# A Scheduling Method of Cross-Layers Optimization of Polling Weight for AOS Multiplexing

Authors: Yuntao Zhao; Bo Bo; Yongxin Feng
Journal: International Journal of Digital Multimedia Broadcasting
 (2019)

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## Abstract

The core mechanism of Advanced Orbit System (AOS) mainly contains the packet channel multiplexing and the virtual channel multiplexing. The multiplexing efficiency and frame time directly affect the performance of the AOS and even the whole system. In this paper, in order to optimize AOS multiplexing performance, a scheduling method of cross-layers optimization of polling weight (CLOPW) is proposed. Different from single sublayer optimization such as the isochronous frame methods, the novel method focuses on factors related to AOS performance of two core sublayers, such as packet distribution, residual function, cache capacity, frame time, and multiplexing efficiency. We build a multiple factors framing model of finite buffer and deduce the formula of packet multiplexing efficiency based on the short correlation. Furthermore, we give the formula for the virtual channel utilization and delay of cross-layer optimization. The experimental results show that the novel scheduling method of cross-layers optimization of polling weight is higher utilization of virtual channel and lower average delay than the isochronous frame method.


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## Body

## 1. Introduction

With the development of space technology, in order to meet the demand of differentiated communications for future multimedia space missions, better realize the sharing of ground and space communication resources, and improve the efficiency of real time, diverse, and dynamic task, it is necessary to extend the concept of ground Internet to space and build a flexible and efficient Space Internetwork. Consultive Committee for Space Data System (CCSDS) [1–3] is an international standard organization composed of multinational space organization, which establishes standardized communication architectures, communication protocol, and service for the next-generation space network. Advanced Orbit System (AOS) [4, 5] proposed by CCSDS is developed on the basis of Common Orbit System (COS) [6]. AOS is a data transmission and communication mechanism, which also is a data processing and management system of space-to-space, space-to-surface. Meanwhile, AOS can process larger capacity and higher rate data than those of COS and build a global, extensive network.The multiplexing mechanism [4], namely, packet channel multiplexing (PCM) in Virtual Channel Link Control (VCLC) sublayer and Virtual Channel Multiplexing (VCM) in Virtual Channel Access (VCA) sublayer, is the core and basis of AOS. According to AOS protocol, the data with different rate and from heterogeneous information sources is normalized into CCSDS standardized packet. These packets are encapsulated into Multiplexing Data Units (M_PDU), which finally form Virtual Channel Data Unit (VCDU) [7]. M_PDU frame time (abbr. frame time) and efficiency directly affect the throughput performance of virtual channel in the next sublayer.In order to analyze, design, and manufacture multiplexers for AOS, researches have done a lot of work on the scheduling method of frame generation and optimization such as the method of isochronous frame and high efficiency frame. The isochronous frame scheduling method [8] is to encapsulate the data packets from higher levels into a frame at a fixed interval time, whose disadvantage is mainly that the method will lead to a decline in multiplexing efficiency [9–11]. High efficiency frame optimization means that the data packets are not released until the arrival data packets fill up a whole M_PDU, whose multiplexing efficiency is almost 100%. But the method will increase the frame time and the packet delay [12, 13]. Y. Tian et al. [14] put forward an adaptive frame optimization model. In the model a threshold value is set. With the value, as soon as the arrival packets fill up a frame, a frame is generated. In another paper [15], the authors indicate that the adaptive model overcome long delay problems, which sometime cause the lower multiplexing efficiency than the isochronous frame optimization. In the paper [16], the authors proposed a virtual channels scheduling method with broad applicability based on movable boundary. In order to optimize the performance of AOS multiplexing, the authors establish a movable boundary between synchronous time slots and asynchronous ones in terms of types of date sources. Bie et al. [17] design a mixed multiplexing optimization mode by the analysis of data types. In the mode, it is changeable for the boundaries of VIP, synchronous, and asynchronous virtual channels.In this paper, a scheduling method of cross-layer optimization of polling weight (CLOPW) is proposed. Different from single sublayer optimization such as the isochronous frame method and other methods [8–17], the novel scheduling method focuses on factors related to AOS performance of two core sublayers, such as packet distribution, residual function, buffer capacity, frame time, M_PDU efficiency, and virtual channel utilization, and builds recursion formula and numerical analysis model. Furthermore, in terms of input and output matching criterion of AOS, we give a computational method of optimized utilization and frame time based on the previous formula and model. The experimental results show that the proposed method on AOS performance, e.g., the virtual channel utilization and delay, is superior to the existing isochronous frame method. The major contributions of our work can be summarized as follows.(a) A Novel Cross-Layer Optimization Scheme for Virtual Channel Scheduling of AOS. Different from the traditional scheme for local optimization in individual layer, the novel cross-layer optimization scheme focuses on factors related to AOS performance from VCLC layer to VCA layer. With integrating and analyzing the influence of upper factors, the cross-layer mapping relationship is established. Accordingly, AOS utilization and delay can achieve global optimization with the cross-layer optimization. It has important practical significance for analyzing, improving, designing, and manufacturing AOS systems in future work.(b) A Computational Method of M_PDU Efficiency in Finite Buffer. According to CCSDS recommended standard, the performance is separately analyzed on respective sublayers. But the output of VCLC sublayer is taken as the input of VCA, whose multiplexing efficiency and frame time directly affect the performance of the VCA, and even the whole system. However, on the one hand, currently it is insufficient on researches of quantitative mathematical analysis and mapping expression between multiplexing efficiency and framing time. On the other hand, the existing studies are based on the ideal condition of infinite buffer. In this paper, we deduce the formula of packet multiplexing efficiency and frame time in finite buffer, which gives a computational method of M_PDU efficiency and provides the theoretic basis for cross-layer optimization and then improves future CCSDS recommendation.(c)  A Simulation Model Based on the Short Correlation Distribution and Matching Criterion of Virtual Channel Input and Output. In order to verify the validity of the packet channel multiplexing model and the scheduling method of CLOPW, we simulated the process of M_PDU multiplexing in VCLC and virtual channel scheduling in VCA. Furthermore, based on short correlation model, we compare the theoretical curves with the simulation results and then analyze the effectiveness.The rest of this paper is organized as follows. Section2 presents the overview of our AOS multiplexing mechanism including packet channel multiplexing and virtual channel multiplexing. Section 3 introduces our proposed method in detail. Based on AOS traffic model and assumption, the scheduling methods and formulas for CLOPW are proposed and derived, which improve M_PDU efficiency in limited cache, virtual channel utilization, delay, etc. In Section 4, there is the experimental result and analysis. Finally, Section 5 is conclusion.


