MARS: The Magnet II Real-Time Scheduling Algorithm

1. 1 MARS: The Magnet IIReal-Time Scheduling Algorithm Hyman, Lazer, and Pacifici 1991 ACM ? Presented by 李孝治

2. 2 Abstract • A real-time scheduling algorithm, MARS, for Asynchronous Time Sharing (ATS) based switching modes. • 3 classes of traffic sources: • real-time video sources • guaranteed maximum end-to-end delay SI for all cells • real-time voice sources • guaranteed maximum end-to-end delay SII •  % cell loss rate • maximum average cell loss gap  • data traffic • guaranteed minimum average throughput • guaranteed maximum average time delay

3. 3 1. Introduction • Goal: • To evaluate the performance of Asynchronous Time Sharing (ATS) based integrated networks • ATS based integrated network is novel: • the concept of quality of service explicitly appears in the design specification at both the edge and the core of the network • the core of the network makes a distinction between traffic classes • it is necessary in order to efficiently provide QoS • it is not a requirement of ATM based integrated networks

4. 4 • The study of this paper is limited to • a switching nodestaken in isolation • This paper • presents the performance of the MAGNET II scheduling algorithm • compares it with the performance of other known algorithms, with • quantitative data • implementation complexity and knowledge

5. 5 2. Review of Past Work • The early literature on real-time scheduling relates to an operation systems environment,in which arriving tasks need to be scheduled at an available processor, such that each task is completed by its deadline • Assume • a priori knowledge of all of the arrival times, processing times, and deadlines for the entire set of tasks to be scheduled

6. 6 • Various criteria for optimization have been used • Cheng and Stankovic [3] • Liu and Laylan • Tobagi and Peha • Baker • Chipalkatti et al. • Ferarri and Verma • Sriram

7. 7 3. The Architecture of the Switching Nodes • 3 elements: • Input Buffers • Switching Fabric • Output Buffers • Fundamental Requirement: • The transfer of information from its inputs to its output such that time delay and blocking sensitiveperformance criteria are met.

8. 8 • 4 traffic classes: Class I, II, III, and C • 4 input buffers / access point. • Traffic arriving at an access point is stored, according to its class, in one of the four buffers. •  = Minimum Average User ThroughputT = Maximum Average User Time Delay

9. 9 3.1 The Multi-class Traffic Model • Contention Packet Loss • Clipping: [Network Congestion]  [Delay > Max Delay, SI or SII] • Blocked: [Buffer Overflow]  [Packet discarded] • For Class II: •  % = Contention packet loss  = Upper bound on the average number consecutively lost packet

10. 10 3.2 The Link Scheduling Model Buffer ManagerLink Scheduler • ATS-based switching node • was first implemented on MAGNET II • and also adopted by TeraNet. 3 input links 3 x (3 x 4) 3 output links J x (3 x 1)input buffers J x (3 x 1)output buffers Ring Switch Fabric

11. Cycle C I II III Class MC MI MI MIII Length of subcycle 11 • Model the output link of TeraNet • A queuing system with 4 buffers + 1 server: • At server: • Fixed capacity - C bits/secFixed cell size - D bits/cell • Service rate = C/D cells/sec • Slotted channel: • MX: dynamically adjusted • Fixed Cycle Length: H =  M

12. F Frame Frame Frame active Emit cellsat rate CI Stop Emit 12 3.3 Real-Time Traffic Source Models • Video: • Fixed frame duration: F = 62.5 ms • Constant cell rate: CI = 1M bps • Active period: active = [10ms, 40ms] (uniformly distributed) • E(t,video) = E[active] CI / F = 4M bps

13. 13 • Voice: • On-off source • Fixed frame duration: F = 62.5 ms • Constant cell rate: CI = 1M bps • Active period: onInactive period: off (exponentially distributed) • E[on] = 352 msE[off] = 650 ms • E(t,voice) = E[on] / (E[on] + E[off]) = 22.5K bps • Data: • Poisson distributed • E(t,data) = 1M bps

14. 14 4. MARS: The MAGNET IIReal-Time Scheduling Algorithm • Assume: 1 server + 3 queues (for Class I, II, and III only) • Scheduler Operations: • H is kept constant; • 2 schedules (lists): number of Class I and II cells to be transmitted during the future cycle; • the lists are updated at the end of each cycle(new cells arrived during the previous cycle); • only the min. amount of resources is allocated to each class; • QoS requirements of Class I must always be met; • exceeding Class II cells are clipped; • the remaining bandwidth (if available) is allocated toClass III traffic.

