTime*60)
        private playTime: double
        Duration of play of the media content in minutes.
        private payLoad: double
        total size of the content in Mbytes.

Has:

public is associated with: session

—end of entity data model detailed listing—

    
    


The following table summarizes the highlights of the previous detailed description of each entity in FIG. 2.








TABLE 1





Entity
Description







client 200
Each client is denoted by an associated unique integer



indexId. The set of active clients is denoted by SActiveClients.



The set of deferred clients is denoted by SQdClients.



Incoming clients are expected to select the content they



wish to view prior to being queued for dispatch by the



CAC sub-system, which requires knowledge of the



client's bandwidth requirements, duration of play, and



cost of service, all of which may vary according to the



selection.


server 220
Servers sit astride a network and can deliver media



content through the network to their clients up to a



designated maximum flow rate. The server is



responsible for accepting or rejecting clients, launching



sessions and associated channels for the former, and



modulating content flows over all channels in an optimal



manner.


channel 210
A channel represents the data path between the server



and the client. The channel buffer is typically located



near or within the clients viewing station. The flow of



content through the channel is set by the flow modulator



sub-system.


contentSelection 230
A server will typically act as a repository for media



content, which it can deliver to clients upon demand. For



our purposes, media content is characterized by its



payload and the play duration, which together imply the



averagePlayRate = (payload*8)/(playTime *60). The



averagePlayRate is none other than the streaming rate



imposed by real-time just-in-time streaming algorithms.


session 240
Every session represents an instance of media content



delivery to an associated client over a designated



channel. The playTimeToGo indicates the time



remaining before the content is fully played out to the



client. The payloadToGo is the amount of content data



as yet undelivered to the channel. A session terminates



when this value reaches zero, at which time



playTimeToGo may still be large, according to the



capacity, the level of the channel buffer, and the media



play rate.









Constraints on Content Flow

Before referring to more Figures, it is imperative to establish some formulas and problem statements which are used in the methods which follow.
The flow of content between entities is subject to the following constraints at all times. Buffer levels are always expressed in Mbytes and data rates in Mbits/sec.
 Σi∈SactiveCients(client.lookup(i).channel.flowRate)<=server.maxFlowRate  (1)
The sum of all channel flows cannot exceed the imposed maximum throughput capacity of the server.

client.lookup(i).channel.flowRate<=client.lookup(i).channel.maxFlowRate for all i∈ΣactiveClients  (2)

The data path from server to client is subject to its own constriction.

client.lookup(i).channel.flowRate<=(client.lookup(i).channel.bufferSize−client.lookup(i).channel.bufferLevel)*8/60+client.lookup(i).session.mediaContent.averagePlayRate, for all i∈ΣactiveClients,  (3)

The channel buffer is never allowed to overflow.

client.lookup(i).channel.flowRate<=client.lookup(i).session.payloadToGo*8/60 for all i∈ΣactiveClients,  (4)

Content that does not exist cannot be delivered. (Constraint 1 will ordinarily prevail except at the very end of a session.)

The constraints listed above are straightforward applications of common sense in relation to the flow of data through constricted channels, out of finite data sources, and into and out of bounded buffers. By contrast, the following constraint, which imposes a minimum channel flow rate instead of a maximum, is less obvious. The minimum value, termed the minFlowRate is set to the flow rate which, if sustained over the balance of the play time to go (playTimeToGo), ensures that all required content will be available when needed—and no sooner—until all content is played out. This floor value can be calculated for i∈ΣactiveClients by the formula:
 client.lookup(i).session minFlowRate=(client.lookup(i).session.payloadToGo*8)/(client.lookup(i).session.playTimeToGo*60)  (5)
Accordingly, the flow rate on the right-hand-side is termed the just-in-time (JIT) flow rate (fJIT).
Thus:

client.lookup(i).channel.flowRate>=client.lookup(i).session.minFlowRate for all i∈ΣactiveClients  (6)

The variable constraint bounds (i.e. the values to the right of the inequality symbol) of equations 1-4 and 6 are re-evaluated on a periodic basis (e.g. once per second) prior to the execution of the CAC procedure and optimizer. In particular, the minFlowRate value starts out at the beginning of a session equal to the streaming rate. By construction the minFlowRate rate never exceeds this initial value so long as constraint 6 is honored. In fact, constraint 5 implies that the minflowRate value must be a diminishing function of time that may hold its value for a time but never rises. As seen from equation 6, the actual data rate of the channel, flowRate, is always greater than or equal to the minFlowRate. By design, and virtue of the fact the present invention uses faster-than-realtime transmissions, the system quickly gets ahead of itself and ensures that after initial conditions, the minFlowRate is always equal to or less than the real-time rate and that it continues to decrease. As we shall see, the CAC procedure exploits this monotonic characteristic of the minimum flow rate over time.
Constraints 2, 3 and 4 are of like kind, each specifying an upper bound on individual channel flows. Whereas the bound for constraint 2 is typically a constant, the bounds on 3 and 4 will vary over time. Nevertheless, only one of the three bounds is effective at any given time, namely the one with the smallest bound value, given by:

client.lookup(i).session.maxFlowRate=minimum of  (7) 

    
    
        1) client.lookup(i).channel.maxFlowRate,
        2) (client.lookup(i).channel.bufferSize−client.lookup(i).channel.bufferLevel)*8/60+client.lookup(i).session.mediaContent.averagePlayRate,
        3) client.lookup(i).session.payloadToGo*8/60

Consequently, formulas 2, 3, and 4 can be consolidated into a single constraint, the bound for which is computed at every scan to be the smallest bound of associated constraints 2, 3 and 4.

client.lookup(i).channel.flowRate<=client.lookup(i).session.maxFlowRate,  (8)

        whereby for all i∈ΣactiveClients, maxflowRate is given by equation (7).

At any one time, individual channel flows are constrained over a range, as follows:

client.lookup(i).session.flowRateRange=client.lookup(i).session.maxFlowRate−client.lookup(i).session.minimumFlowRate  (9)

Value Functions

    
    


The value functions introduced previously can be expressed mathematically as linear functions of channel flows, as follows:
Optimizing Throughput (Maximal Flow)

value=Σi∈SactiveClientsClient.lookup(i).channel.flowRate)  (10

Optimizing Charges (Maximal Charges)

value=Σi∈SactiveClients(client.lookup(i).channel.flowRate*client.lookup(i).costOfService)  (11)

Optimization Problem Statement (FIG. 3)

The optimization problem, which in one embodiment is strictly throughput and in another case is charge, can be stated simply as follows:
Find values for


    
    
        client.lookup(i).channel.flowRate for all i∈ΣactiveClients 
        constrained by inequalities 1 through 5, such that the value obtained by evaluating expression 10 or 11 assumes a maximum.
    
    


Both of these problem formulations are examples of Linear Programming for which a number of well-known and generally effective computational solutions exist. In linear programming one seeks to optimize a linear cost function of variable x

c*x=c1*x1+ . . . +cn*xn  (12)

subject to a set of linear inequality constraints

 A*x<=b  (13)

where xT=(x1, . . . , xn), c=(c1, . . . , cn) are the state variable & cost vectors, A is an n-by-m matrix, bT=(bi, . . . bm) is the constraint vector, and the operator ‘*’ stands for matrix or scalar multiplication.

