Stochastic decomposition in M/M/infinity queues with Markov modulated service rates
Motivated by the need to study transportation systems in which incidents cause traffic to slow down, we consider an M/M/infinity queueing system subject to random interruptions of exponentially distributed durations. System breakdowns, where none of the servers work, as well as partial failures, where all servers work with lower efficiency, are investigated. In both cases, it is shown that the number of customers present in the system in equilibrium is the sum of two independent random variables. One of these is the number of customers present in an ordinary M/M/infinity queue without interruptions.
stochastic decomposition queues markov modulated kummer functions