THE BACKLOG PROCESS IN QUEUES WITH RANDOM SERVICE SPEED

This paper examines the backlog (total amount of unfinished work in th e system) in a single server queue that works in a 'random environment '. Specifically, the service speed is described by an exogenous (non-n egative) 'environment' process. We characterize the time-dependent bac klog via a stochastic integral equation and use this equation to compu te stationary performance measures. For the M/G/1 queue, our results l ead to a generalisation 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 servic e speed. We provide a numerical example that helps to illustrate our r esults.