FIG. 3 is introduced as illustrative of the problem statement and the general methods of the prior art, and is not incorporated as an element of the invention.
The linear programming problem as well as its solution can best be understood with the aid of geometry. FIG. 3, depicting a 2-dimensional Cartesian problem space, inequality constraints (13) define a convex hull H 310 over which a search for an optimum value of x=(x1,x2) is permitted to range. The cost vector c 350 defines an infinite family of equal cost lines (hyper-planes) which lie orthogonal to c. Three examples of such lines are shown in L1 360, L2365, and L3 370., each of progressively higher value. The supreme value of the cost function is obtained by sliding along c 350 till one can go no further, in this instance toward vertex V4 340 of hull H 310. Many well-known methods (e.g. the Simplex Method) work roughly in this fashion, exploiting the fact that at least one optimum point must be at a vertex. In particular, the Simplex method algorithm begins by finding a vertex (e.g. V2 320), and then moves along a sequence of vertices (e.g. V3 330, V4 340) improving itself each time until no further improvement is possible & the summit is reached.
Let us suppose instead that V3 330 were placed along L3 370 along with V4 340. According to prior art methods, V3 330 and V4 340 are the two possible solutions, but the equally valuable points in between them are not. As we shall soon see, the problem of throughput optimization (6) falls in this category.
While vertex V1 300 does not factor into this description, it is depicted in FIG. 3 for completeness.
Flow Modulation
Methods for Maximal Flow
The following sections detail two embodiments to optimize total data flow.
Overview (FIG. 4-a)
FIG. 4-a depicts a scenario involving two flows. The convex hull is in this instance bounded by line segments L1, L2, L3, L4 and L5. L6 is a boundary used in a different embodiment, however the present embodiment uses L5 and not L6. Flow f2 can range over the interval separating line segments L1 from L3, namely f2MIN and f2MAX; the range is depicted as f2RANGE. Flow f1 can range over the interval between lines L2 and L4, namely f1MIN and f1MAX, and depicted as f1RANGE. The sum of flows f1 and f2 is constrained to lie inside of line segment L5 which, by construction, is always orthogonal to the cost vector Cf. Cost vector Cc is also illustrated but used in a distinct embodiment. In the present embodiment only Cf is used. In the illustrated example of the present embodiment, the constraint on total flow is set to 5, and is therefore low enough to cause L5 to intersect L3 and L4. This would not have been true had the value chosen had been 10 instead of 5. With L5 safely out of contention, the convex hull would instead be a simple rectangle bounded by L1 through L4, thereby permitting both flows to assume their respective maxima without interference. In practice operational constraints exist intrinsically or are imposed from the outside so as to ensure cost effective sharing of potentially costly network resources.
Supposing FIG. 4 to be correct, the well-known methods would select vertex V3-5, which lies at the intersection of L3 and L5, or V4-5, which lies at the intersection of L4 and L5. These solutions, though optimal, are undesirable for the present invention as they fail to spread available bandwidth over all channels as fairly as would a centrally located interior point of L5. For this reason, two alternative optimization methods are taught, which are adapted to the particular needs of this problem and ensure a fairer allocation of constrained bandwidth among all channels.
Iterative Procedure (FIG. 5)
In order to optimize use of all available bandwidth, the following general method is used, with the details illustrated in FIG. 5. This method is a solution for the problem illustrated in FIG. 4-a, which geometrically illustrates the optimization problem in the limited case of two flows, f1 and f2. The following description expands the problem to an arbitrary number of clients (and therefore flows) and presents a method for solving this optimization problem.
Referring to FIG. 5, in step 500, values are calculated for the session maxFlowRate and session.minFlowRate for each client as per the minimum and maximum constraint bound expressions in equations 6 and 8, respectively. This step correlates to the determination of f1min, f1max, f2min and f2max from FIG. 4-a. 
The difference between these two yields the session.flowRateRange of each client. Thus:

session.flowRateRange=session maxFlowRate−session.minimumFlowRate

In step 505, the active clients are sorted in an ascending fashion based upon their session.flowRateRange. As will be shown this critical step facilitates allocation of the remaining server bandwidth as evenly as possible among all active channels, thus maximizing the number of channels that benefit by use of the total server bandwidth. An arbitrary assignment of remaining bandwidth is likely to saturate the server before all channels have been assigned extra bandwidth, thereby favoring certain channels on an ad-hoc basis. This step correlates to keeping the solution in bounds of the space delinated by line segments L1-L5 of FIG. 4-a. 
In step 510, each client's channel flow rate is set to the session mimimumFlowRate.
By doing so, it is ensured that the minimum flow constraint is met for each session and that the minimum flow rate is a non-increasing function of time, which is critical to the proper functioning of the CAC procedure. This portion of the process also ensures that the solution, starting from the vertex in FIG. 4-a as defined by the intersection of L1 and L2, moves generally in the direction of vector cf. All clients are also marked as unprocessed.
In the next step, 520, server.flowRate is set to the sum of each active client's session.flowRate.
Next, the following is iterated over all clients in sorted sequence (during any given iteration the selected client is given by its id) by performing steps 530 through 570. In step 530 evaluating the following expressions test for possible server saturation:

delta=(server.maxFlowRate−server.flowRate)/(qty of un-processed clients)

range=client.lookup(id).session.maxFlowRate−client.lookup(id).session.flowRate

If range is greater then delta, this implies that the server can be saturated in this iteration by allocating delta to all unprocessed clients (step 540).
On the other hand, the ‘no’ path for step 530 implies that the server is not saturated and that the present client (given by id) will saturate first. Accordingly, in 550 the delta variable is set as follows:

delta=range

To again correlate this process back to the geometry of FIG. 4-a, server saturation is indicated when the solution which is being sought in the direction of vector cf goes beyond line segment L5.
Next, the flow rate is incremented for all unprocessed clients by delta, causing client id to saturate.
In step 560 the server flow rate is adjusted accordingly:

server.flowRate=server.flowRate+delta*(qty of unprocessed clients)

In step 570 the client given by id, now saturated, is marked as processed.
Algebraic Procedure (FIGS. 4-b and 15) By Interpolation
Referring to FIG. 4-b, the iterative method described in the previous section begins its search for a maximum from vertex Vmin along the direction shown by line C1. In contrast, the present method follows the diagonal line segment Ldiag of the rectangle bounded by lines L1 through L4, starting at vertex Vmin and ending at point V3-4.
Provided it exists, the intersection between Ldiag and L5, indicated by Vf, is optimal on the same basis as any other point lying along the intersection of L5 with the rectangle bounded by L1 through L4, as previously discussed.
Whenever L5 does not intersect this rectangle, the optimal solution is given by vertex V3-4 at which f1 and f2 both assume their respective maxima.
In the first instance, the coordinates for point Vf can be obtained by elementary vector geometry and algebraic manipulation, as follows:

    
    
        First, we define a number of abbreviations,
        fkmin represents client.lookup(k).session.minimum flow rate
        fkrange represents client.lookup(k).session.flow rate range
        fsvfmax represents server.maxflowrate

We seek scale factor x such that the vector sum of (f1min . . . fnmin)+x(f1range . . . fnrange)intersects an equi-cost hyperplace for capacity c.

    
    


The point of intersection is obtained by solving equation:

(f1min+ . . . +fnmin)+x(f1range+ . . . fnrange)=c

Solving for x, we obtain:

x=[fsvrmax−(f1min+ . . . +fnmin)]/(f1range+ . . . +fnrange)

where fsvrmax−(f1min+ . . . +fnmin) represents the unused bandwidth beyond the minimum allocation for each session. For any given session, the optimal flow rate is given by:

fi=fimin+xfirange, if x<1,

or

fi=fimin+firange, if x>1

This solution by interpolation is interesting by virtue of the great efficiency of the calculation, and the fact that no session saturates (x>=1) unless all sessions saturate. In contrast, the previous method entails considerably more computational effort, and tends to saturate sessions with the lowest reserve capacity.
A block diagram for this algorithm is depicted in FIG. 15. Block 1500 establishes the maxim and minima for each flow. For each flow the minimum is subtracted from the maximum to obtain the range. Available Bandwidth is calculated in block 1520, as the difference between the aggregate flow capacity and the sum of flow minima. Factor x is calculated next in block 1540, and tested against 1 in block 1650. Flow rates for each session are computed in block 1560 if x is less than 1, or 1570 in the contrary case.
A Method for Maximal Charge
The following sections detail one embodiment to optimize the total monetary charges within the system. The second method is algebraic in nature, and thus very efficient.
Overview (FIG. 4-a)
Referring back to FIG. 4-a, cost vector Cc lies orthogonal to line L6, which intersects the convex hull at the vertex formed by the intersection of lines L4 and L5, namely V4-5. This cost vector, and the optimal point that it implies, favors flow f1 over flow f2. In this example, as the cost of service for f1 equals 2, thus exceeding the cost of service of 1 set for f2. As the number of flows grow to exceed the number of distinct categories of service (and associated costs of service) the unique optimal solution, depicted in FIG. 4 for the case where every flow has a distinct cost of service, no longer applies. Once again a plurality of flows within a service category vie for bandwidth which a method should endeavor to distribute evenly. This method is derived from the previous one, and optimizes one cost category after another, starting with the most costly and ending with the least costly, or when all available capacity is allocated.
An Iterative Search Procedure (FIG. 6)
Let the service categories be denoted by k=1 . . . N, where k also denotes the cost of service.
Let C1 . . . CN be the partition of SactiveClients that places all clients with cost of service k in set Ck. Partition sets Ck can be ordered to form sequence SeqC=CN . . . C1.
FIG. 6 depicts the method for implementing the method to maximize the cost of service (service charge).
This method is nearly identical to the iterative procedure used to maximize flow. The principle difference stems from the partitioning of clients according to their category (cost) of service: clients charged most are allocated bandwidth preferentially. This is accomplished by adding another level of iteration around the method of FIG. 5. The inner iteration (steps 650 through 680) functions exactly as before, with the difference that its actions are limited to the clients belonging to the given service category k (i.e. Ck). This difference also holds true of step 640 which sorts category k clients according to their flow ranges prior to entry in the bandwidth-allocating inner loop. The outer loop proceeds down a sorted sequence of service categories SeqC (generated in step 630), starting with the category generating the greatest revenue to the service provider. Given a fairly static set of service categories, this sort need be performed only when the categories undergo change. Steps 670, 675 and 680 are identical to their counterparts in the method of FIG. 5 (i.e. 570, 575 and 580).
The net effect of this method is preferential allocation of bandwidth according to category of service, and equitable treatment of clients within the same category of service.
An Iterative Algebraic Procedure (FIG. 16)
The algebraic method used to maximize bandwidth (FIGS. 4b and 15) can be viewed as a special case of cost optimization in which all costs are equal. By construction, all sessions belonging to a given category, starting with the most expensive category, and ending with the least, and updating available bandwidth after each step in sequence, we obtain an iterative algebraic method that scales much better than the preceding method.
A block diagram for this algorithm is depicted in FIG. 16. Block 1600 establishes the maxima and minima for each flow. For each flow, the minimum is subtracted from the maximum to obtain the range. In block 1610, every session flow is assigned the minimum allowed value, which value will apply by default should the iterative procedure run out of bandwidth before all categories can be considered. Block 1620 computes the initial value for available bandwidth, as the difference between the aggregate flow capacity and the sum of flow minima.
Flow values are obtained for each cost category in order of decreasing cost within blocks 1640 through 1675. Factor x is calculated next in block 1540, and tested against 1 in block 1650. Flow rates for each sessions of the category under consideration are computed in block 1660 if x is less than 1, or 1670 in the contrary case. In the former case there is no more bandwidth to allocated to the sessions in the category under consideration.
Call Acceptance Control (CAC)
CAC for Maximal Flow Overview (FIGS. 7-8)
The CAC procedure applicable to this flow optimization relies on the essential step of accepting a new client if and only if the added load induced thereby does not compromise service to existing clients or the new one. This critical step could not be accomplished without the close integration with previously-described flow-modulation methods of FIGS. 5, 6, 15 and 16.
According to the previous discussion, the minimum flow rate is the minimum sustained flow rate that guarantees that the associated viewer will not be subject to interruptions in service due to a shortfall of content from the media server. It follows that whenever data is being delivered at a rate in excess of the minimum flow rate, a downward adjustment toward the minimum level could be accommodated as needed to surrender bandwidth to any newcomer.
FIG. 7 depicts content flow over a channel for the course of a typical session, and also how data is delivered under real-time streaming D. The amount of content delivered is the same in either case, but the manner of delivery differs considerably. A session is launched at time 0 as the network is lightly loaded, and the optimizer sets an accordingly high flow rate. Another client emerges at the end of interval 700, causing a downward adjustment to the flow rate over interval B, as available bandwidth is shared between two sessions. During both of these intervals the minimum flow rate 720 drops quickly, as data accumulates in the client's media buffers. At the end of interval B, a massive influx of clients necessitates that flow be dropped to the minimum flow rate, which now lies substantially below the streaming rate D and is held until all data is delivered at the end of interval C. Note that the minimum flow rate, shown as element 720, diminishes monotonically over time.
The server swing capacity is defined as the difference between the maximum capacity of the server and the total minimum flow rates for all active clients. Therefore:

swingCapacity=server.maxFlowRate−Σi∈SactiveCients (client.lookup(i).session.minFlowRate)  (14)

Given the monotonic decreasing nature of session minimum flow rates, server swing capacity can readily be seen to be a monotonic increasing function of time over the intervals separating client admissions, at which point it undergoes a drop as a new load is taken on. This all-important characteristic implies the following:
Any client admitted for service based on the present value of swing capacity is guaranteed to have sufficient bandwidth at its disposal over the entire future course of the session.
FIG. 8 depicts the server swing capacity 800 over the course of the sessions illustrated in FIG. 7. Swing capacity rises quickly over intervals A & B as data is delivered at high flow rates over the network. It holds steady over interval C when all channels flow at their minimum rate then jumps at the end of C before resuming its monotonic rise once again.
Procedure (FIG. 9)
In this procedure, which executes on a periodic basis, queued clients awaiting bandwidth are scanned in FIFO order. For each one, the required bandwidth is computed as per the client's prior content selection. If the available swing capacity (reduced by a safety margin) exceeds the amount required, then the client is activated and swing capacity is adjusted accordingly. Otherwise, two possible cases are considered: 1) under the FirstFit embodiment, the procedure continues scanning clients to the end of the queue, activating clients whose requirements can be met; 2) under the FIFO embodiment, the procedure ends with the first candidate client whose requirements cannot be met.
In step 900, available server swing capacity is evaluated according to the formula

swingCapacity=server.maxFlowRate−Σi∈SactiveClients (client.get(i).session.minimumFlowRate)

The bandwidth requirement for client id in Step 920 is obtained as follows: required_bandwidth=client.lookup(id).contentSelection.averagePlayRate
The predicate evaluated in Step 940 is given by the expression:

(required_bandwidth<=swingcapacity−server.cac_flowSafetyMargin)

In step 950, client activation entails allocation of a session and a channel, and insertion in the set of active clients eligible for bandwidth allocation by the optimal flow modulator.
In step 960 the swing capacity is diminished by the amount reserved for the activated client:

swingcapacity=swingCapacity−required_bandwidth;

Responding to Variations in Network Capacity (Maximal Flow)
In the CAC procedure for maximal flow, a safety margin was introduced, namely server.cac_flowSafetyMargin, to provide the means for ensuring that the server's swing capacity will never fall below a minimal threshold value.
According to this procedure, the following inequality always holds true:

swingcapacity>=server.cac_flowSafetyMargin  (15)

In the previous discussion, a server's swing capacity provided the basis for determining whether or not a prospective client should be allocated bandwidth.
By holding server.cac_flowSafetyMargin in reserve, the CAC algorithm forces delivery of content at faster than real-time rates among accepted clients, even under the heaviest load. The net effect is to apply upward pressure on client side buffer levels, thus promoting continuous accumulation of content and a jitter-free viewing experience once a session is under way.
In another embodiment, server swing capacity can also be interpreted as specifying the maximum amount by which the server.maxFlowRate constraint can be dropped without affecting service, should such an adjustment prove necessary due, for instance, to an influx of exogenous network traffic that diminishes the amount available for multi-media services. Parameter server.cac_flowSafetyMargin can thus be set so as to guarantee a minimum capacity to tighten the constraint on maximum server flow in response to unexpected load changes that affect the server's ability to service its existing clients as well as new ones.
Anticipating Scheduled Variations in Network Capacity (Maximal Flow)
Overview (FIG. 10)
FIG. 10 depicts how the constraint on maximum flow might be allowed to vary according to the time of day, day of the week, and so forth, in expectation of time-varying traffic flow levels extrapolated from past experience, traffic flow models, etc. Maximum flow rate 1000 can be seen to vary based upon the time of day. In practice, defining the right-hand-side of inequality constraint 1 as a time-dependent expression can impose such time-varying capacities. According to the previous description, the optimizer, which executes on a periodic basis, will automatically seek new flow levels for every active session as the constraint varies. There is, however, no guarantee that an acceptable operating point will be found for all sessions (i.e. one that respects the minimal and maximum constraints on session channel flow). One such example is the case where the server is loaded to the limit and total capacity is curtailed in excess of the aforementioned safety margin. Should such a situation arise the only recourse may well be the termination of a number of established sessions (i.e. load shedding).
The goal is to eliminate service disruptions of this sort by allowing the CAC procedure to look ahead into the future, and accept new clients only if these can be accommodated without any compromise in service in the midst of previously anticipated changes in available network capacity. The following CAC procedure generalizes the previous one: before accepting a client, the test on swing capacity is repeated over a sequence of time segments that cover the proposed viewing period.
Definitions
Let:

t_end(i)=client.lookup(i).session.playTimeToGo+t_now  (16)

Let server.maxFlowRate(t) be server flow capacity as a function of time, as exemplified in FIG. 10.

