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Schedulling

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Abhishek Kesharwani

This document discusses packet scheduling techniques for quality of service (QoS) management in computer networks. It covers max-min weighted fair share scheduling, which assigns weights to flows based on their different QoS requirements. It also discusses fair queuing, processor sharing, generalized processor sharing (GPS), weighted fair queuing (WFQ), and deficit round robin (DRR) scheduling algorithms. GPS provides exact max-min weighted fair share but is an ideal model, while WFQ and DRR are practical implementations that approximate GPS to provide service differentiation and bounded delays. Scheduling algorithms have a "schedulable region" defining all performance bounds they can simultaneously meet for admission control.

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Packet Scheduling for QoS management Part II TELCOM2321 – CS2520 Wide Area Networks Dr. Walter Cerroni University of Bologna – Italy Visiting Assistant Professor at SIS, Telecom Program Slides partly based on Dr. Znati’s material
27 Readings • Textbook Chapter 17, Section 2
28 Max-Min weighted fair share • Max-Min fair share assumes that all flows have equal right to resources • Different flows might have different rights due to different QoS requirements – e.g. voice and video flows require different bandwidth levels – customers of video service are willing to pay more to get the required bandwidth – they must have the same chances as voice customer to get what they need • Associate a weight to each demand to take into account different requirements – normalize demands with corresponding weight – use weights to compute fair share
29 Max-Min weighted fair share: Example • Demands: d1 = d2 = 10, d3 = d4 = 25, d5 = 50 • Bandwidth: C = 100 • Max-Min satisfies d1, d2, d3, and d4 while d5 gets 30 • If d5 has the same right as the others, use weighted Max-Min: 1. Weights: w1 = w2 = w3 = w4 = 1, w5 = 5 2. Weighted demands: d’1 = d’2 = 10, d’3 = d’4 = 25, d’5 = 50 / 5 = 10 3. FS = C / (sum of weights) = 100 / 9 = 11.11 4. d’1, d’2 and d’5 satisfied, d5 gets 50 5. Sum of weights of unsatisfied demands: M = w3 + w4 = 2 6. Bandwidth left: R = 100 – (10 + 10 + 50) = 30 7. FS = 30 / 2 = 15 8. d’3 and d’4 not satisfied they get 15
30 Fairness in Work Conserving Schedulers • If a scheduling policy guarantees fair resource sharing (e.g. Max-Min) it is also protective – a misbehaving source do not get more than fair share • Resources should be assigned based on QoS requirements – Max-Min weighted fair share – weights limited by conservation law • Fair work conserving scheduling policies – Fair Queuing – Processor Sharing – Generalized Processor Sharing – Weighted Fair Queuing
31 Fair Queuing • A router maintains multiple queues – separate queues for different traffic flows or classes – queues are serviced by a round-robin scheduler – empty queues are skipped over • Greedy connections face long delays, but other connections are not affected by it • Drawbacks – no service differentiation – the scheme penalizes flows with short packets ... 1 2 K
32 Processor Sharing • The server is able to serve multiple customers at the same time • Fluid model – traffic is infinitely divisible – service can be provided to infinitesimal amounts of data – the packet size does not count anymore – if N customer are served by server with capacity C, capacity seen by each customer is C / N – ideal model to provide an upper bound on the fairness of other schemes
33 Head-of-Queue Processor Sharing • Separate queues for different traffic flows or classes – head-of-queue packets are served from nonempty queues – following packets wait to be serviced – a nonempty queue is always served • Each queue is assigned a fair share of server capacity – when some flows become silent, their capacity is equally split among the other flows Max-Min fair share – independently of packet size ... 1 2 K 3 in service
34 Processor Sharing: Virtual time • 0 ≤ N(t) ≤ K, number of nonempty queues at time t • r(t) = C / N(t), capacity available to each nonempty queue when N(t) > 0 • tk,i, actual arrival time of packet i to queue k • Lk,i, length of packet i in queue k • Actual service time depends on r(t) – actual service time stretches or shrinks based on arrival and departure events • It is useful to define a virtual time scale v(t) – continuous piecewise linear function of t with slope 1/N(t) • Now it is possible to define – sk,i, virtual starting transmission time of packet i in queue k – fk,i, virtual ending transmission time of packet i in queue k
