Analysis of Transient Virtual Delay in a Finite-Buffer Queueing Model with Generally Distributed Setup Times

Time-dependent queueing delay (virtual waiting time) distribution conditioned by the initial level of buffer saturation is considered in a finite model with Poisson arrivals, generally distributed service times and setup times preceding the first processing in each busy period. Applying theoretical approach based on the idea of embedded Markov chain, integral equations and some results from linear algebra, a compact-form representation for the Laplace transform of queueing delay distribution is obtained. Analytical results are illustrated via numerical considerations confirmed by process-based discrete-event simulations.