Let SeqT(t_now)=advancing sequence of future times, lead by t_now, when server.maxFlowRate(t) undergoes a step change. For instance, at 9:15 in FIG. 10 this sequence reads as follows: 9:15, 9:30, 11:30, 13:30, 6:30, 7:30.
The server swing capacity at a future time t is computed according to the capacity and worst-case client flows at time t.

swingcapacity(t)=server.maxFlowRate(t)−Σt—end(i)>t(client.lookup(i).session.minFlowRate)  (17)

It is noteworthy that the worst-case client flows at time t are express terms of the present minimum flow rates, which cannot increase over time, but might hold steady. Finally, a predicate is defined that tests whether a prospective customer will cause swing capacity to be exceeded at some time t, as follows:












(18) boolean client_fits(i ,t) {









if(client.lookup(i).contentSelection.averagePlayRate < =









swingCapacity(t) - server.cac_flowSafetyMargin)









return true;









else return false;









}










Procedure (FIG. 11)
This procedure is an adaptation of the first, which has been extended to consider swing capacity at times in the future when capacity undergoes scheduled changes. Before accepting a client, its minimal bandwidth requirement (which by construction of the flow modulator will never increase over time) is checked against projected swing capacity at points in time when total available capacity undergoes scheduled step changes, provided these times fall within the proposed content viewing period. A candidate is activated only if all tests succeed.
Step 1100 builds a sequence of time values (SeqT) at which step capacity changes are scheduled to occur. The first element of this sequence is t_now, representing the present.
Beyond step 1100 the queue of waiting clients is scanned in FIFO order, yielding a candidate designated by id at each iteration.
The bandwidth requirement for client id in Step 1120 is obtained as follows:

required_bandwidth=client.lookup(id).contentSelection.averagePlayRate

The worst-case end time for content flow to id is obtained according to the content selected, as follows:

t_end=t_now+client.lookup(id).selected.playTime

Steps 1130 through 1150 are executed within an iteration for each time point t in SeqT falling between t_now and t_end. This iteration is ended in step 1130 if t exceeds the time window of interest, or in step 1150 if the supply of scheduled capacity changes is exhausted.
For each time value, step 1140 compares required bandwidth to projected swing capacity.
Projected swing capacity at time t is:

swingCapacity(t)=server.maxFlowRate(t)−Σt—end(i)>t(client.lookup(i).session.minimumFlowRate)

Note that only active clients whose t_end times occur after t are considered in the sum of minimum flow rates.
The predicate expression used in step 1140 at time t is thus:

(required_bandwidth<=swingCapacity(t)−server.cac_flowSafetyMargin)

Step 1160 performs the same actions as step 660 in the previous CAC flowchart
The first CAC process is a special case of the present one, in which the set of step change times to server.maxFlowRate is empty (i.e. server.maxFlowRate is constant), and SeqT(t_now)==t_now.
In preparing SeqT(t_now), one need only consider future times that will pass before the longest possible content is played out if started at t_now. In order to sidestep problems associated with rollover (at midnight, year 2000, etc.), time is best expressed as a monotonically increasing value (e.g. seconds since Jan. 1 1990).
CAC for Maximal Charges
Overview (FIG. 13)
Previously, a method for flow modulation was presented that maximizes charges to clients with active sessions. The CAC embodiment presented previously was not sufficient as it does not consider the cost of service as a basis for connection acceptance. As a result, it may turn away higher paying customers while granting service to lower paying ones, thereby defeating the purpose for this particular embodiment. Therefore, another embodiment is defined which offers the following features:
1. Awaiting clients are serviced in order of their respective service categories, higher paying clients first.
2. Once accepted, a client is guaranteed to receive acceptable service irrespective of its service category.
3. Under heavy load conditions higher paying customers are more likely to be accepted than lower paying ones.
4. Lower paying customers will no be starved for service when higher paying ones enjoy a surplus.
5. Available bandwidth is not thrown away needlessly while clients are being denied service.
The first objective is easily met by dividing the client queue into as many bands as there are service categories, resulting in a banded queue. Bands are ordered within the queue according to their service categories, with the costliest category in front. As prospective clients arrive and make their selection they are placed in their respective queue band according to their service category (which may be set contractually, according to content selection, etc.).
Our second objective is met by employing a procedure patterned after those presented previously & offering the same guarantee. Toward our third and fourth objectives we propose dividing total available bandwidth in as many strata as there are service categories. As depicted in FIG. 12, two service categories are shown, Premium and Basic, each entailing an associated cost of service. A prospective client is accepted only if there is sufficient swing capacity available within its given service category. The swing capacity for a given category is given by the smaller of 1) the difference between its maximum floor flow rate (corresponding to the top of the stratum for the service category) and the sum of the minimum rates of all active sessions in its category or below, and 2) available swing capacity overall. Finally, our fifth objective is met by allowing the flow optimizer to function freely subject to its operational constraints. The imposed ceilings on call acceptance by category relate to minimum flow rates, which merely impose a floor on actual flow rates. For example, basic clients might well consume all available bandwidth 300 in the absence of any premium customers, yet could be throttled back toward their floor flow rates (which together cannot exceed 200 in this example) at any time should any premium customer suddenly demand service. In contrast, premium customers could consume the entire 300 bandwidth. As lower paying customers appear these would be admitted to the degree that their quota on minimum flow is not exceeded (i.e. 200) and the availability of swing capacity on the system.
Procedure (FIG. 13)
The present procedure requires a number of ancillary definitions, which follow:
Let the service categories be denoted by k=1 . . . N, where k also denotes the cost of service.
Let server.maxMinFlowRate[k−1] be the top of the stratum for service category k. Note that server.maxMinFlowRate [N−1]=server.maxFlowRate.
Let Sk be the set of active client indices with a service category equal to or less than k. Note that S1 is contained in S2, S2 is contained in S3, and so forth, and that SN=SactiveClients.
Let swingcapacity(k) denote available swing capacity for service category k. By construction:

swingCapacity(k)=minimum of: (server.maxMinFlowRate[k−1]−Σi∈Sk(client.lookup(i).session.minFlowRate)),  (19)

(server.maxFlowRate−Σi∈SactiveClients(client.lookup(i).session.minFlowRate)))

Referring to FIG. 13, this method is used for CAC when multiple rate tariffs are in effect, and there is a desire to maximize economic returns to the service provider while offering acceptable service to all.
All waiting clients are scanned in FIFO sequence. The actions taken in Steps 1320 and 1360 are identical to those described in connection with earlier CAC flowcharts.
Step 1340 evaluates a predicate expression that tests whether the required bandwidth can be accommodated without exceeding the lesser of 1) swing capacity available to the client's category of service, and 2) total available swing across all categories of service. The latter factor could be determinative if all available bandwidth were allocated to high paying customers, leaving lower paying ones such as the proposed client unable to draw from their unfilled quota.
Let us suppose that candidate client id belongs to rate category k.
We define the swing capacity available in rate category k as:

swingcapacity(k)=least of: (server.maxMinFlowRate[k−1]−Σi in SK(client.lookup(i).session.minimumFlowRate))

and

(server.maxFlowRate−Σi∈SactiveClients(client.lookup(i).session.minimumFlowRate))