35 Processor Sharing: Example t2,2 = 2 L2,2 = 4 t1,2 = 2 L1,2 = 1 t3,1 = 3 L3,1 = 3 t2,1 = 1 L2,1 = 1 t1,1 = 0 L1,1 = 3 Queue 3Queue 2Queue 1 0 1 2 3 arrival time packet size 1 3 4 C = 1
36 Processor Sharing: Example t = N(t) = v(t) = 0 1 0 1 2 1 2 2 3 3 2 4 3 5 3 6 3 3 7 3 8 3 9 2 4 10 2 11 1 5 12 0 6 queue 1 queue 2 queue 3 t
37 Virtual starting and ending times Recursive definition • fk,i = sk,i + Lk,i/C • sk,i = max [ fk,i–1 , v(tk,i) ] In our example • s1,1 = 0, f1,1 = 3 • s2,1 = 1, f2,1 = 2 • s2,2 = 2, f2,2 = 6 • s3,1 = 2, f3,1 = 5 • s1,2 = 3, f1,2 = 4
38 Packet-based Processor Sharing • Real-life schedulers are not able to serve infinitesimal amounts of data • A packet-based scheduling policy that approximates the PS scheme can be implemented as follows – compute virtual starting and ending times as in the ideal PS – when a packet finishes its service, next packet to be serviced is the one with smallest virtual finishing time – In our example: s1,1 = 0, f1,1 = 3 s2,1 = 1, f2,1 = 2 s1,2 = 3, f1,2 = 4 s3,1 = 2, f3,1 = 5 s2,2 = 2, f2,2 = 6 ideal PS packet-based PS
39 Comparison with FIFO and FQ • Load = capacity • PS gives preference to short packets average delay of flows 2 and 3 smaller than FIFO
40 Comparison with FIFO and FQ • Load > capacity queue builds up • FQ: flow 2 is penalized, although has same load as flow 1 • PS gives preference to short packets and it’s fair
41 Generalized Processor Sharing • PS and its packet-level equivalent provide Max-Min fairness but do not differentiate resource allocation • Generalized Processor Sharing (GPS) is capable of differentiation by associating a weight to each flow • Each nonempty queue is serviced for an infinitesimal amount of data in proportion to the associated weight – server capacity is split among nonempty queues according to weights • GPS provides an exact Max-Min weighted fair share allocation
42 GPS: Formal Definition • GPS is a work conserving scheduler operating at fixed capacity C over K flows • Each flow is characterized by a positive real weight • is the amount of traffic from flow serviced in the interval • GPS server is defined as a server for which for any flow that is backlogged (i.e. has nonempty queue) throughout
43 GPS: Flow Rate • Summing over all flows • Each backlogged flow receives a service rate of • If a source rate is then such rate is always guaranteed independently of the other flows • number of backlogged queues at time • The service rate seen by flow when is with the sum taken over all backlogged queues
44 GPS: Virtual Time • Now virtual time definition must consider weights – only backlogged queues contribute to the virtual time computation – the sum of the weights of backlogged queues may change at arrival and departure times only • continuous piecewise linear function of t with slope • Actual arrival time of packet of flow is • Its length is • Virtual starting and ending transmission times are
45 GPS Emulation: Weighted Fair Queuing • It is a packet-based GPS – compute virtual starting and ending times as in the ideal GPS – when a packet finishes its service, next packet to be serviced is the one with smallest virtual finishing time • Increased computational complexity since scheduler – must keep track of the backlogged flows and their weights – must compute virtual finishing times and sort them out – must update virtual time at arrival and departure events
46 Comparison with FIFO
47 Comparison with FIFO Flow 1 now sends packets at the guaranteed rate = 0.5
48 Weighted Fair Queuing: Delay Bound • WFQ approximates GPS at packet level – Max-Min weighted fair share achieved – weights allow service differentiation • WFQ also keeps queuing delay bounded for well-behaved flows • Assume each flow shaped with a token bucket scheme, token bucket parameters for flow • Choose weights proportional to token rates • Assume all buckets full of tokens when transmission starts from all flows (worst case) – each flow sends a burst and then keeps transmitting at
49 Weighted Fair Queuing: Delay Bound • In case of GPS, each queue is filled up to and is both serviced and feed at rate • Since queue size cannot exceed , the maximum delay experienced by packets of flow is • In case of WFQ, the effect of servicing packets increases the delay, but this is still bounded • End-to-end queuing delay of flow through WFQ hops is actually bounded