## 2. The Mechanism of AOS Multiplexing

The AOS data link layer contains VCLC sublayer and VCA sublayer, which also provide two stages of multiplexing, i.e., packet channel multiplexing and virtual channel multiplexing [5, 18]. The AOS multiplexing process is shown in Figure 1.Figure 1
The AOS multiplexing process.The VCLC sublayer mainly provides two types of services to users, packet service, and M_PDU service. Data from upper layer comes into packet service unit and then is encapsulated into standard CCSDS packet. The M_PDU packet zone contains either payload packets or idle data. When insufficient packets are available at release time of an AOS transfer frame carrying M_PDUs, a M_PDU that contains idle data in its packet zone shall be generated. Meanwhile, the high rate data forms bit stream, which is encapsulated into Bitstream Protocol Data Unit (B_PDU). The B_PDU service provides transfer of a serial string of bits, whose internal structure and boundaries are unknown to the service provider. In virtual channel multiplexing unit, a physical channel is divided into separately logical channels, named Virtual Channel (VC). AOS can define 64 virtual channels at most. Each virtual channel is given a unique Virtual Channel Identifier (VCID). The mechanism of Virtual Channel allows a physical channel to be shared by multiple high-layer communication streams, each of which can have different service requirements.The transformation of data structure of multiplexing is shown in Figure2. Firstly, packet service provides the transformation from non-CCSDS packets to standard CCSDS packets, which is the foundation of transparent transmission between different applications or users on space network. Through packet transformation, some existing protocols and applications need not be redesigned or modified and can directly carry and transmit data. Secondly, the transformed packets are inserted contiguously and in forward order into M_PDU packet zone. When insufficient packets are available at release time, idle packets are inserted into M_PDU packet zone. Thirdly, a M_PDU is inserted into VCDU data field. Since the length of the M_PDU is fixed by management for any particular Virtual Channel, VCDU data field fits exactly within the fixed-length M_PDU. Finally, the VCDU comes into the channel access slot and is transmitted in the physical channel.Figure 2
Transformation of data structure of multiplexing.For processing larger capacity and higher rate data in future multimedia space missions based on AOS, a lot of research results of the multiplexing and scheduling algorithms have been achieved [8, 9, 11, 12, 16, 17, 19–21]. Some of them are designed for specific missions and spacecrafts, and they cannot achieve broad applicability or excellent scheduling performance. Liu et al. [19] proposed a kind of scheduling algorithm based on the urgency function of VCs, which can achieve better performance than the classical scheduling algorithms. But the algorithm ignores the relevance and influence from upper layer. They only consider the urgency of each data frame in local layer. Therefore, the performance of these algorithms is limited in reality. Bie et al. [17] propose an improved algorithm, which considers the influence of the number of remaining frames in each VC when designing the scheduling decision function. However, this algorithm still does not distinguish the frame urgency from the different layers. In the article [20], a novel scheduling algorithm was designed. The scheduling method, estimating the VC urgency and the frame urgency separately, improves the scheduling performance. Further results are developed in [16] by introducing the movable boundary technology into the algorithm of [22], which can decrease the scheduling time delay and increase the channel utilization rate further. These methods of the above articles only focus on the influence factors of each individual sublayer to obtain local optimization. In this paper, we build a multiple factors framing model of finite buffer and propose a scheduling method of cross-layer optimization. We detailedly introduce our proposed method in the following section.


