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appeared in Proc. of IST Mobile & Wireless Telecommunications Summit 2002, Thessaloniki, Greece, June 2002 New Scheduling Algorithm for Providing Proportional Jitter in Differentiated Service Network Thu Ngo-Quynh (*) Holger Karl (**) (*) Interdepartmental Research Center for Networking and Multimedia Technology PRZ / FSP-PV / TUBKOM Tel +49 30 314 27663 Adam Wolisz(**) Klaus Rebensburg (*) (**) Telecommunication Networks Group Department of Electrical Engineering and Computer Science Technical University of Berlin Strasse des 17. Juni 136 10623, Berlin, Germany Email: {thu, klaus}@prz.tu-berlin.de, {wolisz,karl}@ee.tu-berlin.de ABSTRACT There exist a Model of Proportional Jitter Differentiated Service and Proportional Delay Differentiated Serivce, which provides proportional jitter or proportional delay between different classes. This first approach is very appropriated for high-speed networks because it does not require the implementation of the proportional jitter scheduling algorithms at all the routers in the network but at least at the boundary, and hence extremely reduces the complexity. In this paper, a new proportional jitter scheduling algorithm, called Proportional Average Jitter (PAJ), is created for the Model of Proportional Jitter Differentiated Services. In addition, its quality, in terms of long-terms and short-term jitter within only one hop, is also analyzed. Furthermore, the performance of Proportional Jitter Differentiated model using PAJ as scheduling algorithm is compared to this model but using Relative Jitter Packet Scheduling, and to Proportional Delay Differentiated model using Waiting Time Priority, is compared, too. 1. INTRODUCTION Differentiated Service (DiffServ) architecture is an new approach for the Internet, which is designed to improve the quality of service provided by traditional Internet. Relative Differentiated Service, is a variant of DiffServ, which has no quantitative but only qualitative guarantees. This approach can be further refined and quantified to Relative Proportional Differentiated Service [5] and Relative Absolute Differentiated Service. In [1], the authors developed a new Relative Differentiated Model which provides proportional delay between different classes, called Proportional Delay Differentiated Service Model (PDD). This model needs to implement proportional delay scheduling algorithms at every routers in the networks. Based on this model, some proportional delay scheduling schemes are created, as MDP [2], BPR [1], WTP [1], DDTS [3]. In [4] and [6] we described a new model for providing proportional delay jitter between different classes which is called Proportional Jitter Differentiated Service Model (PJD). This model is very simple and efficient for highspeed networks because it is not necessary to have proportional jitter scheduling algorithms at every routers. Relative Jitter Packet Scheduling algorithm [4], which produces proportional jitter between different classes, is specially designed for this PJD model. It is very important to know that we should not only examine the behaviours of PDD and PJD model in a separated context, but in a same network to verify which model can produce better quality of service. The mean of quality of service here is explained as end-to-end delay, because whether we implement a model of PDD or PJD in terms of delay or delay jitter in a network, which we hope is always receiving better end-to-end quality of service, and in this case, a better end-to-end delay, which is the sum of network delay and play out buffer delay. Further more, the play out buffer delay, depending on the Play out Buffer Delay Adjustment Algorithms used at the play out buffer, is adjusted with the variation of network delay, or delay jitter and the loss rate. We analysed and choose Concord algorithm for using in our Model (please see [5] and [6] for more details). These raisons lead us to an interesting question of comparing the quality performance of PDD and PJD model, to know which model could produce better quality of service, in terms of end-to-end delay. In [6] we create a new performance criteria for this comparison, which is called normalized end-to-end delay. The performance of PDD model using WTP as scheduling algorithm is compared to the performance of PJD model using RJPS as scheduling algorithm, in terms of this normalized end-to-end delay, too. Our first result showed that PJD model delivers better quality, especially when the loss at the play out buffer is high. In this paper, a new proportional jitter scheduling algorithm, Proportional Average Jitter (PAJ), is created for the PJD model, and its quality, in terms of long-terms and short-term jitter within only one hop, is also analyzed. Furthermore, the performance of PJD model using PAJ as scheduling algorithm is compared to this model but using RJPS, and to PDD model using WTP. The paper is constructed as follows. Section 2 creates a new scheduling algorithm (PAJ), which is simpler than RJPS and Section 3 evaluates its quality in terms of long-term jitter and short-term jitter ratio. In addition, we compare the quality of some networks using PAJ with the other networks, which use RJPS and WTP in Section 5. The last section concludes the work and outlines further possible research on the direction. 