SERIES OF SINGLE SERVER SYSTEMS WITH BATCH ARRIVALS - Georgieva, Magdalena (Matematichki Bilten, 1993)
In this paper we discuss a single server system with batch arrival with Poisson distribution for the interarrival time of the batches and exponential servicing time. The customers which arrive during the servicing time of one customer in the system, form another batch which leaves the system. In that way a new flow of customers is generated which is directed to another single server system. Continuing this procedure, we can define a series of single server systems. The main result of the paper is formulated in the theorem below, where we determine the distribution of the probabilities for the random variable \(X_{n+1}\) - the number of unserviced customers which leave the \(n^{th}\) system, as well as the first two moments and the variance.