On the design of a finite-capacity queue with phase-type service times and hysteretic control

Abstract We consider the design of a single-server queue with finite buffer capacity. Arrivals follow a Poisson distribution and service times have phase-type distributions. It is possible to switch the service rate between the normal and higher rates. A bi-level hysteretic control policy is considered where two trigger points, say u and l, are used for changes in service rate. When the number in the system exceeds u, the service rate is increased and it returns to the normal level only when the number in the system drops to l (0

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