## 3. A Scheduling Method of Cross-Layer Optimization

For describing the mathematical model more systematic and easy to understand, I listed a table of symbols in Table1.Table 1
the table of symbols.
symbols The meanings of a symbol symbols The meanings of a symbol λ p Arrival rate of Poisson L m p d u M_PDU length l p CCSDS packet length N Number of packets in a M_PDU B Cache capacity η m p d u ( i ) i order M_PDU efficiency p ( n ) Arrival probability of Poisson ξ ( i ) Overflow probability inith gap r Number of residual packets Φ p ( j ) ( r ) thejth order residual packets function i virtual channel number (from 1 toi) α i Weight of the polling time T w Average frame time v i n ( i ) Input rate of VCDU frame in ith C Total output channel capacity v o u t ( i ) Output rate of VCDU frame in ith R Throughput of virtual channel γ Virtual channel utilization D Delay of virtual channel D ¯ Average delay of virtual channel


### 3.1. A Computational Method of Packets Channel Multiplexing

A computational method of packet channel multiplexing is built on the following assumptions.(a) The packets arrival model from different data sources obeys the Poisson probability distribution. The arrival rate is equal toλp.(b) Supposing that M_PDU length was equal toLmpdu, packet length is lp. Lmpdu=N·lp, andN is an integer.(c) The system is carried out in a batch process; i.e., togetherN packets are inserted into one M_PDU packet zone in a frame time Tw. When the amount of arrival packet is less thanN, the idle packets are inserted into M_PDU packet zone.(d) Let the cache capacity beB and B>N.The presence of idle packets causes a decrease in M_PDU efficiency. If extending the frame timeTw to be used to wait for coming packets into buffer, the efficiency would increase, but the delay worsens.Set M_PDU efficiency asη. In the first waiting gap (frame time Tw), the efficiency is expressed as follows, named 1 order M_PDU efficiency, (1)ηmpdu1=1Lmpdu∑n=0Nn·lp·pn+N·lp∑n=N+1Bpnwhere Lmpdu is the length of M_PDU and lp is the length of CCSDS packet. Tw is the time gap. p(n) is packet arrival probability with Poisson distribution. (2)pn=λpTwne-λpTwn!The overflow probability in the first gap is as the following formula.(3)ξ1=pn>B=1-∑n=0BpnFurthermore, the M_PDU efficiency in the second time gapTw was considered. In the second gap, the residual packets from the first gap must be calculated. Let the residual packets probability be Φp′(r), named the first order residual packets function (abbr. 1-RPF), where r is the amount of residual packets. (4)Φ′r=∑q=0NλpTwqe-λpTwq!r=0λpTwN+re-λpTwN+r!r=1,2,3…,B-NWhen arrival packets in the first time gap were less thanN, there are no residual packets in the second gap Tw, and r is equal to 0. Otherwise, when n>N in the first gap,r is the amount of residual packets and n=N+r. So the actual arrival probability is p(N+r) in first gap Tw. The efficiency was expressed as follows: (5)p′′k=∑i=0kΦp′i·pm=k-ik=1,2,⋯,Bwherek is the amount of packets in second gap, which include two parts. One part is the arrival packets with Poisson distribution. The other is the residual packets from the first gap Tw. Therefore, the 2-order M_PDU efficiency is expressed as follows. (6)ηmpdu2=1Lmpdu∑n=0Nn·lp·p′′n+N·lp∑n=N+1Bp′′nThe second-order residual packets function (abbr. 2-RPF) is as follows.(7)Φp′′r=∑q=0N∑i=0qΦp′i·pm=q-ir=0∑i=0N+rΦp′i·pm=N+r-ir=1,2,3…,B-NThe overflow probability in the second gap is as the following formula.(8)ξ2=pn>B=1-∑n=0Bp′′nFrom above the formulas, the recursion formula ofj order M_PDU efficiency can be given, (9)ηmpduj=1lmpdu∑n=0Nn·lp·pjn+N·lp∑n=N+1Bpjnwherep(j)(n),  Φp(j)(r), and ξ(j)are as follows. (10)pjn=∑i=0nΦpj-1i·pm=n-i(11)Φpjr=∑q=0N∑i=0qΦpj-1i·pm=q-ir=0∑i=0N+rΦpj-1i·pm=N+r-ir=1,2…B-N(12)ξj=pn>B=1-∑n=0Bpjn


