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.
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This research was partly supported by Israel Science Foundation Grant No. 1319/11.
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Oz, B., Adan, I. & Haviv, M. A rate balance principle and its application to queueing models. Queueing Syst 87, 95–111 (2017). https://doi.org/10.1007/s11134-017-9536-z
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DOI: https://doi.org/10.1007/s11134-017-9536-z