Open Access
October, 1980 A Duality Theorem for Phase Type Queues
V. Ramaswami, Marcel F. Neuts
Ann. Probab. 8(5): 974-985 (October, 1980). DOI: 10.1214/aop/1176994625


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.


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V. Ramaswami. Marcel F. Neuts. "A Duality Theorem for Phase Type Queues." Ann. Probab. 8 (5) 974 - 985, October, 1980.


Published: October, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0449.60066
MathSciNet: MR586780
Digital Object Identifier: 10.1214/aop/1176994625

Primary: 62K25

Keywords: Duality , Phase type distributions , Queueing theory

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • October, 1980
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