### 3.2. A Scheduling Method of Cross-Layers Optimization of Polling Weight

The virtual channel number is, respectively, from 1 toi. The normalization of scheduling period is 1. αi is weight of the polling time on VCA sublayer. The time slice allocated for each virtual channel is from α1 to αi. αi satisfies the following formula. (13)α1+α2+⋯+αi=1We normalized the polling cycle of the whole virtual channel to 1.Twi represents the average frame time of generating a M_PDU (a M_PDU is encapsulated into a VCDU) on the ith virtual channel, i.e., average normalized time per a VCDU. The input rate of VCDU frame on the ith virtual channel is expressed as vin(i).(14)vini=1TWiIf the total output channel capacity is represented as C, which stands for the maximum VCDU transmission rate in downlink channel, the time slice allocated forith virtual channel is αi. The output rate of ith virtual channel is vout(i). (15)vouti=αiCThere are three situations of output and input rate ofith virtual channel.(a)
When the conditionvin(i)<vout(i) is met, i.e., the input rate of ith virtual channel is lower than the output rate, we need to insert idle packets, which will lead to the decline of virtual channel utilization.(b)
When the conditionvin(i)>vout(i) is met, i.e., the input rate of ith virtual channel is higher than the output rate, it can lead to a gradual increase in the cache and easily overflow.(c)
When the conditionvin(i)=vout(i) is met, i.e., the input rate of ith virtual channel is equal to the output rate, the best match between input and output is achieved. (16)vini=voutiFrom the formula (14), (15), (16), we can get the following: (17)1TWi=αiCThat is(18)αi=1TWiCIn a whole polling cycle, the throughput of virtual channel is represented as R,(19)RTw=η1,η2,⋯,ηi·α1Cα2C⋮αiCwhereη1,η2,⋯,ηi represent the M_PDU multiplexing efficiency, which can be obtained from formula (1).Virtual channel utilization is defined as radio of valid data to total output. The utilization is represented asγ.(20)γ=RCFrom formula (19) to (20), we can get the following.(21)γ=η1,η2,⋯,ηi·α1α2⋮αiThat is (22)γ=η1α1+η2α2,⋯,+ηiαiFrom the formula (1) and (22), the first order utilization of virtual channel with the first order efficiency of M_PDU is represented as γ(1).(23)γ1=∑n=0NnN·λTW1ne-λTW1n!+∑n=N+1BλTW1ne-λTW1n!α1+∑n=0NnN·λTW2ne-λTW2n!+∑n=N+1BλTW2ne-λTW2n!α2⋯+∑n=0NnN·λTWine-λTWin!+∑n=N+1BλTWine-λTWin!αiIn theith virtual channel, the multiplexing efficiency of M_PDU in second time gap can be represented as ηi(2).(24)ηi2=∑n=0NnN·p′′n∣Tf=TWi+∑n=N+1Bp′′n∣Tf=TWiSo the 2-order utilization of virtual channel isγ(2).(25)γ2=∑n=0NnN·p′′n∣Tf=TW1+∑n=N+1Bp′′n∣Tf=TW1α1+∑n=0NnN·p′′n∣Tf=TW2+∑n=N+1Bp′′n∣Tf=TW2α2⋯+∑n=0NnN·p′′n∣Tf=TWi+∑n=N+1Bp′′n∣Tf=TWiαiFurthermore, thejth order utilization of virtual channel is γ(j).(26)γj=∑n=0NnN·pjn∣Tf=TW1+∑n=N+1Bpjn∣Tf=TW1α1+∑n=0NnN·pjn∣Tf=TW2+∑n=N+1Bpjn∣Tf=TW2α2⋯+∑n=0NnN·pjn∣Tf=TWi+∑n=N+1Bpjn∣Tf=TWiαiIn summary, the utilization is related to not only the multiplexing efficiency of M_PDU, but also the frame timeTWi of VCLC sublayer and the distribution weight αi of time slice of virtual channel on VCA sublayers. Suppose that the input rate of virtual channel is matched with the output. Thej order utilization γ(j)can be expressed as follows. (27)γj=∑n=0NnN·pjn∣Tf=TW1+∑n=N+1Bpjn∣Tf=TW11TW1C+∑n=0NnN·pjn∣Tf=TW2+∑n=N+1Bpjn∣Tf=TW21TW2C⋯+∑n=0NnN·pjn∣Tf=TWi+∑n=N+1Bpjn∣Tf=TWi1TWiCWhenvin(i)=vout(i), αi is the function of variable TWi. By changing the polling weight of time slice on VCA sublayer and making it match with M_PDU frame time, the optimization of cross-layer on virtual channel utilization can be realized. The scheduling method is called cross-layer optimization of polling weight (abbr. CLOPW).In terms of formula (19), we define delay of virtual channel asD, which is a function of framing time.(28)D=1RTwFurthermore, the average delay of virtual channel is expressed as(29)D¯LVCDU=M=1N∑k=1NDt=TWkwhereD(t=Tv(k)) represents the delay time under the condition thatt is equal to different frame time Tw(k), and k is from 1 to N. D¯|LVCDU=M represents the average delay time under the condition that the length of VCDU is equal to M.


