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

The core mechanism of Advanced Orbit System (AOS) mainly contains the packet channel multiplexing and the virtual channel multiplexing. Themultiplexing efficiency and frame time directly affect the performance of the AOS and even the whole system. In this paper, in order to optimize AOSmultiplexing performance, a schedulingmethod 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, andmultiplexing efficiency.We build amultiple factors framingmodel 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 anddelay of cross-layer optimization.The experimental results show that the novel schedulingmethod of cross-layers optimization of polling weight is higher utilization of virtual channel and lower average delay than the isochronous frame method.


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][2][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-tospace, 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][10][11].High efficiency frame optimization means that the data packets 2 International Journal of Digital Multimedia Broadcasting 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][9][10][11][12][13][14][15][16][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.Section 2 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.

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.
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 Figure 2. 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.
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][20][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 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.

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 Table 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 to   .
(b) Supposing that M PDU length was equal to   , packet length is   .  =  ⋅   , and N is an integer.
(c) The system is carried out in a batch process; i.e., together N packets are inserted into one M PDU packet zone in a frame time   .When the amount of arrival packet is less than N, the idle packets are inserted into M PDU packet zone.
(d) Let the cache capacity be B and  > .
The presence of idle packets causes a decrease in M PDU efficiency.If extending the frame time   to be used to wait for coming packets into buffer, the efficiency would increase, but the delay worsens.
Set M PDU efficiency as .In the first waiting gap (frame time   ), the efficiency is expressed as follows, named 1 order M PDU efficiency, where   is the length of M PDU and   is the length of CCSDS packet.  is the time gap.() is packet arrival probability with Poisson distribution.
The overflow probability in the first gap is as the following formula.
Furthermore, the M PDU efficiency in the second time gap   was considered.In the second gap, the residual packets from the first gap must be calculated.Let the residual packets probability be Φ   (), named the first order residual packets function (abbr.1-RPF), where  is the amount of residual packets.
When arrival packets in the first time gap were less than N, there are no residual packets in the second gap   , and  is equal to 0. Otherwise, when  >  in the first gap, r is the amount of residual packets and n=N+r.So the actual arrival probability is ( + ) in first gap   .The efficiency was expressed as follows: where k 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   .Therefore, the 2-order M PDU efficiency is expressed as follows.
The second-order residual packets function (abbr.2-RPF) is as follows.
The overflow probability in the second gap is as the following formula.
From above the formulas, the recursion formula of j order M PDU efficiency can be given, where  () (), Φ  () (), and  () are as follows.

A Scheduling Method of Cross-Layers Optimization of
Polling Weight.The virtual channel number is, respectively, from 1 to i.The normalization of scheduling period is 1.   is weight of the polling time on VCA sublayer.The time slice allocated for each virtual channel is from  1 to   .  satisfies the following formula.
We normalized the polling cycle of the whole virtual channel to 1.    represents the average frame time of generating a M PDU (a M PDU is encapsulated into a VCDU) on the i th virtual channel, i.e., average normalized time per a VCDU.The input rate of VCDU frame on the i th virtual channel is expressed as V ()  .
If the total output channel capacity is represented as C, which stands for the maximum VCDU transmission rate in downlink channel, the time slice allocated for i th virtual channel is   .The output rate of i th virtual channel is V ()  .
There are three situations of output and input rate of i th virtual channel.
(a) When the condition V ()  < V ()  is met, i.e., the input rate of i th 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 condition V ()   > V ()  is met, i.e., the input rate of i th virtual channel is higher than the output rate, it can lead to a gradual increase in the cache and easily overflow.
(c) When the condition V ()  = V ()  is met, i.e., the input rate of i th virtual channel is equal to the output rate, the best match between input and output is achieved.
From the formula ( 14), ( 15), ( 16), we can get the following: That is In a whole polling cycle, the throughput of virtual channel is represented as R, where  1 ,  2 , ⋅ ⋅ ⋅ ,   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 as .
From formula (19) to (20), we can get the following.
That is From the formula ( 1) and ( 22), the first order utilization of virtual channel with the first order efficiency of M PDU is represented as  (1) .
In the i th virtual channel, the multiplexing efficiency of M PDU in second time gap can be represented as  (2)   .
So the 2-order utilization of virtual channel is  (2) .
Furthermore, the j th order utilization of virtual channel is  () .
In summary, the utilization is related to not only the multiplexing efficiency of M PDU, but also the frame time   of VCLC sublayer and the distribution weight   of time slice of virtual channel on VCA sublayers.Suppose that the input rate of virtual channel is matched with the output.The j order utilization  () can be expressed as follows.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 as D, which is a function of framing time.
Furthermore, the average delay of virtual channel is expressed as where ( =  V ()) represents the delay time under the condition that t is equal to different frame time   (), and k is from 1 to N. |   = represents the average delay time under the condition that the length of VCDU is equal to M.

Experimental Result and Analysis
In order to verify the validity of the packet channel multiplexing model and the scheduling method of CLOPW in Section 3, 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.

The Experimental of the Packet Channel Multiplexing.
Based on the scheduling method of M PDU efficiency (in Section 3.1) 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   is set to 1,   = 1,  = 10,  = 40.
The relationship between the M PDU efficiency and time is shown in Figure 3.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.
The overflow probability curve is shown in Figure 4.It can be seen from the curve that the 1∼3-order MPDU formula is well fitting with the simulation data.

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 time  V1 ,  V2 of VC 1 or VC 2 and let  V1 +  V2 = 0.8.Meanwhile, we fix the other normalized frame time of the remaining VC 3 ∼VC 16 and let  V3 + V4 +⋅ ⋅ ⋅+ V16 = 0.2.For CLOPW, in terms of formula (18)   = 1/( V ), we let  V1 change from 0.02 to 0.78, and  1 ,  2 follow the change.For isochronous frame method, we use the fixed polling weights, i.e.,  1 =  2 , which do not change with  V1 and  V2 .The 1order and 2-order utilization of CLOPW are compared with those of isochronous frame method [14].The experimental results are shown in Figure 5.
With isochronous frame method, as shown in Figure 5, when M PDU normalized frame time  V1 ,  V2 is relatively low or higher, the normalized utilization of virtual channel is low because less time   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  V1 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  V1 ,  V2 is relatively moderate, i.e., they are approximately equal  V1 =  V2 = 0.4, the normalized utilization reaches the maximum because in this time the fixed polling weights  1 =  2 match frame time ( V1 =  V2 ).The isochronous frame method is consistent with CLOPW.When the CLOPW is adopted, the  polling weight such as  1 ,  2 changes with the frame time  V1 ,  V2 .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.Figure 6 shows the comparison of average delay between CLOPW and isochronous frame method under the change of the VCDU frame length.
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 International Journal of Digital Multimedia Broadcasting 9 delay of CLOPW is always lower than that of isochronous scheduling algorithm.

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.

Figure 2 :
Figure 2: Transformation of data structure of multiplexing.

Figure 3 :
Figure 3: Relationship between the M PDU efficiency and frame time.

Figure 5 :
Figure 5: Comparison of normalized utilization of virtual channel.

Figure 6 :
Figure 6: Comparison of average delay between CLOPW and isochronous frame method.

Table 1 :
the table of symbols.

Table 2 :
is the function of variable   .By changing the polling weight of time slice on VCA sublayer and making it match with M PDU frame time, Simulation Parameters Table of AOS Virtual Channel.