1. LOAD BALANCING IN PACKET SWITCHING Nick Bambos Stanford University *Joint work with Aditya Dua, Stanford

2. Load Balancing … QoS … Fairness Switching in data centers Switching in storage networks Video servers, multimedia streaming … Issues: load balancing, QoS, fairness … …

3. Background Lots of research on maximum throughput scheduling Much less on QoS Giles et al (1997), Li et al (1999), Rai et al (2001), Keslassy et al 2003), … Focus: … on alternative problem formulation

4. Model for Constrained Service When S is used in a time slot, Sq cells (1/0) are removed from queue q Empty queues (download content) in a load-balanced manner that is QoS-aware and fair … … Sq S2 S1 SQ … … ……

5. Input Queued Packet Switches 2x2 switch … simplest model (…not simplistic)… scales to NxN 1212 1111 2121 2222 11 22 01100110 Sa 10011001 Sb Service vectors Sa and Sb

6. Traffic Streams, Inter-Packet Deadlines, Rates Slotted time; packets/cells; all available at 0 Regular Traffic Stream X (1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1, …) Inter-Packet Deadlines = constant T … Rate = 1/T General Traffic Stream X (1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,1, …) Inter-Packet Deadlines = variable Inter-Packet Deadlines (IPD) … soft when exceeded … QoS degrades

7. The Basic Idea – Single Stream 1 Traffic Stream X… desirable (flow control) (0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1, …) Cumulative Traffic (0,0,0,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,6, …) Service Stream S… provided (0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,1, …) Cumulative Service (0,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,4,5,6,7,7,8, …) Deviation D = cumService – cumTraffic (0,1,2,1,1,0,0,0,0,-1,-1,-1,-1,-2,-2,-1,0,1,2,2,2, …)

8. The Basic Idea – Single Stream 2 (0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1, …) desirable traffic stream (0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,1, …) provided service stream Deviation D = cumService – cumTraffic (0,1,2,1,1,0,0,0,0,-1,-1,-1,-1,-2,-2,-1,0,1,2,2,2,… Service leads – unfair to other streams Service lags – QoS compromised Deviation 0 = (0,0,0,0,0,0, …) perfectly matched service to traffic

9. Controlled System Dynamics – 2x2 Switch Ex Evolution of Service-Traffic Deviation of 4 Entangled Streams 01100110 Sa 10011001 Sb D11 D12 D21 D22 D(n+1) = D(n) + Sa – X(n+1) D(n+1) = D(n) + Sb – X(n+1)

10. Cost Structure – 2x2 Switch Ex Per Slot C[D] = C[D11] + C[D12] + C[D21] + C[D22] C[Dxy] Dxy Service Leads Service Lags C = C[D(1)] + C[D(2)] + … + C[D(N)] Cumulative Control Problem: Find service sequence S(1), S(2), …,S(n),…,S(N) to miimize cumulative cost up to N … perfectly aligned traffic-service streams have 0 cost

11. Service Control C[Dxy] Dxy Service Leads Service Lags Control (DP Formulation) Service sequence S(1), S(2), …,S(n),…,S(N) minimizing cumulative cost up to N Summary of Controls: - Myopic policies are good (Prop) … and easy for 2x2 switches - For NxN switches too many permutations … check 2x2 neighbors (Giaccone et al 2003) … convex relaxations

12. Performance - 3x3 Switch 3x3 switch … 6 service configurations Benchmark … round-robin on 6 configurations 150,000 packets C[D] = |D| IPDs = 4/2 from MC Policies … myopic / exhaustive … myopic / neighbors 2x2 … myopic / convex relaxation

13. Symmetric Load / IPDs

14. Asymmetric Load / IPDs

15. Conclusions Load balancing, QoS, and fairness can be captured into the same model The model operates on micro time-scales (IPD), as opposed to macro (rates) Versions of the formulation/solution must be tuned to particular situations

16. Thank You!