## 3.1. A Computational Method of Packets Channel Multiplexing

A computational method of packet channel multiplexing is built on the following assumptions.(a) The packets arrival model from different data sources obeys the Poisson probability distribution. The arrival rate is equal toλp.(b) Supposing that M_PDU length was equal toLmpdu, packet length is lp. Lmpdu=N·lp, andN is an integer.(c) The system is carried out in a batch process; i.e., togetherN packets are inserted into one M_PDU packet zone in a frame time Tw. When the amount of arrival packet is less thanN, the idle packets are inserted into M_PDU packet zone.(d) Let the cache capacity beB and B>N.The presence of idle packets causes a decrease in M_PDU efficiency. If extending the frame timeTw to be used to wait for coming packets into buffer, the efficiency would increase, but the delay worsens.Set M_PDU efficiency asη. In the first waiting gap (frame time Tw), the efficiency is expressed as follows, named 1 order M_PDU efficiency, (1)ηmpdu1=1Lmpdu∑n=0Nn·lp·pn+N·lp∑n=N+1Bpnwhere Lmpdu is the length of M_PDU and lp is the length of CCSDS packet. Tw is the time gap. p(n) is packet arrival probability with Poisson distribution. (2)pn=λpTwne-λpTwn!The overflow probability in the first gap is as the following formula.(3)ξ1=pn>B=1-∑n=0BpnFurthermore, the M_PDU efficiency in the second time gapTw was considered. In the second gap, the residual packets from the first gap must be calculated. Let the residual packets probability be Φp′(r), named the first order residual packets function (abbr. 1-RPF), where r is the amount of residual packets. (4)Φ′r=∑q=0NλpTwqe-λpTwq!r=0λpTwN+re-λpTwN+r!r=1,2,3…,B-NWhen arrival packets in the first time gap were less thanN, there are no residual packets in the second gap Tw, and r is equal to 0. Otherwise, when n>N in the first gap,r is the amount of residual packets and n=N+r. So the actual arrival probability is p(N+r) in first gap Tw. The efficiency was expressed as follows: (5)p′′k=∑i=0kΦp′i·pm=k-ik=1,2,⋯,Bwherek is the amount of packets in second gap, which include two parts. One part is the arrival packets with Poisson distribution. The other is the residual packets from the first gap Tw. Therefore, the 2-order M_PDU efficiency is expressed as follows. (6)ηmpdu2=1Lmpdu∑n=0Nn·lp·p′′n+N·lp∑n=N+1Bp′′nThe second-order residual packets function (abbr. 2-RPF) is as follows.(7)Φp′′r=∑q=0N∑i=0qΦp′i·pm=q-ir=0∑i=0N+rΦp′i·pm=N+r-ir=1,2,3…,B-NThe overflow probability in the second gap is as the following formula.(8)ξ2=pn>B=1-∑n=0Bp′′nFrom above the formulas, the recursion formula ofj order M_PDU efficiency can be given, (9)ηmpduj=1lmpdu∑n=0Nn·lp·pjn+N·lp∑n=N+1Bpjnwherep(j)(n),  Φp(j)(r), and ξ(j)are as follows. (10)pjn=∑i=0nΦpj-1i·pm=n-i(11)Φpjr=∑q=0N∑i=0qΦpj-1i·pm=q-ir=0∑i=0N+rΦpj-1i·pm=N+r-ir=1,2…B-N(12)ξj=pn>B=1-∑n=0Bpjn


