1. 1 GPS Example 2: Arrivals o Eleven Sources. First source gets 0.5. Other 10 sources get 0.05 each. First source sends 11 cells. 2-11 send one each at t=0. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 Time 01020 p 11 1 GPS Example 2: Arrivals

2. 2 GPS Example 2: Service o Each cell of the first source takes 2 units of time. Sources 2-11 take 20 units each. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 Time 01020 p 11 1

3. 3 WFQ: Service o Packets finish at the same time or earlier than GPS. Some packets finish much earlier. Long period of no service  Unfair. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 Time 01020 p 11 1

4. 4 Worst Case Fair Weighted Fair Queuing (WF2Q ) o WF2Q fixes the unfairness problem in WFQ. o WFQ: Among packets waiting in the system, pick one that will finish service first under GPS. o WF2Q: Among packets waiting in the system that have started service under GPS, select one that will finish first under GPS. o WF2Q provides service close to GPS (difference in packet service time bounded by max. packet size). o WF2Q+ is an simpler implementation of WF2Q o Refs: Jon Bennett, Hui Zhang.

5. 5 WF2Q: Service S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 Time 01020 p 11 1

6. 6 Stochastic Fair Queueing (SFQ) o Allows # of queues less than the number of flows o Hash to queues  O(1) time for enqueuing o Packets are serviced in round-robin o If buffers full, packet in the longest queue is pushed out o Known Results: O(1) operation. o # of queues needs to be a small multiple of # of ACTIVE flows rather than total number of flows o Known Problems: Flows hashing to the same queue not isolated o Refs: McKenney, Shreedhar and Varghese

7. 7 Deficit Round Robin (DRR) o Use hashing to assign flows to queues o Per-Queue Quota, Per-Queue Credit (called deficit) o Send packet if Credit  packet size o After service: Credit = Credit-packet size o Known Results: Fair. O(1). o Latency depends upon frame size = sum of max packet sizes = fn of # of flows o Ref: Shreedhar and Varghese

8. 8 DRR+ q Allows mixing delay critical shaped traffic with best effort q When a delay critical packet arrives at an empty queue, the queue is placed at the head of the round- robin list q Ref: Shreedhar and Varghese

9. 9 Surplus Round Robin (SRR) o Similar to DRR o Deficits (Credits) are allowed to be negative o Ref: Adiseshu et al, Floyd