A state-dependent queue alternating between arrivals and services

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.