## 3.2. A Scheduling Method of Cross-Layers Optimization of Polling Weight

The virtual channel number is, respectively, from 1 toi. The normalization of scheduling period is 1. αi is weight of the polling time on VCA sublayer. The time slice allocated for each virtual channel is from α1 to αi. αi satisfies the following formula. (13)α1+α2+⋯+αi=1We normalized the polling cycle of the whole virtual channel to 1.Twi represents the average frame time of generating a M_PDU (a M_PDU is encapsulated into a VCDU) on the ith virtual channel, i.e., average normalized time per a VCDU. The input rate of VCDU frame on the ith virtual channel is expressed as vin(i).(14)vini=1TWiIf the total output channel capacity is represented as C, which stands for the maximum VCDU transmission rate in downlink channel, the time slice allocated forith virtual channel is αi. The output rate of ith virtual channel is vout(i). (15)vouti=αiCThere are three situations of output and input rate ofith virtual channel.(a)
When the conditionvin(i)<vout(i) is met, i.e., the input rate of ith virtual channel is lower than the output rate, we need to insert idle packets, which will lead to the decline of virtual channel utilization.(b)
When the conditionvin(i)>vout(i) is met, i.e., the input rate of ith virtual channel is higher than the output rate, it can lead to a gradual increase in the cache and easily overflow.(c)
When the conditionvin(i)=vout(i) is met, i.e., the input rate of ith virtual channel is equal to the output rate, the best match between input and output is achieved. (16)vini=voutiFrom the formula (14), (15), (16), we can get the following: (17)1TWi=αiCThat is(18)αi=1TWiCIn a whole polling cycle, the throughput of virtual channel is represented as R,(19)RTw=η1,η2,⋯,ηi·α1Cα2C⋮αiCwhereη1,η2,⋯,ηi represent the M_PDU multiplexing efficiency, which can be obtained from formula (1).Virtual channel utilization is defined as radio of valid data to total output. The utilization is represented asγ.(20)γ=RCFrom formula (19) to (20), we can get the following.(21)γ=η1,η2,⋯,ηi·α1α2⋮αiThat is (22)γ=η1α1+η2α2,⋯,+ηiαiFrom the formula (1) and (22), the first order utilization of virtual channel with the first order efficiency of M_PDU is represented as γ(1).(23)γ1=∑n=0NnN·λTW1ne-λTW1n!+∑n=N+1BλTW1ne-λTW1n!α1+∑n=0NnN·λTW2ne-λTW2n!+∑n=N+1BλTW2ne-λTW2n!α2⋯+∑n=0NnN·λTWine-λTWin!+∑n=N+1BλTWine-λTWin!αiIn theith virtual channel, the multiplexing efficiency of M_PDU in second time gap can be represented as ηi(2).(24)ηi2=∑n=0NnN·p′′n∣Tf=TWi+∑n=N+1Bp′′n∣Tf=TWiSo the 2-order utilization of virtual channel isγ(2).(25)γ2=∑n=0NnN·p′′n∣Tf=TW1+∑n=N+1Bp′′n∣Tf=TW1α1+∑n=0NnN·p′′n∣Tf=TW2+∑n=N+1Bp′′n∣Tf=TW2α2⋯+∑n=0NnN·p′′n∣Tf=TWi+∑n=N+1Bp′′n∣Tf=TWiαiFurthermore, thejth order utilization of virtual channel is γ(j).(26)γj=∑n=0NnN·pjn∣Tf=TW1+∑n=N+1Bpjn∣Tf=TW1α1+∑n=0NnN·pjn∣Tf=TW2+∑n=N+1Bpjn∣Tf=TW2α2⋯+∑n=0NnN·pjn∣Tf=TWi+∑n=N+1Bpjn∣Tf=TWiαiIn summary, the utilization is related to not only the multiplexing efficiency of M_PDU, but also the frame timeTWi of VCLC sublayer and the distribution weight αi of time slice of virtual channel on VCA sublayers. Suppose that the input rate of virtual channel is matched with the output. Thej order utilization γ(j)can be expressed as follows. (27)γj=∑n=0NnN·pjn∣Tf=TW1+∑n=N+1Bpjn∣Tf=TW11TW1C+∑n=0NnN·pjn∣Tf=TW2+∑n=N+1Bpjn∣Tf=TW21TW2C⋯+∑n=0NnN·pjn∣Tf=TWi+∑n=N+1Bpjn∣Tf=TWi1TWiCWhenvin(i)=vout(i), αi is the function of variable TWi. By changing the polling weight of time slice on VCA sublayer and making it match with M_PDU frame time, the optimization of cross-layer on virtual channel utilization can be realized. The scheduling method is called cross-layer optimization of polling weight (abbr. CLOPW).In terms of formula (19), we define delay of virtual channel asD, which is a function of framing time.(28)D=1RTwFurthermore, the average delay of virtual channel is expressed as(29)D¯LVCDU=M=1N∑k=1NDt=TWkwhereD(t=Tv(k)) represents the delay time under the condition thatt is equal to different frame time Tw(k), and k is from 1 to N. D¯|LVCDU=M represents the average delay time under the condition that the length of VCDU is equal to M.


## 4. Experimental Result and Analysis

In order to verify the validity of the packet channel multiplexing model and the scheduling method of CLOPW in Section3, we simulated the process of M_PDU multiplexing in VCLC and virtual channel scheduling in VCA. We build a 16-channel simulation model, whose data is partly derived from [21] and extended on this basis. Simulation parameters of AOS Virtual Channel are shown in Table 2. Furthermore, based on short correlation model with Poisson distribution, we compare the theoretical curves with the simulation results and then analyze the effectiveness.Table 2
Simulation Parameters Table of AOS Virtual Channel.
VC No. Data type Service type Arrival rate  (frame/s) urgency Transmission type VC1 surveillance Video Bitstream 5.15×102 0 SYN VC2~3 Voice and Video Bitstream 6.76×102 0 SYN VC3~6 System data Path 5.97×102 1 ASYNC VC7~8 Telemetry of vital signal Path 3.78×102 2 ASYNC VC9 Delay telemetry Path 4.26×102 3 ASYNC VC10~12 Internet data Internet 2.57×102 4 ASYNC VC13~14 Payload data Path 8.27×102 3 ASYNC VC15~16 CCD images Bitstream 1.23×103 2 ASYNC


