Parallel exponential queues with dependent service rates

A system of two parallel single-server exponential queues is considered. These queues operate independently except that the service rate in each queue changes whenever the other queue is empty. By treating one of the queues as bounded, this model can be shown to have a matrix-geometric steady state vector which can be computed efficiently. Algorithms are also developed to compute the characteristics of the departure stream of customers from each queue. Some numerical results are presented, and based on these results an efficient approximation scheme for the system is developed which may possibly be extended to systems with more than two parallel queues.