50 Weighted Fair Queuing: Delay Bound • maximum packet size of flow • • server capacity at node maximum delay at the first node due to burst transmission (same as GPS) maximum delay when a packet arrives at each node just after its supposed starting time and must wait for preceding packet maximum delay due to packet-level service: each arriving packet must wait for the one currently in service
51 GPS Emulation: Weighted Round Robin • Each flows is characterized by its – weight – average packet size • The server divides each flow weight by its mean packet size to a obtain a normalized set of weights • Normalized weights are used to determine the number of packets serviced from each connection in each round • Simpler scheduler than WFQ • Mean packet size may not be known a-priori
52 GPS Emulation: Deficit Round Robin • DRR modifies WRR to handle variable packet sizes without knowing the mean packet size of each flow in advance – DRR associates each flow with a “deficit counter” – in each turn, the server attempts to serve one “quantum" worth of bits from each visited flow • A packet is serviced if the sum of the deficit counter and the quantum is larger than the packet size – if the packet receives service, its deficit counter is reduced by the packet size – if the packet does not receive service, a quantum is added to its deficit counter • During a visit, if connection is idle, its deficit counter is reset to 0 – prevents a connection from cumulating service while idle
53 Scheduling and admission control • Given a set of currently admitted connections and a descriptor for a new connection request, the network must verify whether it is able to meet performance requirements of new connection • It is also desirable that the admission policy does not lead to network underutilization • A scheduler define its “schedulable region” as the set of all possible combinations of performance bounds that it can simultaneously meet – resources are finite, so a server can only provide performance bounds to a finite number of connections • New connection requests are matched with the schedulable region of relevant nodes
54 Scheduling and admission control • Schedulable region is a technique for efficient admission control and a way to measure the efficiency of a scheduling discipline – given a schedulable region, admission control consists of checking whether the resulting combination of connection parameters lies within the scheduling region or not – the larger the scheduling region, the more efficient the scheduling policy No. of class 1 requests No. of class 2 requests (C1,C2) (C1MAX,0) schedulable region (0,C2MAX)

More Related Content

Schedulling

  • 1. Packet Scheduling for QoS management Part II TELCOM2321 – CS2520 Wide Area Networks Dr. Walter Cerroni University of Bologna – Italy Visiting Assistant Professor at SIS, Telecom Program Slides partly based on Dr. Znati’s material
  • 3. 28 Max-Min weighted fair share • Max-Min fair share assumes that all flows have equal right to resources • Different flows might have different rights due to different QoS requirements – e.g. voice and video flows require different bandwidth levels – customers of video service are willing to pay more to get the required bandwidth – they must have the same chances as voice customer to get what they need • Associate a weight to each demand to take into account different requirements – normalize demands with corresponding weight – use weights to compute fair share
  • 4. 29 Max-Min weighted fair share: Example • Demands: d1 = d2 = 10, d3 = d4 = 25, d5 = 50 • Bandwidth: C = 100 • Max-Min satisfies d1, d2, d3, and d4 while d5 gets 30 • If d5 has the same right as the others, use weighted Max-Min: 1. Weights: w1 = w2 = w3 = w4 = 1, w5 = 5 2. Weighted demands: d’1 = d’2 = 10, d’3 = d’4 = 25, d’5 = 50 / 5 = 10 3. FS = C / (sum of weights) = 100 / 9 = 11.11 4. d’1, d’2 and d’5 satisfied, d5 gets 50 5. Sum of weights of unsatisfied demands: M = w3 + w4 = 2 6. Bandwidth left: R = 100 – (10 + 10 + 50) = 30 7. FS = 30 / 2 = 15 8. d’3 and d’4 not satisfied they get 15
  • 5. 30 Fairness in Work Conserving Schedulers • If a scheduling policy guarantees fair resource sharing (e.g. Max-Min) it is also protective – a misbehaving source do not get more than fair share • Resources should be assigned based on QoS requirements – Max-Min weighted fair share – weights limited by conservation law • Fair work conserving scheduling policies – Fair Queuing – Processor Sharing – Generalized Processor Sharing – Weighted Fair Queuing
