A Duality Theorem for Phase Type Queues

V. Ramaswami · Marcel F. Neuts

13 citations0/0 files storedThe Annals of Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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.

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References

1980The N/G/1 queue and its detailed analysis 1978Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector 1978Renewal processes of phase type 1976Moment formulas for the Markov renewal branching process 1965On the maximum of the queue GI/M/1

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