15. 15 • To determine the bandwidth allocation: • At the end of each cycle • The scheduler generates 2-dimensional (hI > hII) schedules, with hk =  Sk  / H  - 1 (k=1,2) • 2 logical partitions (bins) for Class I and II • Mk[i,j]: the number of Class k cells that at the beginning of cycle i are predicted to be scheduled in the next hk cycles, j < hk.

16. 16 • The updating process for Class I traffic: • MI[i,j] = min(MI[i-1,j+1]+OI[i,j+1],H) • OI[i,j] = max(0,MI[i-1,j+1]+OI[i,j+1]-H)

17. 17 • The updating process for Class II traffic: • MII[i,j] = min(MII[i-1,j+1]+OII[i,j+1],R[j,j])OII[i,j] = max(0,MI[i-1,j+1]+OII[i,j+1]-R[I,j])whereR[I,j] = H- MI[i,j] j = 0,1,…,hI H - (1/hI)  MI[i,j] j = hI,…, hII-1

18. 18 5. Experimental Results • Compare MARS with • SPS (Static Priority Scheduling) • MLT (Minimum Laxity Threshold) • Assume • Link capacity C = 100M bps • Fixed cell size D = 1024 bits/cell • Fixed cycle size H = 39 cells • QOS = [SI,SII,,,T] • SI,SII = max. delay of Class I and II traffic (in seconds) •  = percentage of contention packet loss •  = max. gap between consecutive packet loss (in cells) • T = max. average user time delay (in seconds)

19. 19 • Experiment 1 • KI = KII =[0..20] calls, KIII = [0..80] Poisson data callsH = 39 cellsQOS = [1ms, 1ms, 0.001, 5.0, 1ms]Fixed KI and KIII  Find KII • For KI < 10: same performance of the 3 algorithms.For KI > 10: MARS and MLT allow more KII users.

20. 20 • Let KIII = 0 in Experiment 1: • KI increases  KII decreases • MARS/MLT > SPS • When KI = 16: • MARS/MLT: KII = 500 voice calls. • SPS: KII = 0

21. 21 • Experiment 2: (for smaller delay) • H = 9 cellsQOS = [400s, 800s, 0.001, 5.0, 1ms] • Same performance of the 3 algorithms. • Little effect for SPS;Drastic decreases for MARS and SPS

22. 22 • Conclusions from EXP 1 and 2: • (1) When Class I and II requires smaller delays, the SPS is very nearly optimal. (Same in EXP. 1 and 2) • (2) When Class I and II have larger traffic, a significant gain in utlilization can be achieved by usin one of the more complex algorothms, MARS or MLT. (KI > 10)

23. 23 • Experiment 3: (for correlated and bursty traffic) • CI = 10Mbps  50Mbps • active = [10ms, 40ms]  [2ms, 8ms] • E[active] = 25ms  5ms • F = 62.5ms • E(t,video) = E[active] CI / F = 4Mbps • Only when both Class I and II loads are low is the performance of SPS, MARS, and MLT the same.

24. Let KIII = 0 in Experiment 3: 24 • Worse performance when bursty traffic. • Improved by using MARS and MLT.

25. 25 6. Conclusions (1) • When the network load is highly correlated (video or on-off voice),MARS and MLT improved the performance considerably. • When the cells are multiplexed together,their correlation decreases as the number of sources increases. The improvement due to MARS and MLT is considerably smaller.

26. 26 6. Conclusions (2) • Resources allocation: • SPS : Class I traffic first • smaller delay for Class I traffic • MARS and MLT : that is necessary to satisfy Class I QoS parameters • maximum delay for Class I traffic • Class II and III have more resources, and thus, the multiplexer has a greater network utilization factor.

27. 27 6. Conclusions (3) • MARS has at most twice the computation time of SPS, while MLT runs much slower. • MARS and MLT are closed to the upper bound for network utilization. • Additional knowledge requirement for MLT leads to substantial increase in complexitywithout proportional improvement in network utilization. MARS is recommended for real-time scheduling algorithms in ATS-based nodes.