1. Lecture 4#-1 Scheduling: Buffer Management

2. Lecture 4#-2 The setting

3. Lecture 4#-3 Buffer Scheduling  Who to send next?  What happens when buffer is full?  Who to discard?

4. Lecture 4#-4 Requirements of scheduling  An ideal scheduling discipline m is easy to implement m is fair and protective m provides performance bounds  Each scheduling discipline makes a different trade-off among these requirements

5. Lecture 4#-5 Ease of implementation  Scheduling discipline has to make a decision once every few microseconds!  Should be implementable in a few instructions or hardware m for hardware: critical constraint is VLSI space m Complexity of enqueue + dequeue processes  Work per packet should scale less than linearly with number of active connections

6. Lecture 4#-6 Fairness  Intuitively m each connection should get no more than its demand m the excess, if any, is equally shared  But it also provides protection m traffic hogs cannot overrun others m automatically isolates heavy users

7. Lecture 4#-7 Max-min Fairness: Single Buffer m Allocate bandwidth equally among all users m If anyone doesn’t need its share, redistribute m maximize the minimum bandwidth provided to any flow not receiving its request m Ex: Compute the max-min fair allocation for a set of four sources with demands 2, 2.6, 4, 5 when the resource has a capacity of 10. s1= 2; s2= 2.6; s3 = s4= 2.7 m More complicated in a network.

8. Lecture 4#-8 FCFS / FIFO Queuing  Simplest Algorithm, widely used.  Scheduling is done using first-in first-out (FIFO) discipline  All flows are fed into the same queue

9. Lecture 4#-9 FIFO Queuing (cont ’ d)  First-In First-Out (FIFO) queuing m First Arrival, First Transmission m Completely dependent on arrival time m No notion of priority or allocated buffers m No space in queue, packet discarded m Flows can interfere with each other; No isolation; malicious monopolization; m Various hacks for priority, random drops,...

10. Lecture 4#-10 Priority Queuing  A priority index is assigned to each packet upon arrival  Packets transmitted in ascending order of priority index. m Priority 0 through n-1 m Priority 0 is always serviced first  Priority i is serviced only if 0 through i-1 are empty  Highest priority has the m lowest delay, m highest throughput, m lowest loss  Lower priority classes may be starved by higher priority  Preemptive and non-preemptive versions.

11. Lecture 4#-11 Priority Queuing Transmission link Packet discard when full High-priority packets Low-priority packets Packet discard when full When high-priority queue empty

12. Lecture 4#-12 Round Robin: Architecture Flow 1 Flow 3 Flow 2 Transmission link Round robin Hardware requirement: Jump to next non-empty queue r Round Robin: scan class queues serving one from each class that has a non-empty queue

13. Lecture 4#-13 Round Robin Scheduling  Round Robin: scan class queues serving one from each class that has a non-empty queue

14. Lecture 4#-14 Round Robin (cont’d)  Characteristics: m Classify incoming traffic into flows (source- destination pairs) m Round-robin among flows  Problems: m Ignores packet length (GPS, Fair queuing) m Inflexible allocation of weights (WRR,WFQ)  Benefits: m protection against heavy users (why?)

15. Lecture 4#-15 Weighted Round-Robin  Weighted round-robin m Different weight w i (per flow) m Flow j can sends w j packets in a period. m Period of length  w j  Disadvantage m Variable packet size. m Fair only over time scales longer than a period time. If a connection has a small weight, or the number of connections is large, this may lead to long periods of unfairness.

16. Lecture 4#-16 DRR algorithm  Choose a quantum of bits to serve from each connection in order.  For each HOL (Head of Line) packet, m if its size is <= (quantum + credit) send and save excess, m otherwise save entire quantum. m If no packet to send, reset counter (to remain fair)  Each connection has a deficit counter (to store credits) with initial value zero.  Easier implementation than other fair policies m WFQ

17. Lecture 4#-17 Deficit Round-Robin  DRR can handle variable packet size 1500 300 1200 20001000 Second Round First Round Head of Queue A B C 0 Quantum size : 1000 byte  1st Round m A’s count : 1000 m B’s count : 200 (served twice) m C’s count : 1000  2nd Round m A’s count : 500 (served) m B’s count : 0 m C’s count : 800 (served) 500

