The analysis and performance of batching arbiters

Abstract

A class of arbiters, known as batching arbiters, is introduced and defined. A particularly simple decentralised example of a batching arbiter is described, with motivation given for the batching arbiter model adopted. It is shown that under reasonable assumptions, batching arbiters can be described by a finite state Markov chain. The key steps in the analysis of the arbiter performance are the method of assigning states, evaluation of state transition probabilities and showing that the Markov chain is irreducible. Arbiter performance parameters are defined, such as proportion of time allocated to each requester and mean waiting time for each requester. Apart from results describing the steady state behavior of the arbiter for general system parameters, a number of limiting results are also obtained corresponding to light and heavy request loading. Finally, numerical results of practical interest are presented, showing the performance parameters of the arbiter versus request rates for various configurations.