Transient Behaviour of the Interrupted Poisson Process
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1982 · Volume 44 · Issue 3
DOI: 10.1111/j.2517-6161.1982.tb01220.x
Abstract
Kuczura (1973) introduced the use of the Interrupted Poisson Process (IPP) as a simplified model for overflow telephone traffic, and derived some of its equilibrium properties. This paper presents the time-dependent factorial-moment generating function for the IPP. From this function are derived the joint moments of the numbers of calls in progress at any number of instants in time. In particular, the covariance of the numbers of calls in progress at any two instants leads to a formula for the variance of scan-measured traffic. The results make it possible to calculate the moments of various estimators of the variance of traffic. The paper also gives a new decomposition of interarrival times, and displays one limiting form of the IPP as a batch arrival process with geometrically distributed number of arrivals per batch. All these results are of perfectly general applicability. They add to the repertory of analytically tractable queuing processes. Likely fields of application are sickness insurance, equipment maintenance, transportation, neurophysiology and nuclear physics.
Keywords
overflow traffic, peaked traffic, variance estimation, batch arrivals, measured traffic
Enable JavaScript for citation tools and additional paper interactions.