A max-algebra approach to modeling and simulation of tandem queueing systems

TL;DR

This paper introduces a max-algebra framework for modeling and simulating tandem queueing systems, enabling linear state equations, calculation of transition matrices from service times, and efficient performance analysis.

Contribution

It develops a novel max-algebra approach to model tandem queues with finite and infinite buffers, including methods to compute transition matrices and performance measures.

Findings

Transition matrices derived from service times

Representation of system performance measures

Efficient serial and parallel simulation procedures

Abstract

Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems theory, and it is determined by a transition matrix inherent in the system. The departure epochs of a customer from the queues are considered as state variables, whereas its service times are assumed to be system parameters. We show how transition matrices may be calculated from the service times, and present the matrices associated with particular models. We also give a representation of system performance measures including the system time and the waiting time of customers, associated with the models. As an application, both serial and parallel simulation procedures are presented, and their performance is outlined.