A linear algebraic approach to queueing theory

A survey of the basic formulas of queueing theory is presented, indicating their limitations in dealing with non-exponential service time distributions and non-steady-state behavior. The authors then describe a linear algebraic formulation which is a complete procedure for dealing with non-exponential servers. The formulation is invariant to a class of similarity transformations and thus does not depend on the phases used to describe the servers. The authors show how to treat M/G/1, G/M/1 and G/G/1 queues using this formalism. Finally, they show how transient properties of queueing systems can be calculated, using the same mathematical objects which were used for analyzing their steady-state properties