Abstract
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.
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