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Heavy Traffic Queue Management Using Policy Based Approach and Network Calculus 1

S.Rajeev1 Senior Member IEEE, K.V.Sreenaath2

Dean - Research & Development, SNS College of Technology, Coimbatore 2 Security Engineer, Motorola India Pvt. Ltd., Bangalore

email : [email protected], [email protected] Abstract—Traffic management includes queuing, buffer management and scheduling that are key in delivering network efficiency. Effective management of the network requires appropriate queuing algorithm at the active router. Heavy traffic is the rate at which the processor can work close to the rate of arrival of work. Policy based queue management gives the flexibility to choose and implement queuing algorithm dynamically suiting different requirements. Network calculus is based on the mathematical theory of diods and in particular the Min-Plus diod. It is developed for efficiently managing the flow problems encountered in networking. In this paper we present the real time implementation of policy based queue management for heavy traffic using IXP 1200[1] network processor and Ponder Policy Toolkit[2] with appropriate model for Network Calculus. Index Terms—Policy Management, Heavy traffic analysis, Network processor, RED queuing

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I. INTRODUCTION

N heavy traffic, the processor ideal time is small due to the fact that the difference between the arrival and the service curve is negligible. When the idle time of the processor is very less then the queue management should be efficient enough so that the performance of the network is high. But unfortunately different queuing algorithms such as RED, REM, DropTail, SFQ and DRR are suitable for delivering efficiency in network with different needs. For example DropTail is useful when the emphasis is on the throughput alone whereas RED and REM is useful when the emphasis is on both throughput and bandwidth utilization. To handle these multiple requirements Policy Based Queue Management is employed. Policy is defined as “a definite goal, course or method of action to guide and determine present and future decisions.” [3] In general, policies can be seen as plans of an organization to achieve its objectives. This may involve a set of rules to govern the behavior of network and its components (resources, users, applications, etc.), and the specification of a set of actions to be performed.

II. HEAVY TRAFFIC CONDITION Let Q(t) denoted the size of the physical queue at real time t. The physical queue is parameterized by n, where the traffic intensity goes to unity as n → ∞, and Qn(t) denotes the size of the nth member of this sequence at real time t. Owing to the small difference between the arrival and service rates, the queue builds up over time. The heavy traffic condition,

1   1 n   bn  b   a, n d , n  as n → ∞

-----(1.1)

The traffic intensity is

n 

d , n a, n

----- (1.2) If b < 0 in ( 1.1) , so that the queues are barely stable, then, for any moderate initial condition the size builds up slowly to an asymptotic average of O(√n). If b > 0, so that the queue is barely unstable, then, its size goes to infinity, but slowly, so that at time nt there are O(√n ) queued. The basic arrival and service rates are usually very high, and it is more appropriate to scale the number queued, but not time. Then the parameter n denotes the basic size or speed of the system, and the difference between arrival and service rate in real time is O(√n ). A. Multiple Arrival Streams of Different Rates Heavy traffic consists of multiple stream of different rates where there are finite number of independent input streams, called Ak,n, 1 ≤ k ≤ k . It is assumed that the service time distributions do not depend on the arrival class. Let the kth arrival stream have interarrival times

{al , k , n , l  }

B. Frequent Arrivals For some centering constants ∆a,k,n that converge to 1/λa,k , k ≤ k, define



a, k, n

1 nt  al ,k ,n  (t )   1  a,k ,n  n l 1   

∆a,k ≡

----- (1.3)

For moderate frequent arrival, the heavy traffic condition is given by

1 1 1   k lim n k 1 a , k ,n  a , 0,n  d , n   0 n      ----- (1.4) C. Bursty Arrival In application where the interarrival or service intervals are correlated, the correlation usually arises from some specific aspects of the physical model, and not in the form of a process where the convergence to a wiener process is a priori obvious. Bursty in the sense, the arrival rate and service time vary with time. D. Queuing Delay Queuing delay depends largely on the rate at which traffic arrives at the queue, the transmission rate of the link, and the nature of the arriving traffic, that is, whether the traffic arrives periodically or whether it arrives in bursts. The average rate at which bits arrive at the queue is La bits/sec. The queue is very big, so that it can hold an infinite number of bits. The ratio La/R, called traffic intensity (a- packets/sec) R- transmission rate and L bits/packet, often plays an important role in estimating the extent of the queuing delay. If La/R > 1, then the average rate at which bits arrive at the queue exceeds the rate at which the bits can be transmitted from the queue. Unfortunately the queue will tend to increase without bound and queuing delay will approach infinity. The nature of the arriving traffic impacts the queuing delay when La/R