A Duality Theorem for Phase Type Queues

Abstract

A duality theorem of Heathcote exhibiting a relationship between first passage times of the queue length in the GI/M/1 queue and the busy period of its dual M/G/1 queue is generalized to the phase type queues GI/PH/1 and PH/G/1. The phase type distributions include a number of well-known models such as generalized Erlang and hyperexponential as special cases and form a versatile class with a number of interesting closure properties.