  • 6. 31 Fair Queuing • A router maintains multiple queues – separate queues for different traffic flows or classes – queues are serviced by a round-robin scheduler – empty queues are skipped over • Greedy connections face long delays, but other connections are not affected by it • Drawbacks – no service differentiation – the scheme penalizes flows with short packets ... 1 2 K
  • 7. 32 Processor Sharing • The server is able to serve multiple customers at the same time • Fluid model – traffic is infinitely divisible – service can be provided to infinitesimal amounts of data – the packet size does not count anymore – if N customer are served by server with capacity C, capacity seen by each customer is C / N – ideal model to provide an upper bound on the fairness of other schemes
  • 8. 33 Head-of-Queue Processor Sharing • Separate queues for different traffic flows or classes – head-of-queue packets are served from nonempty queues – following packets wait to be serviced – a nonempty queue is always served • Each queue is assigned a fair share of server capacity – when some flows become silent, their capacity is equally split among the other flows Max-Min fair share – independently of packet size ... 1 2 K 3 in service
  • 9. 34 Processor Sharing: Virtual time • 0 ≤ N(t) ≤ K, number of nonempty queues at time t • r(t) = C / N(t), capacity available to each nonempty queue when N(t) > 0 • tk,i, actual arrival time of packet i to queue k • Lk,i, length of packet i in queue k • Actual service time depends on r(t) – actual service time stretches or shrinks based on arrival and departure events • It is useful to define a virtual time scale v(t) – continuous piecewise linear function of t with slope 1/N(t) • Now it is possible to define – sk,i, virtual starting transmission time of packet i in queue k – fk,i, virtual ending transmission time of packet i in queue k
  • 10. 35 Processor Sharing: Example t2,2 = 2 L2,2 = 4 t1,2 = 2 L1,2 = 1 t3,1 = 3 L3,1 = 3 t2,1 = 1 L2,1 = 1 t1,1 = 0 L1,1 = 3 Queue 3Queue 2Queue 1 0 1 2 3 arrival time packet size 1 3 4 C = 1
  • 11. 36 Processor Sharing: Example t = N(t) = v(t) = 0 1 0 1 2 1 2 2 3 3 2 4 3 5 3 6 3 3 7 3 8 3 9 2 4 10 2 11 1 5 12 0 6 queue 1 queue 2 queue 3 t
  • 12. 37 Virtual starting and ending times Recursive definition • fk,i = sk,i + Lk,i/C • sk,i = max [ fk,i–1 , v(tk,i) ] In our example • s1,1 = 0, f1,1 = 3 • s2,1 = 1, f2,1 = 2 • s2,2 = 2, f2,2 = 6 • s3,1 = 2, f3,1 = 5 • s1,2 = 3, f1,2 = 4
  • 13. 38 Packet-based Processor Sharing • Real-life schedulers are not able to serve infinitesimal amounts of data • A packet-based scheduling policy that approximates the PS scheme can be implemented as follows – compute virtual starting and ending times as in the ideal PS – when a packet finishes its service, next packet to be serviced is the one with smallest virtual finishing time – In our example: s1,1 = 0, f1,1 = 3 s2,1 = 1, f2,1 = 2 s1,2 = 3, f1,2 = 4 s3,1 = 2, f3,1 = 5 s2,2 = 2, f2,2 = 6 ideal PS packet-based PS
  • 14. 39 Comparison with FIFO and FQ • Load = capacity • PS gives preference to short packets average delay of flows 2 and 3 smaller than FIFO
  • 15. 40 Comparison with FIFO and FQ • Load > capacity queue builds up • FQ: flow 2 is penalized, although has same load as flow 1 • PS gives preference to short packets and it’s fair
  • 16. 41 Generalized Processor Sharing • PS and its packet-level equivalent provide Max-Min fairness but do not differentiate resource allocation • Generalized Processor Sharing (GPS) is capable of differentiation by associating a weight to each flow • Each nonempty queue is serviced for an infinitesimal amount of data in proportion to the associated weight – server capacity is split among nonempty queues according to weights • GPS provides an exact Max-Min weighted fair share allocation
  • 17. 42 GPS: Formal Definition • GPS is a work conserving scheduler operating at fixed capacity C over K flows • Each flow is characterized by a positive real weight • is the amount of traffic from flow serviced in the interval • GPS server is defined as a server for which for any flow that is backlogged (i.e. has nonempty queue) throughout
  • 18. 43 GPS: Flow Rate • Summing over all flows • Each backlogged flow receives a service rate of • If a source rate is then such rate is always guaranteed independently of the other flows • number of backlogged queues at time • The service rate seen by flow when is with the sum taken over all backlogged queues
