A heterogeneous arrival and service queueing loss model

Abstract

AbstractConsider a single‐server exponential queueing loss system in which the arrival and service rates alternate between the paris (γ1, γ1), and (γ2, μ2), spending an exponential amount of time with rate cμi in (γi, μi), i = 1.2. It is shown that if all arrivals finding the server busy are lost, then the percentage of arrivals lost is a decreasing function of c. This is in line with a general conjecture of Ross to the effect that the “more nonstationary” a Poisson arrival process is, the greater the average customer delay (in infinite capacity models) or the greater the precentage of lost customers (in finite capacity models). We also study the limiting cases when c approaches 0 or infinity.