The predicate expression invoked by step 1340 can now be written as follows:

(required_bandwidth<=swingCapacity(k)−server.cac_flowSafetyMargin)

This algorithm processes queued clients in band sequence, and within every band in FIFO order. If the predicate evaluates to true, the client is activated. Otherwise two possible cases are considered: 1) under the FirstFit embodiment, the procedure continues scanning clients to the end of the banded queue, activating clients whose requirements can be met; 2) under the FIFO embodiment, the procedure ends with the first candidate client whose requirements cannot be met. Many other variations on these two embodiments might also be considered.
Anticipating Scheduled Variations in Network Capacity (Maximal Charge) Overview
The procedure applicable to optimization of delivery charges is obtained by blending elements of the CAC method depicted in FIG. 13 into the method depicted in FIG. 11, which applies without change. To understand how this might work it may be useful to visualize a version of FIG. 10 stratified along its length in the manner of FIG. 8. As the maximum flow level undergoes a step change, so too do the widths of its constituent strata in equal proportion.
Procedure
As previously mentioned, the CAC method (FIG. 11) applies to this circumstance also, provided we alter the definition of two routines, (17) and (18), upon which that procedure relies, yielding (20) and (21), and adopt the banded queue organization outlined in the previous section.
The server swing capacity at a future time t is computed according to the capacity and worst-case client flows at time t.

swingCapacity(k, t)=minimum of((server.maxFlowRate(t)*(server.maxMinFlowRate[k−1]/server.maxMinFlowRate[N−1])Σi e Sk & (t—end(i)>t)(client.lookup(i).session.minFlowRate)),  (20)

(server.maxFlowRate−Σi∈SactiveClients & (t—end(i)>t)(client.lookup(i).session.minFlowRate))

Finally, we define a predicate that tests whether a prospective customer will cause swing capacity to be exceeded at some time t, as follows:













(21) boolean client_fits(i ,t) {









k = client.lookup(i).costOfService;



if(client.lookup(i).contentSelection.averagePlayRate <=









swingCapacity(k,t) - server.cac_flowSafetyMargin)









return true;









else return false;









}










System Description

Referring to FIG. 14, a block diagram illustrating a preferred embodiment for a system implementing the methods presented herein is shown.
Block 1485 depicts plurality of network-based client computers that receive data from a server over the course of a session. Every client sessions has an associated session block 1435 within the server by means which a flow rate of content from client to server is effected and regulated to a given flow rate set-point. The flow optimizer 1430 manages bandwidth utilization across all sessions that have been admitted by the system call admission control (CAC) and the bandwidth call admission control blocks, labeled 1400 and 1420 respectively. Specifically, the flow optimizer 1430 modulates the flow rate set-point of every active session so as to optimize aggregate flow or, more generally, cost.
Call Admission Control
Whenever a client contacts a server requesting service, the server must determine whether or not to admit the client. This admission function is performed in two separate phases. The system call admission control block 1400 considers whether or not sufficient internal resources exist to support the request. Toward this end, the system CAC 1400 estimates the needs of the prospective client with respect to a set of limited system resources such as I/O bandwidth, cache memory, open files, threads, etc. A request is denied if any required resource cannot be obtained. In the contrary case, the request is passed on to the Bandwidth CAC, which tests if the client fits and admits or rejects the client accordingly. The swing capacity is computed by the flow optimizer 1430 on a periodic basis according to equations (14) and (17) as appropriate. The managed bandwidth must reflect the true capacity of the attached network and the adapters leading thereto. This parameter should not be set arbitrarily high to prevent rejection of client requests. Doing so will cause the system to admit calls that cannot be properly handled, thereby diminishing the quality of the viewing experience.
Having admitted a client, block 1430 creates a client session block 1435, which then begins to converse with its client-resident counterpart, 1480) during their launch phase. Thereafter, the flow optimizer 1430 assumes control, and modulates flow over the session until either all content is delivered, or a failure to deliver is detected, or one of a number of VCR-like stream control events intervene (e.g. pause, rewind, fast-forward).
Server and Client Session Control Blocks
Data Transport Channel 1450 is responsible for transporting data packets originating from the flow regulator 1440 within the server to the former's peer entity 1460 within the client. The mode of communication between the peer entities may be connection-oriented (e.g. TCP, which delivers a byte stream in order, without duplication or loss) or datagram-oriented (e.g. UDP). Best-efforts datagram service is typically enhanced with acknowledgements to facilitate rapid recovery from occasional packet loss, out-of-sequence delivery, and duplication.
Peered session control channels 1445 and 1465 permit configuration and status data, together with miscellaneous commands, to be sent from client to server and vice-versa. A reliable connection-oriented transport service is typically employed for this purpose (e.g. TCP). Data and commands alike are multiplexed over this channel in the service of other entities within the clients or server. Thus, a datagram-oriented data transport channel 1460 within a client 1485 might employ the session control channel to ferry selective acknowledgements to its peer in the server. Similarly, the flow meter 1465 within the client 1485 forwards the measured flow rate to the associated flow regulator 1440 within the server.
The flow regulator 1440 obtains content data from a cache or disk, at the current offset into the content file, which it forwards as packets to the data transfer channel 1450. The size and/or pacing of the packets are determined by the flow regulator 1440 in order to achieve the flow rate set-point imposed by the flow optimizer 1430. The flow regulator 1440 is also responsible for determining the channel flow capacity to the client, which is the least of a configured value obtained from the client and a measured value. Toward this end, during the launch phase, the flow regulator 1440 might send content data packets to the client flow meter 1475 in a series of packet trains at progressively higher peak flow rates ending with the configured maximum flow rate, if any. The highest measured flow rate reported by the client flow meter 1475 is accepted as the flow rate capacity, which is posted for use by the flow optimizer 1430. Subsequently, the flow regulator 1440 will compare the flow rate set-point with the flow rates reported by the flow meter 1465, and down grade capacity as needed should the measured flow rate fall consistently fall below the requested flow rate. Whenever such a downgrading occurs, the flow regulator 1440 will test for subsequent relaxation of a transient constriction by means of the aforementioned series of packet trains in which the peak packet flow rate exceeds the delivered flow rate.
The buffer manager 1470 accepts data from the flow meter 1465, which data is retained until it is consumed or passed over the content consumer 1480. The buffer will typically be implemented as a ring buffer in memory or on disk. The write cursor will lag the read cursor by a no less than a specifiable time interval so as to permit rewinds of acceptable scope without requiring selective data re-retrieval from the server.
Flow Optimizer 1430
The flow optimizer 1430 assumes control over a session once it has been launched, and its channel capacity has been determined. Subsequently, it modulates the flow rate set-point of every session such as to optimize aggregate flow or charges across all active sessions, subject to a variety of min/max constraints on sessions flows, and a maximum constraint on aggregate session flow, as previously discussed.
The flow optimizer 1430 continues to modulate session flow until all content has been delivered, or one of a number of session anomalies intervene, as follows:
A downgraded session flow capacity drops below the minimum session flow rate. The session is dropped by the optimizer 1430 as a solution involving this channel does not exist. The user is forced to apply for re-admission, with the option of accepting slower than real-time delivery at the present encoding rate, or accepting a degraded viewing experience at a reduced encoding rate better adapted to the presently available bandwidth.
A pause VCR command is received from the client. Flow to the client can continue until the client-side buffer is topped off, after which time flow drops to zero. The session is permanently dropped should the pause persists too long. Until that time, the CAC safety margin is temporarily increased by the jit (Just-In-Time) flow rate of the paused session. In this way the session can be resumed without the need for re-admission and the jit bandwidth is made available to currently sessions so long as the pause persists.
A VCR Jump-Forward command is received from the client. This action is problematic as it causes the just-in-time flow rate (calculated at the new forward offset) to increase, in violation of the assumptions of the CAC algorithm. It must be noted that this violation will occur even if the content that is sought has already been delivered to the client-side buffer. One workable policy is to force the client to apply for re-admission at the forward offset and with a suitably modified buffer level.
A VCR Jump-Backward (Rewind) command is received. This action may entail the need for re-transmission of content, as previously discussed. The just-in-time flow rate will decrease as per the new position and adjusted buffer contents.
Tunable Minimum Constraint
A parameterized family of minimum flow constraints can be defined as follows:

wherein: fk(t)=Target content flow rate for session k;  (22)

    
    
        fkJIT(t)=Just-in-time flow rate for session k;
        
            (RHS of Equation (5))
        
        
        β=Burst tuning factor (positive or zero); and
        fkmin(t)=Minimum (reserved) flow rate for session k.
    
