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- Title
A rate balance principle and its application to queueing models.
- Authors
Oz, Binyamin; Adan, Ivo; Haviv, Moshe
- 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 $$n-1$$ to $$n+1$$ coincides with the corresponding rate from $$n+1$$ to $$n-1$$ . 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.
- Subjects
BIRTH rate; DEATH rate; QUEUEING networks; APPLICATION servers (Computer software); STOCHASTIC processes
- Publication
Queueing Systems, 2017, Vol 87, Issue 1/2, p95
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-017-9536-z