Distribution of total flow of calls in group arrival queueing systems (Q1103515)

Queueing systems with group arrival of calls are considered in which the instants of arrival form a very simple flow. In addition to its arrival time, each cell is characterized also by its length, and the joint distribution function of the length of a call and of its service time is assigned. For the case of zero initial conditions, the Laplace-Stieltjes transform \(\delta\) (s,t) is obtained for the total flow of calls present at a given time t in a system with infinitely many servers, as well as the Laplace transform with respect to t of the function \(\delta\) (s,t) for a system with infinite queue and a single server.