1 Objectives Analysis Overview Investigate effect of packet - PDF document

On Packet Marking Function of Active Contents Queue Management Mechanism: Should I t Be Linear, Concave, or Convex? � Introduction – RED (Random Early Detection) Hiroyuki Ohsaki and – Research Objectives Masayuki Murata Analysis � – Derivation of Average Queue Occupancy – Derivation of Optimal Packet Marking Function Graduate School of � Numerical Examples Information Science and – Comparison of Packet Marking Functions: Technology, Osaka � Linear, Concave, and Convex University, Japan � Conclusion 1 2 Background RED Known Problems � AQM (Active Queue Management) mechanisms � Parameter sensitivity – Studied by many researchers – Effectiveness is dependent on four control parameters (minth, maxth, maxp, wq) – Supports the congestion control mechanism of TCP – Average queue length is dependent on traffic load � RED (Random Early Detection) � i.e., the number of active TCP connections – A representative AQM mechanism � Parameter tuning difficulty – Randomly discards an arriving packet – The optimal setting of control parameters is � Keeps the average queue length small dependent on several factors � Achieves high link utilization � More deeply understanding on RED is necessary – Its operation algorithm is quite simple 3 4 Question on RED Packet Marking RED Packet Marking Probability Probability Analytically known facts � RED randomly discards an arriving packet with a � probability proportional to its average queue length – TCP throughput is inversely proportional to p^ (1/2) � p: the packet loss probability in the network packet marking probability 1.0 – For M/M/1 queue, the average queue length is (rho/(1-rho)) � rho: utilization factor normal operating region – So, should the packet marking probability not be changed linearly to the average queue length? � Question maxp – Whether the packet marking probability should be proportional to the average queue length or not? minth maxth 5 6 average queue length 1

Objectives Analysis Overview � Investigate effect of packet marking function on its performance � 1. Replace the packet marking function of RED with a – Steady state performance generic function f(x) – Transient state performance � 2. Combine two analytic models Show how packet marking function should be determined � – Stochastic model of TCP window size – Utilize analytic results of TCP and RED steady state analyses – Deterministic model of RED queue length � Consider three classes of packet marking functions � 3. Analyze toward what value the average queue – Linear, concave, and convex length converges... – Show which packet marking functions is the best... � for good transient state performance and robustness – for a given average queue length 7 8 1. Replace Packet Marking Function and Define Queue Occupancy 2. Combining Two Analytic Models � The packet marking function is replaced by � Expected value of TCP window size: w(p) – b: the number of packets required for returning an ACK packet – p: the packet loss probability in the network � Introduce “queue occupancy” 9 10 3. Analyze Average Queue Length 2. Combining Two Analytic Models (Cont’d) Convergence Point � Queue length of RED in steady state: q � Average queue length convergence point: q(x) – N: the number of TCP connections – w: TCP window size – B: maximum transmission capacity of RED router – tau: two-way propagation delay of TCP connection � Queue occupancy in steady state: x^ * 11 12 2

Effect of Packet Marking Function Optimal Packet Marking Function � x^ * becomes a linear function if f(x) is given by To optimize the steady state and transient state performances... � – f(x) must be dynamically changed according to N � N: the number of active TCP connections � However, the above function is impractical since... – RED has no capability to know the number of TCP connections Question � – For practical purposes, what type of packet marking function is the best for steady state and transient state performances? 13 14 Three Packet Marking Function Classes: Linear, Concave, Convex RED Packet Marking Probability � Linear � RED randomly discards an arriving packet with a probability proportional to its average queue length packet marking probability 1.0 � Concave normal operating region convex � Convex maxp linear concave minth maxth 15 16 average queue length RED Queue Occupancy (Linear Case) RED Queue Occupancy (Concave Case) • medium steady state • medium steady state • large steady state • large steady state queue occupancy queue occupancy queue occupancy queue occupancy • unstable transient • unstable transient • stable transient • stable transient state performance state performance state performance state performance 17 18 3

RED Queue Occupancy (Convex Case) Conclusion � Analyze effect of packet marking function on RED's performance – Steady state performance – Transient state performance Show how the packet marking function should be determined � – Utilize analytic results of TCP and RED steady state analyses – Derive the optimal packet marking function � Consider three classes of packet marking functions • small steady state • small steady state – Linear, concave, and convex queue occupancy queue occupancy – Show RED with concave packet marking function is the best... • unstable transient • unstable transient � in terms of good transient state performance and state performance state performance robustness 19 20 4