A rate balance principle and its application to queueing models

Binyamin Oz (), Ivo Adan and Moshe Haviv
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Binyamin Oz: University of Auckland
Ivo Adan: Technische Universiteit Eindhoven
Moshe Haviv: The Hebrew University of Jerusalem

Queueing Systems: Theory and Applications, 2017, vol. 87, issue 1, No 5, 95-111

Abstract: Abstract We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth-and-death-like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from $$n-1$$ n - 1 to $$n+1$$ n + 1 coincides with the corresponding rate from $$n+1$$ n + 1 to $$n-1$$ n - 1 . We demonstrate how useful this observation is by deriving well-known, as well as new, results for non-memoryless queues with state-dependent arrival and service processes. We also use the rate balance principle to derive new results for a state-dependent queue with batch arrivals, which is a model with non-birth-and-death-like transitions.

Keywords: Rate balance; G/M/1; M/G/1; Birth–death process; Batch arrivals; Conditional distribution; Residual lifetime; 60G17; 60K25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11134-017-9536-z

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