### 4.1. The Experimental of the Packet Channel Multiplexing

Based on the scheduling method of M_PDU efficiency (in Section3.1) and the assumption (in Section 3.2), we simulated the process of M_PDU multiplexing in VCLC sublayer. Meanwhile, the simulation result is compared with the recursion formula. And the length of packets lp is set to 1, λp=1,  N=10,  B=40.The relationship between the M_PDU efficiency and time is shown in Figure3. We adopt Poisson distribution model to simulate the CCSDS packet arrival process. In terms of arrival packets in different simulation time, we plot the relation curve of M_PDU efficiency vs. time, named S-M_PDU1, S-M_PDU2, and S-M_PDU3. Serial numbers 1, 2, 3 indicate the order of simulation. Meanwhile, we use the proposed computational method of Packets Channel Multiplexing to get the efficiency-time function and plot the theoretical relation curve such as M_PDU1, M_PDU2, and M_PDU3, which, respectively, represent 1-order, 2-order, and 3-order M_PDU formula. It can be seen from Figure 3 that the theoretical relation curve is well fitting with the simulation curve, which shows that the computational method can depict multiplexing process well in VCLC sublayer. With the growth of the frame time, M_PDU efficiency increases first and then decreases. Because in the short frame time there are few arrival packets, MPDU packet zone is inserted into a large amount of idle packets, resulting in low efficiency. With the increase of arrival packets, idle packets drop and MPDU efficiency is growing. Yet due to limited cache capacity, with the continuous increase of frame time the overflow probability rises, which result in a decline of the M_PDU efficiency.Figure 3
Relationship between the M_PDU efficiency and frame time.The overflow probability curve is shown in Figure4. It can be seen from the curve that the 1~3-order MPDU formula is well fitting with the simulation data.Figure 4
Overflow probability of AOS multiplexing.


### 4.2. The Experimental of CLOPW

In order to analyze the performance for CLOPW, we compare the normalized utilization of virtual channel and average delay with isochronous frame method. Set virtual channel capacity C to 10000 frames/sec. Let the number of virtual channels be 16. We change M_PDU normalized frame timeTv1,Tv2 of VC1 or VC2 and let Tv1+Tv2=0.8. Meanwhile, we fix the other normalized frame time of the remaining VC3~VC16 and let Tv3+Tv4+⋯+Tv16=0.2. For CLOPW, in terms of formula (18) ai=1/(TviC), we let Tv1 change from 0.02 to 0.78, and a1,α2 follow the change. For isochronous frame method, we use the fixed polling weights, i.e., a1=α2, which do not change with Tv1 and Tv2. The 1-order and 2-order utilization of CLOPW are compared with those of isochronous frame method [14]. The experimental results are shown in Figure 5.Figure 5
Comparison of normalized utilization of virtual channel.With isochronous frame method, as shown in Figure5, when M_PDU normalized frame time Tv1,Tv2 is relatively low or higher, the normalized utilization of virtual channel is low because less time Twi leads to the low efficiency of M_PDU, which causes the decline of normalized utilization of virtual channel. On the other hand, a long frame time Tv1 contributes to improving the M_PDU efficiency, but that would result in an overflow increase, which causes the decline of normalized utilization. When M_PDU normalized frame time Tv1,Tv2 is relatively moderate, i.e., they are approximately equal Tv1=Tv2=0.4, the normalized utilization reaches the maximum because in this time the fixed polling weights a1=α2 match frame time (Tv1=Tv2). The isochronous frame method is consistent with CLOPW. When the CLOPW is adopted, the polling weight such as α1,α2 changes with the frame time Tv1,Tv2. The less frame time is allocated for short polling time slices, and the long frame time matches long polling time slices, which would improve normalized utilization of virtual channel. It can be shown in the Figure 5 that CLOPW method, whether it is of 1-order or 2-order, has higher normalized utilization than isochronous frame method as a whole.Furthermore, the average delay is studied. Figure6 shows the comparison of average delay between CLOPW and isochronous frame method under the change of the VCDU frame length.Figure 6
Comparison of average delay between CLOPW and isochronous frame method.As the length of the VCDU frames increases, the average delay of CLOPW and the isochronous frame method are slowly increasing. At the same VCDU length, the average delay of CLOPW is always lower than that of isochronous scheduling algorithm.