18. Lecture 4#-18 DRR: performance  Handles variable length packets  Backlogged source share bandwidth equally  Preferably, packet size < Quantum  Simple to implement m Similar to round robin

19. Lecture 4#-19 Generalized Processor Sharing

20. Lecture 4#-20 Generalized Process Sharing (GPS)  The methodology: m Assume we can send infinitesimal packets single bit m Perform round robin. At the bit level  Idealized policy to split bandwidth  GPS is not implementable  Used mainly to evaluate and compare real approaches.  Has weights that give relative frequencies.

21. Lecture 4#-21 GPS: Example 1 50 60 30 Packets of size 10, 20 & 30 arrive at time 0

22. Lecture 4#-22 GPS: Example 2 5 15 30 40 45 Packets: time 0 size 15 time 5 size 20 time 15 size 10

23. Lecture 4#-23 GPS: Example 3 5 15 30 45 60 Packets: time 0 size 15 time 5 size 20 time 15 size 10 time 18 size 15

24. Lecture 4#-24 GPS : Adding weights  Flow j has weight w j  The output rate of flow j, R j (t) obeys:  For the un-weighted case (w j =1):

25. Lecture 4#-25  Non-backlogged connections, receive what they ask for.  Backlogged connections share the remaining bandwidth in proportion to the assigned weights.  Every backlogged connection i, receives a service rate of : Fairness using GPS Active(t): the set of backlogged flows at time t

26. Lecture 4#-26 GPS: Measuring unfairness  No packet discipline can be as fair as GPS m while a packet is being served, we are unfair to others  Degree of unfairness can be bounded  Define: work A (i,a,b) = # bits transmitted for flow i in time [a,b] by policy A.  Absolute fairness bound for policy S m Max (work GPS (i,a,b) - work S (i, a,b))  Relative fairness bound for policy S m Max (work S (i,a,b) - work S (j,a,b)) assuming both i and j are backlogged in [a,b]

27. Lecture 4#-27 GPS: Measuring unfairness  Assume fixed packet size and round robin  Relative bound: 1  Absolute bound: < 1  Challenge: handle variable size packets.

28. Lecture 4#-28 Weighted Fair Queueing

29. Lecture 4#-29 GPS to WFQ  We can ’ t implement GPS  So, lets see how to emulate it  We want to be as fair as possible  But also have an efficient implementation

30. Lecture 4#-30

31. Lecture 4#-31 Queue 1 @ t=0 Queue 2 @ t=0 GPS:both packets served at rate 1/2 Both packets complete service at t=2 t 1 1 2 0 Packet-by-packet system (WFQ): queue 1 served first at rate 1; then queue 2 served at rate 1. Packet from queue 1 being served Packet from queue 2 being served Packet from queue 2 waiting 1 t 1 2 0 GPS vs WFQ (equal length)

32. Lecture 4#-32 Queue 1 @ t=0 Queue 2 @ t=0 2 1 t 3 0 2 Packet from queue 2 served at rate 1 GPS: both packets served at rate 1/2 queue 2 served at rate 1 Packet from queue 1 being served at rate 1 Packet from queue 2 waiting 1 t 1 2 0 3 GPS vs WFQ (different length)

33. Lecture 4#-33 Queue 1 @ t=0 Queue 2 @ t=0 1 t 1 2 0 WFQ: queue 2 served first at rate 1; then queue 1 served at rate 1. Packet from queue 1 being served Packet from queue 2 being served Packet from queue 1 waiting 1 t 1 2 0 GPS: packet from queue 1 served at rate 1/4; Packet from queue 2 served at rate 3/4 GPS vs WFQ Weight: Queue 1=1 Queue 2 =3 Packet from queue 1 served at rate 1

34. Lecture 4#-34 Completion times  Emulating a policy: m Assign each packet p a value time(p). m Send packets in order of time(p).  FIFO: m Arrival of a packet p from flow j: last = last + size(p); time(p)=last; m perfect emulation...

