The backlog process in queues with random service speed - Texas A&M University (TAMU) Scholar

This paper examines the backlog (total amount of unfinished work in the system) in a single server queue that works in a random environment. Specifically, the service speed is described by an exogenous (non-negative) environment process. We characterize the time-dependent backlog via a stochastic integral equation and use this equation to compute stationary performance measures. For the M/G/1 queue, our results lead to a generalization of the Pollaczek-Khintchine transform equation for backlog that explains why congestion is greater in a queue with random service speed than in an equivalent queue with constant service speed. We provide a numerical example that helps to illustrate our results. 1996 Taylor & Francis Group, LLC.

The backlog process in queues with random service speed Academic Article