Approximation of discrete-time polling systems via structured Markov chains

We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routing. The key step of our approximation is the translation of the polling system to a structured Markov chain, while truncating all but one queue. Numerical experiments show that the approximation is very accurate in general. Our study is motivated by networks on chips with multiple masters (e.g., processors) sharing a single slave (e.g., memory)

A two-level traffic shaper for an on-off source

This paper studies a two-level traffic shapero The cell arrival process is modeled by an on-off fluid source. The output rate of the shaper is regulated by the content of a finite token bank. Our interest focuses on the stationary joint distribution of the content of the cell buffer and the content of the token bank, from which various performance measures such as the steady-state cell delay and burst duration can be obtained. The system is analysed using an approximative model based on a stochastic discretization of the content of the token bank. We believe that this discretization technique has much wider applicability. Numerical results show the quality of the approximation and demonstrate the effect of the shaping mechanism

A coupled processor model with simultaneous arrivals and ordered service requirements

We study a coupled processor model with simultaneous arrivals. Under the assumption of ordered input, the Laplace-Stieltjes transform of the joint stationary amount of work in the system can be explicitly calculated by relating it to the amount of work in a parallel queueing system without coupling. This relation is first exploited for the system with two coupled queues. The method is then extended to higher dimensions. Keywords: Coupled processors; multivariate workloa

End-to-end delays in polling tree networks

We consider a tree network of polling stations operating in discrete-time. Packets arrive from external sources to the network according to batch Bernoulli arrival processes. We assume that all nodes have a service discipline that is HoL-based. The class of HoL-based service disciplines contains for instance the Bernoulli and limited service disciplines, and hence also the classical exhaustive and 1-limited. We obtain an exact expression for the overall mean end-to-end delay, and an approximation for the mean end-to-end delay of packets per source. The study is motivated by Networks on Chips where multiple processors share a single memory

Polling systems with regularly varying service and/or switchover times

We consider a polling system consisting of K queues and a single server S who visits the queues in a cyclic order. The polling discipline in each queue is the gated or exhaustive service discipline. We investigate the tail behaviour of the waiting time distributions at the various queues in the case that at least one of the service time or switchover time distributions has a regularly varying tail

Fitting discrete distributions on the first two moments

In this paper we present a simple method to fit a discrete distribution on the first two moments of a given distribution. With the fitted distribution we solve approximately Lindley's equation for the discrete-time DIGl1 queue using a moment-iteration method. Numerical results show excellent performance of the method. Key words: two-moment fits, discrete distributions, Lindley's equation, moment-iteration method