    


This family converges on fk(t)>=fkJIT(t) when β approaches 0. A β value of 0.1, for example, ensures a minimum flow rate that exceeds the JIT flow rate by 10%. Thus, non-zero values of β force early delivery of content to a player's media buffer, with beneficial effects on the viewing experience.
Alternative Call Admission Control
The traditional CAC algorithm compares the flow rate requirement of a prospective client with the unused bandwidth (obtained by subtracting the aggregate flow target from the server flow capacity) and grants service if unused bandwidth is not exceeded. This procedure may break down as the optimizer causes all available bandwidth to be used if it can, thereby reducing unused bandwidth to zero in the best case, even when a new client could be accommodated with a healthy margin to spare.
Nevertheless, a simple variation on this idea can be used. Available bandwidths can be defined as the difference between server flow capacity and the sum of minimum flow rates for each session computed according to (22) as follows:

favailable=fSvrmax−(f1min+ . . . +fnmin)  (23) 

wherein: favailable=Available bandwidth

    
    
        fSvrmax=Server aggregate flow capacity; and
        fnmin=Minimum (reserved) flow rate for session n.
    
    


Service is granted if the computed minimum flow rate of the prospective client is less than available bandwidth even when unused bandwidth is zero.
Toward a Tunable QOS
In the preceding discussion it is assumed that all clients share the same value of β. One might also consider a scheme whereby a client receives a β value according to the class/cost of service that client has signed up for: the greater the cost (and expected quality of service, or QOS) the greater the value of β.
Instead of maximizing charges by the methods described above, a variation on the algorithm to maximize flow is considered whereby the reserve flow computation for every session takes into account the individual β value of the associated client. In this fashion a single algorithm can serve either end. The optimizer first ensures that every session receives its required minimum bandwidth (which would now typically depend on β and elapsed session time) before allocating any excess bandwidth more or less evenly to all by interpolation. (According to FIG. 15.)
The scheme is simpler computationally than the iterative interpolation method shown in FIG. 16; it is also arguably more fair and stable with respect tot he allocation of available bandwidth.
Deadline-Driven Content Distribution
In delivering viewable or audible content to a player, the optimization algorithm imposes a minimum flow rate that ensures that all content is delivered by the implied deadline, which is the last moment of a play session. Notwithstanding, the optimizer attempts to deliver content earlier according to bandwidth availability within the server taken as a whole. A similar, though far simpler scenario arises relative to the distribution of content from an optimized server to a target device, whenever the delivery must be accomplished by a designated time, or equivalently, within a given elapsed time, and when overlapped non-blocking consumption of the content at a fixed rate is not required.
One example concerns the application where a session bundle comprises a session associated with the featured program together with sessions for every advertisement scheduled to interrupt the feature program at a designated time. Each session is endowed with a separate media buffer, which, in the case of ads, would typically be large enough to accommodate the ad in full, thereby permitting a seamless transition to the ad at the appointed time.
In adapting the optimizer to the needs of content distribution we must revisit the formulation of the flow constraints, as follows:
1. Media buffers are not of a concern, let alone buffer overflow, and it can be assumed that all content received is saved away in a file on disk, or in memory awaiting further use.
2. For these same reasons, the value of β may be zero, at which the minimum flow rate equals the just-in-time rate obtained by dividing the content as yet undelivered by the time till deadline:

fkJIT(tk)=LkTOGO/(Tk−tk)  (24)

    
    
        wherein: LkTOGO=Content to go for session k, i.e., as yet undelivered by the server at time t, (client.lookup (k).session.payloadToGo).
    
    


Given the arbitrary format of the file to be distributed, T no longer signifies the “duration of play” at the average play rate (averagePlayRate); rather, T represents the elapsed time to the deadline measured at the moment the delivery session was launched, and t represents the elapsed time since session launch.
Session Bundles
A session bundle is a set of sessions that flow along a shared channel, and are thus subject to an aggregate flow constraint equal to the capacity of the shared channel. One important application of session bundles is connected with ad insertion.
It is not enough to treat each of the constituent sessions as independent with respect to the flow optimizer, for this practice might well result in session flow targets that do not exceed channel capacity when considered singly, yet exceed this same shared capacity when summed together.
A Solution to This Problem Involves Two Distinct Steps:
1. The sessions bundle is treated as a virtual session by the server optimizer, subject to the minimum flow constraint obtained by summation of the individual session minima, and a maximum constraint that is the least of (a) the sum of the least of constraints (3) and (4) for each session, and (b) the shared channel capacity client.lookup(k).channel.maxFlowRate (fkcap). The flow optimizer then generates an aggregate flow target for all channels virtual sessions by interpolation, using:

Cost(t)=f1(t)+ . . . +fn(t)  (25)

The cost vector in this instance is the n-dimensional unit vector, where n is the number of active clients.

c=(1, 1, . . . , 1)  (26)

Now it is possible to have an achievable aggregate flow target for the session bundle k that we must apportion optimally among the constituent sessions. Fortunately for us, our interpolation procedure of FIG. 15 can be applied again to the sessions in our bundle, but where the aggregate flow target generated above replaces the aggregate flow constraint fSvrmax 
Specifically:
For every flow fki, within session bundle k, the optimal flow rate is obtained by interpolation between minimum and maximum session flows:

fkiopt=fkimin+α*(fkimax−fkimin)  (27)

α=[(fKbundle−fk1min+ . . . fknmin)]/[(fk1max−fk2min)++(Fknmax−fknmin)]  (28)

and the value of fkbundle is obtained from a higher level optimization in which session bundle k is treated as a virtual session for which:

fkmin=fk1min+ . . . +fknmin  (29)

fkmax=min(fk1max+ . . . +fknmax,fkcap)  (29)

It must be noted that session bundles are typically dynamic in nature, outliving many if not all of their constituent sessions. Before a session is added to the bundle two CAC decisions must be reached:

    
    
        (1) establish bandwidth availability within the bundle; and
        (2) bandwidth availability within the server.
    
    


Relationship to Adaptive Rate Control
The flow optimization methods should be viewed as constituting the lowest and perhaps only the first of many supervisory control layers to sit astride all streaming sessions, which comprise their own hierarchical stack of control functions; rate adaptive control sitting above a flow rate regulator which relies on a transport entity.
Channel capacity is known to vary widely over time. A capacity drop to below the minimum reserve flow rate is problematic as it causes the latter to rise in violation of its monotonicity assumption. In a server with available bandwidth to spare such a rise can be accommodated by the flow optimizer (by bumping the session's minimum flow reservation to the higher value) provided the flow deficit can be made up in the near term by draining pre-delivered content from the media buffer. Should either of these resources approach depletion, stream degradation to a lesser bit-rate or frame rate may be the only viable option short of a pause. Whether up or down, any rate change is a change to fe, which must be preceded by change to session's reserve flow rate allocation by the optimizer.
As can be seen, the optimizer and rate adapter must be integrated with care. One possible approach would be to modify a rate adapter such that it renegotiates its proposed fe value with the flow optimizer prior to effecting the rate change it deems appropriate based on information provided by the flow regulator. Rate increases might well be subject to deferral under heavy load conditions, awaiting bandwidth availability. The opposite is true of rate flow decreases: these would be forestalled as long as possible by the optimizer on a system that is not fully loaded, as previously discussed.
Live Events
Referring to FIG. 17, the method of the present application can be extended to the optimization of “live”, time-shifted “near-live” events, and cascaded delivery, wherein one server delivers content to another while the latter accepts clients for the same content. The extension assumes the following characteristics of the server and the live performance:
1. The performance is of a fixed duration T known in advance, encoded at an average rate fe, with a projected content payload of fe*T;
2. The origin server at the point of injection delays the stream by a small dwell time TDWELL on the order of seconds (e.g. 10). Notwithstanding, the delayed content is available for early delivery to mirrored servers and players with the aim of providing these with a modicum of isolation from network jitter affecting the timely delivery of the live video frames.
3. Throughout the live event, captured content is stored in a file, thereby permitting late joiners to view the “live event” starting from any point between the present and the event start time;
4. At the conclusion of the live event, the encoded content, now fully captured to a file, is available for viewing over the balance of the admission window (e.g., 60 minutes in FIG. 17).
The optimisation of live events and video on demand (VOD) differ principally in one respect, namely in the formulation of the server content underflow constraint.
For VOD, this constraint is

LkTOGO(t) is initialised to the content size (fe*T) at that start of play, and  (31)

decremented as content is delivered to the client. Δt is the time interval between successive periodic optimizations (e.g. 1 second). In practice this constraint rides well above other operative maximum flow constraints (e.g. buffer overflow, channel capacity) until the very last calculation of the session flow target by the optimiser.

