A state-dependent queue alternating between arrivals and services

P.R. Parthasarathy and R. Sudhesh

International Journal of Operational Research, 2010, vol. 7, issue 1, 16-30

Abstract: A queueing system usually involves an arrival process, service time distribution, service discipline, system capacity, etc. and steady-state performance measures extensively studied. However, time-dependent probabilities are important in applications and they do not involve convergence conditions. Further, several different models can have the same steady-state probabilities. We consider a novel state-dependent queueing system which alternating between arrival and service-states. We assume that the arrival, service and transfer rates depend on the number present in the system. Time-dependent system size probabilities and the duration of the busy period are obtained in a closed form for state-independent rates. We present numerical illustrations when the parameters are state-dependent. We have employed Continued Fractions effectively to achieve these transient results for this complex system.

Keywords: busy period; continued fractions; interrupted Poisson process; state-dependent rates; transition probabilities; state-dependent queueing. (search for similar items in EconPapers)
Date: 2010
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