This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.
Federgruen, Awi, and H. C. Tijms. "Computation of the stationary distribution of the queue size in an M/G/1 queueing system with variable service rate." Journal of Applied Probability 17, no. 2 (June 1980): 515-522.
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