For a live stream, this constraint must additionally reflect the fact that content is streaming into the server (where it builds up), even as the server streams it out toward clients, and that the latter activity cannot possibly overtake the former.
Referring to FIG. 17, (which illustrates how optimised live streams behave) line L1 depicts the build-up of freshly captured content to the server. Line L2, which is delayed (time-shifted) relative to L1 by the dwell time TDWELL, represents the live performance as cast and viewable by clients. One such client is admitted at time A and joins the live session at the live moment B. The dashed curved line linking points B and C shows a plausible build-up of content in the client's media buffer in advance of play, as the viewer continues its advance along line L2. Past point C the top of the media buffer tracks the live capture stream and thenceforth advances along line L1. In this instance, the time shift between the live performance as cast (L2) and the live performance as captured (L1) imposes a maximum on the amount of content that could ever accumulate in a client media buffer, irrespective of its actual capacity.
Another client, admitted at time t=10, is interested in viewing the live stream from the beginning without missing anything. As before, the dashed line joining 10 and D depicts a plausible build-up of content in the client's media buffer in advance of play, as the viewer continues its advance along line L3, which is time-shifted by (10+TDWELL) minutes relative to L1. The greater time shift (now between L1 and L3) permits more extensive pre-buffering of “near live” content.
The present constraints do not impose suitable flow limits at and beyond points C and D when the client delivery streams finally links up with the live capture stream, in the live moment. Consequently the optimiser may propose flow targets that cannot be realized.
Accordingly, the following modification for use in connection with live or cascaded streams is made:

fk(t)<=[(LkTOGO(t)−LiveTOGO(t)]/Δt  (32)

    
    
        for a live event delivered at flow rate fe, we have

LiveTOGO(t)=max(fe*(T−TDWELL−t),0)  (33)

    
    


LiveTOGO(t) is the span between projected content size fe*T (level line L0 in FIG. 17) and the content capture level line L1, whereas LkTOGO(t) is the gap between L0 (i.e., fe*T) and the dashed curved line representing the content level delivered to the media buffer. The latter must always exceed the former. As the two approach one another this constraint takes effect, causing LkTOGO(t) to always exceed LiveTOGO(t) as it decreases at rate fe.
Viewers joining late and willing to see the live performance with some delay relative to the live case enjoy higher potential levels of isolation from network disturbances, and thus QOS, by virtue of their greater effective buffer capacity. By the same token, such viewers afford the optimizer greater latitude to optimize the flow of VOD and “live” content across load fluctuations, thereby enhancing server capacity. Viewers that wish to experience the live event in “real-time” nevertheless benefit by a modestly enhanced QOS conferred by a dwell time's worth of content in their buffers.
SUMMARY
A method and system for call/connection acceptance and flow modulation for network delivery of video/audio programming is thus provided. Although several embodiments have been illustrated and described, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirit of the invention or the scope of the claims.

## Claims

1. A method of bandwidth allocation for delivery of stored digital content from at least one server device to at least one client device by way of a network, the method comprising the steps of:
a) prescribing a control variable which represents a target flow rate of content from the server device to each client device by: 
i) forming a hyperplane of control variables that aggregate to a maximum allowed aggregate flow rate; 
ii) computing a first vector of minimum allowed client flow rates; 
iii) computing a second vector of maximum allowed client flow rates; 
iv) determining a multi-dimensional shape of which an interior diagonal spans the first and second vectors; and 
v) finding a solution of control variables at a point of intersection between the diagonal and the hyperplane; 

b) determining time-varying constraints on the target flow rate of the content; 
c) determining a cost function of the control variables for all clients wherein the cost function represents an aggregate flow rate and is a sum of all flow rates for all clients; and 
d) prescribing bandwidth to all clients based upon a value of the control variables that maximize the cost function.

2. The method of claim 1 wherein step (d) comprises performing periodic computations to update the value of the control variable such that the bandwidth can be continuously allocated to each client.

3. The method of claim 2 wherein a new client is accepted by:
i) determining an admission capacity of the bandwidth; 
ii) admitting a prospective client if the clients minimum allowed value of the control variable is less than the admission capacity; and 
iii) wherein a client admitted for service is guaranteed to have sufficient content flow over the entire session.

4. The method of claim 3 wherein:
the admission capacity equals a server swing capacity reduced by a predetermined safety margin which may be zero, the swing capacity equaling a difference between a server flow capacity and a sum of a minimum allowed flow rate for all clients.

5. The method of claim 4 wherein the minimum allowed value of the control variable is initialized to an average consumption rate.

6. The method of claim 4 wherein the minimum allowed value of the control variable is initialized to the average consumption rate multiplied by a factor greater than one.

7. The method of claim 4 wherein the server flow capacity varies in a step-wise function over time according to a predetermined schedule and the method of accepting a new client further comprises:
i) determining a sequence of future step changes of server flow capacity; 
ii) determining at each time in the sequence of future step changes a value for a future worst swing case capacity, the worst case swing capacity being obtained from the server flow capacity at the time by subtracting an extrapolated present minimum allowed flow rate for all active clients that are potentially active in the future; 
iii) admitting a prospective client if a minimum allowed value of the control variable is less than a capacity obtained from the sequence and a present capacity; 
iv) whereby a new client can be admitted without compromising the service to existing clients in the presence of previously scheduled server flow capacity changes and all clients accumulate content in their buffers to the extent of their respective buffer capacity.

8. The method according to claim 7 wherein the method of accepting a new client further comprises:
i) partitioning available bandwidth into partitions representing a prescribed service charge; 
ii) determining a maximum-minimum capacity for a service charge to be the maximum allowed sum of all minimum allowed flow rates for all clients incurring an equal or lesser service charge, the maximum-minimum capacity equaling the sum of bandwidth allocations for all service charges less than or equal to the service charge; 
iii) determining a service-charge-specific swing capacity for a given service charge as the difference between the maximum-minimum capacity for a service charge and the sum of all minimum allowed flow rates for all clients incurring the service charge or a lesser service charge; 
iv) determining the server swing capacity to be the server flow capacity minus a margin and minus the sum of the minimum allowed flow rate for all clients; and 
v) determining a service-charge-specific capacity to be the least of the server swing capacity and the charge specific swing capacity.

9. The method of claim 8 wherein the method of accepting a new client further comprises:
i) determining the sequence of future times of step changes to server flow capacity over a proposed consumption period; 
ii) determining for each time in the sequence of future times, a future worst-case value for a service-charge-specific capacity, the worst case value being obtained by using the extrapolated present minimum allowed flow rate of all presently active clients that are potentially active at the time in the future; and 
iii) admitting a client incurring a given service charge if the minimum flow rate of the client is less than the capacity obtained from a sequence and a present service-charge-specific capacity.

10. The method of claim 3 wherein step (b) comprises determining time-varying constraints wherein:
i) an aggregate flow rate for all clients does not exceed a predetermined server flow capacity; 
ii) a flow rate from the server to the client does not exceed a maximum allowed flow rate for the client; 
iii) a flow rate to the client will never cause a buffer of the client to overflow; 
iv) a flow rate to the client stops when the content is exhausted; and 
v) a flow rate from the sever will never be less than the client's minimum allowed flow rate which may vary over time and may be zero.

