Distributed Admission Control and Congestion Pricing

1. Distributed Admission Control and Congestion Pricing Peter Key peterkey@microsoft.com http://research.microsoft.com/network/disgame.htm

2. Subplot … Can guarantees be provided using pricing alone? Refs: F.P. Kelly (Stats Lab, Cambridge Uni.), P.B Key , S.Zachary (Heriot-Watt Uni.),Distributed Admission Control, preprint

3. Outline • Introduction • Congestion Pricing • Adaptive Admission Control • Mathematical Framework • Examples • Binomial Model • Virtual Queue marking • Critical Timescales • Discussion Commodity markets and Futures

4. Resource system (‘network’) Resource j  Capacity Cj User /route r  Ajr links users to resources

5. Basic Idea • Users generate load (packets) • Network sends back signals (load dependent) • Signals : proportional to load • Act as feedback indicators • Represent pricing signals • marginal incremental costs (derivatives …) • congestion costs • real money or virtual / distributed mint

6. Optimisation Framework (for fairness) System optimum U is utility C is cost function,eg User optimum

7. Solution Consistent set of taxes (prices) and load exist s.t. EgNetwork chooses taxes, user chooses load, solution is network, user and System optimal. But dependent on Utility function, so ….

8. Matching prices to load • For bounded prices, have to match price load to capacity • ie, require maximum amount users prepared to pay < maximum network can charge • Eg, if xr satisfies then require

9. Admission Control • Send a number of probe packets through the network • Enter the network if none of these packets are marked • Assume: Poisson arrivals, rate  • Let a(mj) be probability accepted at node j independently

10. User policy M probe packets Enter if less than m probe Packets marked User /route r 

11. Product form distribution Equilibrium distribution for the number of calls in progress v a(n) v a(n-1) n n+1 n-1 n+1 n

12. Fixed Point Approximation • Define stationary acceptance probability for J={j}, R={r} • Then fixed point approximation for network has unique solution

13. Acceptance ProbabilitiesExample 1 • Eg , let 1-aj(mj) be probability any of a number of probe packets are marked • Eg for a burst-scale model, where there is long-range dependence

14. Rejection Probabilities & PDFs Rejection probabilities Equilibrium CDF n Setup: =50, thresholds 10, 20

15. PDFs n Setup: =50, thresholds 10, 20 Setup: =100, thresholds 10, 20

16. Shadow Prices (buffered) Fixed Service Rate packets Max Queue Length Q Q Mark all packets from start of ‘busy period’ until last packet loss. Queue Length Time

17. Virtual Queue Marking • Put arrivals into a virtual queue, and mark on this • Capacity capacity cv c, eg c • Buffer size bv b , eg b

18. Virtual Queue Example • Suppose we want to track derivative of queue , (or suppose cost=P[exceed thresh) • M/M/1 (can use other SRD processes) • Equate derivate to a VQ with reduced rate • For virtual queue, rate , thresh K-1, put

19. VQ Thresholds

20. average rate ms line rate m m s s Timescales Application Network Connection Seconds Critical timescale Reaction (RTT) ms Packet Level

21. Critical Timescales • Large deviation approach (many sources asymptotic – Courcoubetis and Weber) where t* and s* are extremals, t* is the critical timescale. If mark as shadow price, is typical marking time

22. Critical timescales for VQ • Eg for a Gaussian process, arrival rate , Hurst parameter H

23. Critical timescales • Example 1

24. Critical timescales • Example 2 • BUT, need to have critical timescale less than time between arrivals (for decisions to be independent) • This is (mean holding time)/(number of calls) in equilibrium 0 as n • Hence, • keep virtual queue small, just for cell scale

25. Congestion Prices (Timescales) 60 secs LAN) 1 Sec (Backbone)

26. Example 2 – packet marking • Mark packets if size of Virtual Queue exceeds threshold • IfM probe packets sent • where  is mean packet service time (if connections generate packets at rate r, service rate is c, then =r/c, and 1/  represents “capacity” of queue )

27. Rejection Probabilities & PDFs, VQ marking Rejection probabilities Equilibrium CDF n Setup: =50, thresholds 5,10

28. PDFs n Setup: =50, thresholds 5,10 Setup: =100, thresholds 5,10

29. Blocking vs. Marking (price) VQ marking, threshold K=10, capacity (1/)=100 Blocking marking 1 Probe packet 5 Probe packets

30. Mixing adaptive and non-adaptive traffic • Simple model: two types of traffic • Non-adaptive traffic, requires unit bandwidth • Adaptive traffic: reacts to signals can halve its bandwidth requirement • Suppose price (congestion marking probability) not to go above 0.2 • Gives acceptance boundaries

31. Price regions

32. Acceptance Boundaries

33. To give a price blocking of 10-4 Prop. Of adaptive traffic required Total arrival rate Capacity =25.5 (eg LAN with voice, PCM coding)

34. Discussion • Congestion pricing works well for adaptive applications • We have constructed a model for streams/flows where decisions made by end-systems • System is robust, and can be analysed /engineered

35. Facilitators • Critical timescales (of marking) small compared to interarrival times, (comparable to RTTs?) • Small buffers in Virtual Queue (compared to transmission delay) to detect quickly • Target loads below 100% … • Simple feedback signal, eg ECN bit/byte • Signal reflects costs • Prices need to match demand • User interface simple (risk apportionment)