  • 19. 44 GPS: Virtual Time • Now virtual time definition must consider weights – only backlogged queues contribute to the virtual time computation – the sum of the weights of backlogged queues may change at arrival and departure times only • continuous piecewise linear function of t with slope • Actual arrival time of packet of flow is • Its length is • Virtual starting and ending transmission times are
  • 20. 45 GPS Emulation: Weighted Fair Queuing • It is a packet-based GPS – compute virtual starting and ending times as in the ideal GPS – when a packet finishes its service, next packet to be serviced is the one with smallest virtual finishing time • Increased computational complexity since scheduler – must keep track of the backlogged flows and their weights – must compute virtual finishing times and sort them out – must update virtual time at arrival and departure events
  • 22. 47 Comparison with FIFO Flow 1 now sends packets at the guaranteed rate = 0.5
  • 23. 48 Weighted Fair Queuing: Delay Bound • WFQ approximates GPS at packet level – Max-Min weighted fair share achieved – weights allow service differentiation • WFQ also keeps queuing delay bounded for well-behaved flows • Assume each flow shaped with a token bucket scheme, token bucket parameters for flow • Choose weights proportional to token rates • Assume all buckets full of tokens when transmission starts from all flows (worst case) – each flow sends a burst and then keeps transmitting at
  • 24. 49 Weighted Fair Queuing: Delay Bound • In case of GPS, each queue is filled up to and is both serviced and feed at rate • Since queue size cannot exceed , the maximum delay experienced by packets of flow is • In case of WFQ, the effect of servicing packets increases the delay, but this is still bounded • End-to-end queuing delay of flow through WFQ hops is actually bounded
  • 25. 50 Weighted Fair Queuing: Delay Bound • maximum packet size of flow • • server capacity at node maximum delay at the first node due to burst transmission (same as GPS) maximum delay when a packet arrives at each node just after its supposed starting time and must wait for preceding packet maximum delay due to packet-level service: each arriving packet must wait for the one currently in service
  • 26. 51 GPS Emulation: Weighted Round Robin • Each flows is characterized by its – weight – average packet size • The server divides each flow weight by its mean packet size to a obtain a normalized set of weights • Normalized weights are used to determine the number of packets serviced from each connection in each round • Simpler scheduler than WFQ • Mean packet size may not be known a-priori
  • 27. 52 GPS Emulation: Deficit Round Robin • DRR modifies WRR to handle variable packet sizes without knowing the mean packet size of each flow in advance – DRR associates each flow with a “deficit counter” – in each turn, the server attempts to serve one “quantum" worth of bits from each visited flow • A packet is serviced if the sum of the deficit counter and the quantum is larger than the packet size – if the packet receives service, its deficit counter is reduced by the packet size – if the packet does not receive service, a quantum is added to its deficit counter • During a visit, if connection is idle, its deficit counter is reset to 0 – prevents a connection from cumulating service while idle
  • 28. 53 Scheduling and admission control • Given a set of currently admitted connections and a descriptor for a new connection request, the network must verify whether it is able to meet performance requirements of new connection • It is also desirable that the admission policy does not lead to network underutilization • A scheduler define its “schedulable region” as the set of all possible combinations of performance bounds that it can simultaneously meet – resources are finite, so a server can only provide performance bounds to a finite number of connections • New connection requests are matched with the schedulable region of relevant nodes
  • 29. 54 Scheduling and admission control • Schedulable region is a technique for efficient admission control and a way to measure the efficiency of a scheduling discipline – given a schedulable region, admission control consists of checking whether the resulting combination of connection parameters lies within the scheduling region or not – the larger the scheduling region, the more efficient the scheduling policy No. of class 1 requests No. of class 2 requests (C1,C2) (C1MAX,0) schedulable region (0,C2MAX)