Waiting time estimates in symmetric ATM-oriented rings with the destination release of used slots

This paper considers the basic access mechanism in asynchronous transfer mode (ATM)-oriented rings which, like Orwell, ATM ring, and ALine, apply destination release of used slots. The released slots may be reused by the destination station, or in some protocols, they must be given to the next station. Such a mechanism can be modeled by a multiple-server multiqueue system, where switchover times between consecutive polling instants of the queues are nonzero. The server polls the queues according to a certain polling discipline, which is dependent on the service time. This paper presents approximate mean minipacket waiting times in such systems. The approximation is based on a polling queueing model with Markovian server routing. Poisson arrivals and a symmetric workload model for minipackets having a full and partial traffic matrix are assumed. The performance characteristics are compared between the alternative option

Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Markovian polling systems with an application to wireless random-access networks

Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating function of) the joint queue length distribution conditioned on a point in time when the server visits a certain queue. From this functional equation, expressions for the (cross-)moments of the queue lengths follow. We also derive a pseudo-conservation law for this class of polling systems. Using these results, we compute expressions for certain system parameters that minimise the total expected amount of work in systems that arise from the wireless random-access network setting. In addition, we derive approximations for those parameters that minimise a weighted sum of mean waiting times in these systems. Based on these expressions, we also present an adaptive control algorithm for finding the optimal parameter values in a distributed fashion, which is particularly relevant in the context of wireless random-access networks

Queue-length balance equations in multiclass multiserver queues and their generalizations

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for {\em multidimensional} queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships, and are obtained for any external arrival process and state dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (i) providing very simple derivations of some known results for polling systems, and (ii) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a non-stationary framework

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)