11. The method of claim 10 wherein the maximum allowed flow rate to the client is given by the minimum of one selected from the following:
i) a client flow rate ceiling; 
ii) a flow rate required to fill the client buffer before the next periodic computation; and 
iii) a flow rate required to complete the delivery of the content before the next periodic computation.

12. The method of claim 11 wherein:
i) the minimum allowed client flow rate cannot increase over time, but may decrease such that an initial value of the control rate is no less than an average consumption rate; 
ii) the control variable for the client is always greater than or equal to the current minimum allowed client flow rate; and 
iii) the client buffer will never underflow until the content is fully consumed at the average consumption rate.

13. The method of claim 12 wherein the minimum client flow rate is a product of a constant content flow rate from the client to the server that causes a last piece of content to be delivered at the last possible moment as the client buffer is being drained at the average consumption rate, with a factor greater or equal to one.

14. The method of claim 13 wherein the minimum client flow rate is initialized to the average consumption rate.

15. The method of claim 13 wherein the minimum client flow rate is initialized to the average consumption rate multiplied by a factor greater than one.

16. The method of claim 13 further comprising the step of calculating the minimum client flow rate periodically.

17. The method of claim 1 wherein the cost function represents a service charge and is the sum of the client flow rates multiplied by the client's cost of service.

18. The method of claim 17 wherein:
step (a) comprises: 
i) determining a maximum allowed flow rate and a minimum allowed flow rate for each client; 
ii) determining a flow rate range for each client as the difference between the maximum allowed flow rate and the minimum allowed flow rate; and 
iii) initializing a current flow rate for each client as the minimum allowed flow rate and summing the flow rate into the total server flow rate; and 
step (d) comprises: 
i) computing remaining server bandwidth as the difference between the maximum server flow capacity and the total server flow rate; and 
ii) allocating remaining server bandwidth to remaining clients wherein all clients with a given cost of service receive bandwidth equally to the extent of their respective ranges, and no client with a given cost of service being allocated bandwidth unless all clients with a higher cost of service have received their maximum possible allocation of bandwidth.

19. The method of claim 1 wherein step (v) comprises finding a solution of control variables at the second vector if there is no point of intersection between the diagonal and the hyperplane.

20. The method of claim 1 wherein step (a) comprises:
i) computing the sum of the minimum allowed flow rates to all active clients; 
ii) computing the sum of the flow rate ranges for all active clients; 
iii) computing the difference between the maximum allowed aggregate flow rate and the sum of the minimum; 
iv) computing a factor as the ratio of the difference over the sum of the ranges; 
v) if the factor exceeds 1, the control variable is set to the maximum allowed client flow rate; and 
vi) if the factor is less than 1, computing the control variable by multiplying the client range by the factor and then adding the result to the minimum allowed client flow rate.

21. The method of claim 1 wherein:
step (a) comprises: 
i) determining the maximum allowed flow rate and minimum allowed flow rate for each client; 
ii) determining the flow rate range for each client as the difference between the maximum flow rate and the minimum flow rate; and 
iii) initializing the control variable for each client as said minimum allowed flow rate and summing the flow rate into a total server flow rate; and 
step (d) comprises: 
i) computing remaining server bandwidth as the difference between the maximum server flow capacity and the total server flow rate; and 
ii) allocating remaining server bandwidth to remaining clients to the extent of their respective ranges.

22. The method of claim 21 wherein the step of allocating remaining server bandwidth further comprises the clients receiving the bandwidth equally to the extent of their respective ranges.

23. The method of claim 1 wherein the maximized value of the control variable can be determined by:
i) determining a maximum and minimum flow rate for each client; 
ii) determining a range between the maximum and minimum flow rates in order to find a flow rate range; 
iii) determining available bandwidth by finding the difference between an aggregate flow capacity and a sum of the minimum flow rate; 
iv) determining a flow variable by dividing the unused bandwidth by the flow rate range; 
v) prescribing the control variable to be the minimum flow rate added to the flow rate range if a flow variable is less than one or prescribing the control variable to be the minimum flow rate added to the flow rate range corrected by a flow variable if the flow variable is greater than one such that the control variable is easily calculated for each client.

24. The method of claim 1 wherein at least one session is a session bundle and:
1) the minimum flow constraint is computed as the sum of the minimum flow rate constraints for all bundled sessions; 
2) the maximum flow constraint is the least of 1) the sum of the maximum individual flow rate constraints of each session and 2) the flow capacity of the channel shared among the bundled sessions; and 
3) the target flow rate is computed for the session is apportioned among bundled constituent sessions.

25. The method of claim 24 wherein the bundled session is an advertisement.

26. A system for allocating bandwidth between a server device and at least one client device, the system comprising:
a call acceptance module operative to receive an incoming request for service; 
a flow regulator configured to deliver content at a modulated target flow rate, the content being delivered between the server device and a respective client device when a call is accepted by the call acceptance module; and 
a flow optimizer configured to modulate the target flow rate of the flow regulator in order to optimize an aggregate flow of content by performing the following procedure: 
a) prescribing a control variable which represents a target flow rate of content from the server device to each client device by 
i) forming a hyperplane of control variables that aggregate to a maximum allowed aggregate flow rate; 
ii) computing a first vector of minimum allowed client flow rates; 
iii) computing a second vector of maximum allowed client flow rates; 
iv) determining a multi-dimensional shape of which an interior diagonal spans the first and second vectors; and 
v) finding a solution of control variables at a point of intersection between the diagonal and the hyperplane; 

b) determining time-varying constraints on the target flow rate of the content; 
c) determining a cost function of the control variables for all clients wherein the cost function represents an aggregate flow rate and is a sum of all flow rates for all clients; and 
d) prescribing bandwidth to all clients based upon a value of the control variables that maximize the cost function.

27. The system of claim 26 wherein the flow optimizer is configured to modulate the flow rate of the flow regulator in order to optimize charges for the content.

28. The system of claim 26 wherein the flow optimizer is configured to determine a control variable which corresponds to an optimized flow rate.

29. The system of claim 28 wherein the flow optimizer is configured to generate a cost function of the control variable that corresponds to a maximized value of the control variable.

30. The system of claim 26 wherein the flow regulator is configured to deliver the modulated flow rate of content in response to the control variable.

31. The system of claim 30 wherein the call acceptance module is configured to accept a call based upon a value of the control variable.

32. The system of claim 26 wherein the flow optimizer is configured to determine a maximized value of the control variable by:
i) determining a maximum and minimum flow rate for each client; 
ii) determining a range between the maximum and minimum flow rates in order to find a flow rate range; 
iii) determining unused bandwidth by finding the difference between an aggregate flow capacity and a sum of the minimum flow rate; 
iv) determining a flow variable by dividing the unused bandwidth by the flow rate range; 
v) prescribing the control variable to be the minimum flow rate added to the flow rate range if the flow variable is less than one or prescribing the control variable to be the minimum flow rate added to the flow rate range corrected by the flow variable if the flow favorable is greater than one such that the control variable is easily calculated for each client.

33. A method of bandwidth allocation for delivery of stored digital content from at least one server device to at least one client device by way of a network, the method comprising the steps of:
a) prescribing a control variable which represents a target flow rate from the server to each client device based upon the amount of buffer of the client by: 
i) forming a hyperplane of control variables that aggregate to a maximum allowed aggregate flow rate; 
ii) computing a first vector of minimum allowed client flow rates; 
iii) computing a second vector of maximum allowed client flow rates; 
iv) determining a multi-dimensional shape of which an interior diagonal spans the first and second vectors; and 
v) finding a solution of control variables at a point of intersection between the diagonal and the hyperplane; 

b) determining time-varying constraints on the flow rate of the content; 
c) determining a cost function of the control variables for all clients in response to a size of the client's buffer wherein the cost function represents an aggregate flow rate and is a sum of all flow rates for all clients; and 
d) prescribing bandwidth to all clients based upon a value of the control variables that maximize the cost function.