Characterising interdeparture times for bursty input streams in the queue with pooled renewal arrivals

A stationary queueing system is described in which a single server handles several competing arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. In the first instance, one of the streams has interarrival times given by a hyperexponential distribution, while all of the others are Poisson arrival streams. The principal results for this scenario are the Laplace-Stieltjes transform and the squared coefficient of variation, for the hyperexponential class, of the interdeparture time distribution. In the sequel these exact results are used as approximations of the case of general renewal interarrival streams. Numerical examples are given and the accuracy of the approximation is discussed.