Queueing theory, generally considered a branch of operations research, is applicable in a wide variety of situations encountered in commerce, business, industry, public service, and engineering.

Most queueing applications and a large part of queueing theory are based on the assumption that arriving flows form a Poisson process. However, for some special applications, this assumption is inadequate; thus, alternative mathematical models are expected to be employed to simulate arriving flows. A doubly stochastic Poisson process, for example, is better than a Poisson process, when used to measure the number of claims due to a catastrophic event.

This paper discusses a single-sever queueing system with a doubly stochastic Poisson arriving flow, under heavy traffic conditions. After giving a brief introduction to this special queueing model in Sections 1 and 2, the authors formulate the main result of this paper, a theorem on the existence of a limiting regime, in Section 3. In the next two sections, they discuss different cases of convergence of a limiting stationary queue length under heavy traffic. Several examples of computations of coefficient sigma² are also presented, in Section 6.

Overall, this is a well-written paper that should give interested readers a good sense of the queueing theory of a special model of arriving flows, such as a doubly stochastic Poisson process.