# Time-dependent analysis of an M / M / c preemptive priority system with two priority classes

Queueing Systems, Jul 2017

We analyze the time-dependent behavior of an M / M / c priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least c high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most $$c - 1$$ high-priority customers. We then show how to compute the remaining Laplace transforms recursively, by making use of a variant of Ramaswami’s formula from the theory of M / G / 1-type Markov processes. While the primary focus of our work is on deriving Laplace transforms of transition functions, analogous results can be derived for the stationary distribution; these results seem to yield the most explicit expressions known to date.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs11134-017-9541-2.pdf

Jori Selen, Brian Fralix. Time-dependent analysis of an M / M / c preemptive priority system with two priority classes, Queueing Systems, 2017, 1-37, DOI: 10.1007/s11134-017-9541-2