2. PROPORTIONAL AVERAGE JITTER SCHEDULING ALGORITHM (PAJ) A way to interpret the Proportional Jitter Differentiation model is that the normalized average jitter, defined as normalized − PAJ = j i * ∆ i , must be equal in all classes, ji i.e. normalized − PAJ ji normalized − PAJ = ji * ∆i = j k * ∆k = j k A scheduler that aims to equalize the normalized average jitter among all classes is described next. We refer to this algorithm as Proportional Average Jitter scheduling algorithm. Assume that there was at least one departure from class i before the time t, the normalized average jitter of class i at time t is −PAJ normalized ji (t) = ∑jitter−of −all− packets−served*∆ = S *∆ i −of − packets − served Number i i Pi Where S i is the sum of delay jitter of all packets of backlogged classes, and Pi is the number of packets served. Suppose that a packet has to be selected for transmission at time t. PAJ chooses the backlogged class with the maximum normalized average jitter at t: normalized − PAJ k = arg max j i (t ) The packet at the head of queue k is transmitted, its P queuing delay is defined, and hence its delay jitter j k k +1 , too. The variable S k and Pk are then updated as S k = S k + j kPk +1 , and the new normalized average jitter normalized − PAJ jk (t ) is recomputed from the equation above. The selection of the maximum normalized average jitter, requires at most N-1 comparisons with N is the number of classes, which is a minor overhead for the small number of classes we consider here. The main computation overhead of PAJ is a division, after each packet departure. This operation would not be an issue for network interfaces of up to 1Gbps. The basic idea in PAJ is that if some packets are serviced from class j with the maximum normalized average jitter, the delays of these packets stays similar and hence its jitter will not increase any more, and thus the increase of S j due to these packets will be minimized. So serving some packets from class j tends to reduce the difference from the normalized average jitter of the other classes. In the long run, if the scheduler always minimizes the difference between the normalized average jitters in this manner, we expect that the normalized average jitters will be about the same. The similarities of PAJ and RJPS are now obvious. In the same way that PAJ chooses for service the class with the maximum normalized jitter, RJPS chooses for service the class with the maximum normalized average assumed jitter. PAJ attempts to minimize in this manner the differences of the class normalized average jitter. RJPS maintains normalized average jitter of a moving window and for all packets in the queue, thus making the forwarding behaviour more responsive to current queue conditions, but is more complicated than PAJ. A. Simulations The objective of this simulation study is to evaluate the behaviour of PAJ scheduler in terms of long-term jitter ratio and short-term jitter ratio (this short-term jitter ratio is calculated over a moving window of 200 packets) within only one hop. Our simulation study (using ns2.1b7a Simulator) shows that PAJ scheduler approximates the proportional jitter differentiation model. The simulation model is as follows. PAJ scheduler uses packet sources of type on-off traffic. The topology used contains only one hop. There are a total of 2 classes 0 and 1. Flow 1 and Flow 2 belong to class 0, while Flow 3 and Flow 4 belong to class 1. We run and collect our simulations in 100 seconds. A1. Behaviour of PAJ with heavy load In this simulation, the jitter differentiation parameters of class 0 and 1 are ∆ 0 = 2, ∆ 1 = 1 . The predefined ratio between class 0 and class 1 are 0.5. The link utilization in this simulation is set to 100%. The Flow 1 has the burst time of 40ms and idle time of 10ms. For Flow 2 it is 50ms and 20ms respectively. Class 1 has Flow 3 of 60ms burst time and 15ms idle time and Flow 4 of 45ms burst time and 20ms idle time. The total speed of class 0 and class 1 is 3.5 Mps. The first experiment intended to test the performance of PAJ scheduler in terms of longterm jitter ratio and short-term jitter ratio. Average long-term jitter: The graph 2a shows that average long-term jitter ratio for 2 classes achieves the predefined ratio 2:1. This ratio is achieved after a time of fluctuation of about 6s seconds. Average short-term jitter: Figure 2b shows that the short-term jitter ratio