A rate balance principle and its application to queueing models

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.