Editorial introduction

Venkat Anantharam, Ralph L. Disney, Jean Walrand
1993 Queueing systems  
Queueing network theory has a long history, starting with the early attempts to model telephone networks. The subject has grown into a rich area being fed both by new applications and by the use of increasingly sophisticated tools from the theory of probability and stochastic processes. Thus one finds applications to diverse technologies such as packet switched and circuit switched communication networks, computer networks, personal communication networks, job shops, flexible manufacturing
more » ... ms, and to the timing analysis of distributed software systems. The mathematical tools being used include general point process and marked point process theory, Markov decision theory, martingales, renewal and regenerative processes, diffusion processes, perturbation analysis, and techniques from the theory of (max, +) algebras. This special issue of QUESTA was developed with the aim of demonstrating the vitality of the field to the extent possible within the framework of survey articles by some of the prominent researchers. We hope it will have the effect of catalyzing further developments in the area. The papers of Harrison and Nguyen and of Dai and Wang deal with the area of Browniaa models of queueing networks. The former paper is a survey of the area. It discusses how one can write down a Brownian approximation to queueing networks in heavy traffic based on heuristic arguments, and justifies these arguments in the case of single class networks and multiclass networks with feedforward routing. It focuses on the analysis of the distribution of sojourn times using Brownian approximations and offers a couple of numerical examples to illustrate how this approach can be used for performance analysis in practice. The latter paper is devoted to a counterexample 9 J.C. Baltzer AG Science Publishers
doi:10.1007/bf01158926 fatcat:cvr33c7wjbgdpclctchuyiozmu