Distributed Admission Control and Congestion Pricing Peter Key

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

Outline zIntroduction yCongestion Pricing zAdaptive Admission Control yMathematical Framework yExamples xBinomial Model xVirtual Queue marking xCritical Timescales zDiscussion Commodity markets and Futures

Resource system (network) Resource j Capacity C j User /route r A jr links users to resources

Basic Idea zUsers generate load (packets) zNetwork sends back signals (load dependent) zSignals : proportional to load yAct as feedback indicators yRepresent pricing signals xmarginal incremental costs (derivatives …) xcongestion costs xreal money or virtual / distributed mint

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

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

Matching prices to load zFor bounded prices, have to match price load to capacity zie, require maximum amount users prepared to pay < maximum network can charge zEg, if x r satisfies then require

Admission Control zSend a number of probe packets through the network zEnter the network if none of these packets are marked zAssume: Poisson arrivals, rate zLet a(m j ) be probability accepted at node j independently

User policy User /route r M probe packets Enter if less than m probe Packets marked

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

Fixed Point Approximation zDefine stationary acceptance probability for J={j}, R={r} zThen fixed point approximation for network has unique solution

Acceptance Probabilities Example 1 zEg, let 1-a j (m j ) be probability any of a number of probe packets are marked zEg for a burst-scale model, where there is long- range dependence

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

PDFs Setup: =50, thresholds 10, 20 n Setup: =100, thresholds 10, 20

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

Virtual Queue Marking zPut arrivals into a virtual queue, and mark on this zCapacity capacity c v c, eg c zBuffer size b v b, eg b

Virtual Queue Example zSuppose we want to track derivative of queue, (or suppose cost=P[exceed thresh) zM/M/1 (can use other SRD processes) zEquate derivate to a VQ with reduced rate zFor virtual queue, rate, thresh K-1, put

VQ Thresholds

Timescales Connection Reaction (RTT) Packet Level average rate Seconds line rate ms s ApplicationNetwork msms s Critical timescale

Critical Timescales zLarge 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

Critical timescales for VQ zEg for a Gaussian process, arrival rate, Hurst parameter H

Critical timescales zExample 1

Critical timescales zExample 2 yBUT, need to have critical timescale less than time between arrivals (for decisions to be independent) yThis is (mean holding time)/(number of calls) in equilibrium 0 as n zHence, ykeep virtual queue small, just for cell scale

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

Example 2 – packet marking zMark packets if size of Virtual Queue exceeds threshold zIfM probe packets sent zwhere 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 )

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

PDFs Setup: =50, thresholds 5,10 n Setup: =100, thresholds 5,10

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

Mixing adaptive and non- adaptive traffic zSimple model: two types of traffic yNon-adaptive traffic, requires unit bandwidth yAdaptive traffic: reacts to signals can halve its bandwidth requirement zSuppose price (congestion marking probability) not to go above 0.2 zGives acceptance boundaries

Price regions

Acceptance Boundaries

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

Discussion zCongestion pricing works well for adaptive applications zWe have constructed a model for streams/flows where decisions made by end-systems zSystem is robust, and can be analysed /engineered

Facilitators zCritical timescales (of marking) small compared to interarrival times, (comparable to RTTs?) zSmall buffers in Virtual Queue (compared to transmission delay) to detect quickly zTarget loads below 100% … zSimple feedback signal, eg ECN bit/byte zSignal reflects costs zPrices need to match demand zUser interface simple (risk apportionment)