An analytical method for the calculation of the number of units at the arrival instant in a discrete time G/G/1‐queueing system with batch arrivals

In this paper, we analyze a G/G/1‐queueing system with batch arrivals in the discrete time domain. On the basis of the waiting time distribution, we present an analytical approach for the calculation of the number of units in the queue at the arrival instant. This approach is exact within an ϵ‐environment. In addition, the computing times are low such that a huge set of computations can be performed in a short time. We close our paper with a set of numerical experiments. Our research is motivated through various applications in the field of logistics, where it is of important interest to know the distribution of the number of units waiting to be proceeded at the moment of a new arrival.