Combined delay and loss common-control queuing system

The paper presents a detailed study of a combined delay and loss common-control queuing system which has a limited waiting capacity. The common-control queuing system considered is one with a Poisson input, first-come-first-served queue discipline and a negative exponential distribution for both the operating time of the common control and the service time of the server. The stationary-state probabilities of the system, the loss probability, the waiting probability and the waiting-time distribution function are obtained in explicit form. It is shown that, using the unified approach (the notion of combined delay and loss), the system studied includes the pure-delay and pure-loss systems as special cases. In addition, many results reported in the literature can be derived from those presented in the paper.