## 4.1. The Experimental of the Packet Channel Multiplexing

Based on the scheduling method of M_PDU efficiency (in Section3.1) and the assumption (in Section 3.2), we simulated the process of M_PDU multiplexing in VCLC sublayer. Meanwhile, the simulation result is compared with the recursion formula. And the length of packets lp is set to 1, λp=1,  N=10,  B=40.The relationship between the M_PDU efficiency and time is shown in Figure3. We adopt Poisson distribution model to simulate the CCSDS packet arrival process. In terms of arrival packets in different simulation time, we plot the relation curve of M_PDU efficiency vs. time, named S-M_PDU1, S-M_PDU2, and S-M_PDU3. Serial numbers 1, 2, 3 indicate the order of simulation. Meanwhile, we use the proposed computational method of Packets Channel Multiplexing to get the efficiency-time function and plot the theoretical relation curve such as M_PDU1, M_PDU2, and M_PDU3, which, respectively, represent 1-order, 2-order, and 3-order M_PDU formula. It can be seen from Figure 3 that the theoretical relation curve is well fitting with the simulation curve, which shows that the computational method can depict multiplexing process well in VCLC sublayer. With the growth of the frame time, M_PDU efficiency increases first and then decreases. Because in the short frame time there are few arrival packets, MPDU packet zone is inserted into a large amount of idle packets, resulting in low efficiency. With the increase of arrival packets, idle packets drop and MPDU efficiency is growing. Yet due to limited cache capacity, with the continuous increase of frame time the overflow probability rises, which result in a decline of the M_PDU efficiency.Figure 3
Relationship between the M_PDU efficiency and frame time.The overflow probability curve is shown in Figure4. It can be seen from the curve that the 1~3-order MPDU formula is well fitting with the simulation data.Figure 4
Overflow probability of AOS multiplexing.


## 4.2. The Experimental of CLOPW

In order to analyze the performance for CLOPW, we compare the normalized utilization of virtual channel and average delay with isochronous frame method. Set virtual channel capacity C to 10000 frames/sec. Let the number of virtual channels be 16. We change M_PDU normalized frame timeTv1,Tv2 of VC1 or VC2 and let Tv1+Tv2=0.8. Meanwhile, we fix the other normalized frame time of the remaining VC3~VC16 and let Tv3+Tv4+⋯+Tv16=0.2. For CLOPW, in terms of formula (18) ai=1/(TviC), we let Tv1 change from 0.02 to 0.78, and a1,α2 follow the change. For isochronous frame method, we use the fixed polling weights, i.e., a1=α2, which do not change with Tv1 and Tv2. The 1-order and 2-order utilization of CLOPW are compared with those of isochronous frame method [14]. The experimental results are shown in Figure 5.Figure 5
Comparison of normalized utilization of virtual channel.With isochronous frame method, as shown in Figure5, when M_PDU normalized frame time Tv1,Tv2 is relatively low or higher, the normalized utilization of virtual channel is low because less time Twi leads to the low efficiency of M_PDU, which causes the decline of normalized utilization of virtual channel. On the other hand, a long frame time Tv1 contributes to improving the M_PDU efficiency, but that would result in an overflow increase, which causes the decline of normalized utilization. When M_PDU normalized frame time Tv1,Tv2 is relatively moderate, i.e., they are approximately equal Tv1=Tv2=0.4, the normalized utilization reaches the maximum because in this time the fixed polling weights a1=α2 match frame time (Tv1=Tv2). The isochronous frame method is consistent with CLOPW. When the CLOPW is adopted, the polling weight such as α1,α2 changes with the frame time Tv1,Tv2. The less frame time is allocated for short polling time slices, and the long frame time matches long polling time slices, which would improve normalized utilization of virtual channel. It can be shown in the Figure 5 that CLOPW method, whether it is of 1-order or 2-order, has higher normalized utilization than isochronous frame method as a whole.Furthermore, the average delay is studied. Figure6 shows the comparison of average delay between CLOPW and isochronous frame method under the change of the VCDU frame length.Figure 6
Comparison of average delay between CLOPW and isochronous frame method.As the length of the VCDU frames increases, the average delay of CLOPW and the isochronous frame method are slowly increasing. At the same VCDU length, the average delay of CLOPW is always lower than that of isochronous scheduling algorithm.


## 5. Conclusion

In the paper, we analyze the mechanism of the AOS multiplexing model in VCLC and VCA sublayer. We derive the M_PDU multiplexing efficiency under finite buffer, which is applied to cross-layer optimization. Furthermore, a scheduling method of cross-layers optimization of polling weighted, called CLOPW, is proposed. The novel scheduling method gives the formula for the virtual channel utilization and delay of cross-layer optimization. With fixed packet length of M_PDU under the condition of short correlation traffic model, CLOPW is more suitable for virtual channel multiplexing of AOS. The experimental results show that CLOPW is higher utilization of virtual channel and lower average delay than the isochronous frame method. The method can provide theoretical support for the construction and operation of AOS development.



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*Source: 2560623-2019-03-24.xml*