A queue with independent and identically distributed arrivals

Journal of Applied Probability, vol. 62, pp. 319–346

Abstract

Abstract In this paper we consider the workload of a storage system with the unconventional feature that the arrival times, rather than the interarrival times, are independent and identically distributed samples from a given distribution. We start by analyzing the ‘base model’ in which the arrival times are exponentially distributed, leading to a closed-form characterization of the queue’s workload at a given moment in time (i.e. in terms of Laplace–Stieltjes transforms), assuming the initial workload was 0. Then we consider four more general models, each of them having a specific additional feature: (a) the initial workload being allowed to have any arbitrary non-negative value, (b) an additional stream of Poisson arrivals, (c) phase-type arrival times, (d) balking customers. For all four variants the transform of the transient workload is identified in closed form.

Authors 2

1. Michel Mandjes corresponding Aachen

   Leiden University · University of Amsterdam

   Affiliation as printed

   Leiden University and University of Amsterdam

2. Daniël Rutgers corresponding Aachen

   Leiden University

   Affiliation as printed

   Leiden University