35. Lecture 4#-35 Round Robin Emulation  Round Robin (equal size packets) m Arrival of packet p from flow j: m last(j) = last(j)+ 1; m time(p)=last(j);  Idle queue not handle properly!!! m Sending packet q: round = time(q) m Arrival: last(j) = max{round,last(j)}+ 1 m time(p)=last(j);  What kind of low level scheduling?

36. Lecture 4#-36 Round Robin Emulation  Round Robin (equal size packets) m Sending packet q: m round = time(q); flow_num = flow(q); m Arrival: m last(j) = max{round,last(j)} m IF (j < flow_num) & (last(j)=round) THEN last(j)=last(j)+1 m time(p)=last(j);  What kind of low level scheduling?

37. Lecture 4#-37 GPS emulation (WFQ)  Arrival of p from flow j: m last(j)= max{last(j), round} + size(p); m using weights: last(j)= max{last(j), round} + size(p)/w j ;  How should we compute the round? m We like to simulate GPS: m round(t+x) = round(t) + x/B(t) m B(t) = active flows  A flow j is active while round(t) < last(j)

38. Lecture 4#-38 WFQ: Example (equal size) Time 0: packets arrive to flow 1 & 2. last(1)= 1; last(2)= 1; Active = 2 round (0) =0; send 1 Time 1: A packet arrives to flow 3 round(1) = 1/2; Active = 3 last(3) = 3/2; send 2 Time 2: A packet arrives to flow 4. round(2) = 5/6; Active = 4 last(4) = 11/6; send 3 Time 2+2/3: round = 1; Active = 2 Time 3 : round = 7/6 ; send 4; Time 3+2/3: round = 3/2; Active = 1 Time 4 : round = 11/6 ; Active=0

39. Lecture 4#-39 Worst Case Fair Weighted Fair Queuing (WF 2 Q)

40. Lecture 4#-40 Worst Case Fair Weighted Fair Queuing (WF 2 Q)  WF 2 Q fixes an unfairness problem in WFQ. m WFQ: among packets waiting in the system, pick one that will finish service first under GPS m WF 2 Q: among packets waiting in the system, that have started service under GPS, select one that will finish service first GPS  WF 2 Q provides service closer to GPS m difference in packet service time bounded by max. packet size.

41. Lecture 4#-41

42. Lecture 4#-42

43. Lecture 4#-43

44. Lecture 4#-44

45. Lecture 4#-45 Multiple Buffers

46. Lecture 4#-46 Buffers  Input ports  Output ports  Inside fabric  Shared Memory  Combination of all Buffer locations Fabric

47. Lecture 4#-47 Input Queuing fabric Inputs Outputs

48. Lecture 4#-48 Input speed of queue – no more than input line Need arbiter (running N times faster than input) FIFO queue Head Of Line (HOL) blocking. Utilization: Random destination 1- 1/e = 59% utilization due to HOL blocking Input Buffer : properties

49. Lecture 4#-49 Head of Line Blocking

50. Lecture 4#-50

51. Lecture 4#-51

52. Lecture 4#-52  The fabric looks ahead into the input buffer for packets that may be transferred if they were not blocked by the head of line.  Improvement depends on the depth of the look ahead.  This corresponds to virtual output queues where each input port has buffer for each output port. Overcoming HOL blocking: look-ahead

53. Lecture 4#-53 Input Queuing Virtual output queues

54. Lecture 4#-54  Each output port is expanded to L output ports  The fabric can transfer up to L packets to the same output instead of one cell. Overcoming HOL blocking: output expansion Karol and Morgan, IEEE transaction on communication, 1987: 1347-1356

55. Lecture 4#-55 fabric L Input Queuing Output Expansion

56. Lecture 4#-56 Output Queuing The “ideal” 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2

57. Lecture 4#-57 Output Buffer : properties  No HOL problem  Output queue needs to run faster than input lines  Need to provide for N packets arriving to same queue  solution: limit the number of input lines that can be destined to the output.

58. Lecture 4#-58 Shared Memory a common pool of buffers divided into linked lists indexed by output port number FABRIC MEMORY

59. Lecture 4#-59 Shared Memory: properties Packets stored in memory as they arrive Resource sharing Easy to implement priorities Memory is accessed at speed equal to sum of the input or output speeds How to divide the space between the sessions