fluctuates strongly and can reach up to 3.5 and down to 0.17, although the predefined ratio is only 0.5 A2. Behaviour of PAJ scheduler under different load distribution The second experiment aimed to investigate the longterm jitter ratio and short-term jitter ratio between these two classes under different load distribution. Similar to the first experiment, this scenario is set with the predefine jitter ratio 0.5. The Flow 1 has the burst time of 100ms and idle time of 30ms. For Flow 2 it is 90ms and 40ms respectively. Class 1 has Flow 3 of 60ms burst time and 35ms idle time, Flow 4 of 75ms burst time and 30ms idle time. There are 8 simulations in this scenario, in which the load pattern between two classes varied from symmetric to asymmetric distributions. Figure 3 denotes the load distribution of these two classes in percentage. Results derived from these experiments showed that in most cases, the performance of long-term jitter ratio of PAJ stays nearly constant. As we seen in the graph, when the load distribution between classe 0 and 1 is very asymmetric (10%-90% or 90%-10%), the PAJ produces a long-term jitter ratio of 0.6753 and 0,4172, while the predefined ratio is 0.5. In addition, the maximum and minimum long-term jitter ratio are very different from the average and predefined ratio, too. In the other cases, when the load distribution between classes is symmetric (50%-50%), the long-term jitter ratio reachs a very good accurate. The short-term jitter ratio produced by PAJ fluctuates much more than long-term jitter ratio. As shown in the graphs 3, the maximum of short-term jitter ratio could reach the value of 87, while the predefined ratio is only 0.5 when the load distribution between two classes is 80%-20%. The average short-term jitter ratios in these 8 cases are around the predefined ratio 0.47318, 0,48823, 0,4648, 0,6231, 1.0127, 0.9786, 1.17786, 2.24526, 2.6751 respectively. That means the quality of short-term jitter ratio depends strongly on the load distribution between classes. 3. COMPARISON OF PDD AND PJD MODEL It is necessary to note that whether we implement PDD or PJD model, our goal is to receive better end-to-end quality of service, that means better end-to-end delay, which is the sum of network and playout buffer delay. In our simulation, we decided to use Concord algorithm as playout buffer delay adjustment algorithm at the receiver end [7]. This algorithm constructs a Packet Delay Distribution and calculate the total end-to-end delay from a predefined loss rate ratio at the receiver. Concord is notable because it defines a solution for synchronization, that operates under the direct influence of application-supplied paramteres for QoS control. In particular, these parameters are used to allow a trade-off between the packet lateness rates, total end-to-end delay and skew. Thus an application can directly indicate an acceptable lost packet rate, rather than by having the synchonization mechanism operate by always trying to minimize losses due to lateness. According to our arguments in [6], we will analyze PJD model, which uses PAJ as its scheduling algorithm, PJD model which uses RJPS and PDD model using WTP. In [6], different network topologies are examined, which use RJPS and WTP in different positions (core or egress) of the network. For PAJ scheduler, we add two new topologies, too. These two new topologies use PAJ at every router or only at egress router. All these topologies are illustrated in the following figures: WTP WTP For long-term jitter ratio, as depicted in Figure 4, our PAJ reaches a very good quality because this ratio is approximately 0.5, which is predefined ratio, too. But the short-term jitter ratio is very unstable . In these 6 cases, the average short-term jitter ratio are 0.5165, 0.5369, 0.5037, 1.3695, 0.5524, 0.5912 respectively and the maximum value of this ratio could reach particularly to 24.01. The smallest minimum value in these 6 cases is 0.01255 (case 4) WTP Network Topology 1 FIFO FIFO FIFO WTP Network Topology 2 A4.Behaviour of PAJ scheduler under different traffic conditions In this section, we investigate the performance of the long-term jitter ratio and short-term jitter ratio of PAJ scheduler under different conditions, as the traffic profiles varies .The scenario is similar to the section A.2 and A.3. As shown in the Figure 4, the long-term jitter ratios stay stable, but the short-term jitter ratio varies, too. WTP RJPS RJPS RJPS RJPS Network Topology 3 FIFO FIFO FIFO RJPS Network Topology 4 PAJ PAJ PAJ Network Topology 5 PAJ produces smaller normalized end-to-end delay, but this delay fluctuates very strongly. FIFO FIFO FIFO PAJ Network Topology 6 Figure 5. Different Network Topologies The Network Topology number 1, which uses WTP at every routers in its network, is based on the PDD model, while the others are based on the PJD model. According to [6], we have defined a new performance comparison criteria for comparing the quality of these networks. This performance criteria is called normalized end-to-end delay Pk and calculated as: Pk = ∑i =1 N Where D endtoend ,i NTk ∑ N i =1 * ∆i ∆i Pk is the normalized end-to-end delay of Network Topology numbered k, and D endtoend ,i NTk is the end-to-end delay of class i of network topology number k. We say that the Network Topology, whose normalized end-to-end delay is smaller, is better. We simulated for a network similar to the Figure 5, but has only 3 routers. The algorithm PAJ, RJPS and WTP are implemented at different positions of this network, core or boundary. There are a total of 2 classes: Class 0 and 1 with the weight of 1.0 and 3.0. At the first router there are 4 flows, at the second and third router there are only 2 flows. We run and collect our simulations in 100 seconds. At the receiver, we use Concord algorithm as Playout Buffer Delay Adjustment Algorithm with the size of the moving window of 3000 packets, and the loss ratio is set to 15%. The normalized end-to-end delay is shown in the graph 6. It is easy to see that the normalized end-to-end delay produced by network using PAJ (NT5 and NT6) is not balanced as the others topologies, which use RJPS or WTP. However, this normalized end-to-end delay of NT5 stays smaller than NT1, NT2, NT3 and NT4. Particularly, NT1, which uses PAJ only at the egress router and the others are FIFO, performs a very oscillated normalized end-to-end delay, but some time smaller than NT4 and NT6. 4. CONCLUSION In the paper we developed a new scheduling mechanism called Proportional Average Jitter PAJ which is more simple than the old proportional jitter scheduling algorithm RJPS. Our measurement verifies the quality of PAJ scheduler in terms of long-term jitter ratio and short-term jitter ratio over only one hop under different load distributions and different traffic profiles. Furthermore, The performance of PDD and PJD model are alsocompared with each others, and the quality of some networks using PAJ, WTP and RJPS at different positions (core or egress) is investigated, too. Our first result showed that network using PAJ scheduler could REFERENCES 1. C. Dovrolis, D. Stiliadis and P. Ramanathan. Proportional Differentiated Services: Delay Differentiation and Packet Scheduling. In Proceedings of the 1999 ACM SIGCOMM Conference, Cambridge MA, September 1999. 2. T. Nandagopa, Narayanan Venkitaraman, R. Sivakumar and V. Bharghavan. Delay Differentiation and Adaptation in Core Stateless Networks. IEEE INFOCOM 2000, Tel Aviv, Israel, March 2000. 3. H. T. Nguyen and Helmut Rzehak. An Adaptive Bandwidth Scheduling for Throughput and Delay Differentiation. In Proceeding of ICN’01, July 11-13, 2001, Colmar, France. 4. T. Ngo-Quynh, H. Karl, A. Wolisz, K. Rebensburg. Relative Jitter Packet Scheduling for Differentiated Service. In Proceeding of 9th IFIP Working Conference on Performance Modelling and Evaluation of ATM&IP Networks IFIP ATM&IP 2001. 5. T. Ngo-Quynh, H. Karl, A. Wolisz, K. Rebensburg. The Influence of Proportional Jitter and Delay on Endto-End Delay in Differentiated Service Network. In Proceeding of IEEE International Symposium on Network Computing and Application NCA’01, Cambrige, MA, USA. February 2002. 6. T. Ngo-Quynh, H. Karl, A. Wolisz, K. Rebensburg. Using only Proportional Jitter Scheduling at the boundary of a Differentiated Service Network: simple and efficient. To appeared in 2nd European Conference on Universal Multiservice Networks ECUMN’02, April 8-10, 2002,Colmar, France 7. N. Shivakumar, C. J. Sreeman, B. Narendran and P. Agrawal. The Concord algorithm for synchronization of networked multimedia streams. International Conference on Multimedia Computing and Systems, 1995. Figure 2a 1 0,8 Class 0/1 0,6 0,4 0,2 97,4 89,9 82,4 74,9 67,4 60 52,5 45 37,5 30 22,5 15 7,53 0 0,04 Long Term Jitter Ratio (PAJ Scheduler) 1,2 Time (s) Different Load Distributions between classes Different Load Distributions between classes 100 90 1 Min 0,8 0,6 Ave 0,4 Max 0,2 Short Term Jitter Ratio Long Term Jitter Ratio 1,2 Min 80 70 Ave 60 Max 50 40 30 20 10 0 0 1090% 10-90% 20-80% 30-70% 40-60% 50-50% 60-40% 70-30% 80-20% 90-10% 2080% 3070% 4060% 5050% 6040% 7030% 8020% 9010% Figure 3. Jitter ratio when different load distributions between classes Different Traffic Profiles Different Traffic Profiles 0,7 0,5 Ave 0,4 Max 0,3 0,2 0,1 25 Min 20 Ave Max 15 10 5 0 0 Case 1 Case 2 Case 3 Case 4 Case 5 Case 1 Case 6 Case 2 Case 3 Case 4 Case 5 Case 6 Figure 4. Jitter ratio when different traffic profiles Loss 15% 8 7 W TP+W TP+W TP 6 FIFO+FIFO+W TP 5 RJPS+RJPS+RJPS 4 FIFO+FIFO+RJPS 3 PAJ+PAJ+PAJ 2 FIFO+FIFO+PAJ 1 93,3 85,5 77,8 70 62,2 54,4 46,7 38,9 31,1 23,3 15,6 7,77 0 0 Normalized Delay (s) Long Term Jitter Ratio Min Short term Jitter Ratio 30 0,6 Time (s) Figure 6. Performance comparison