An analytical method for the calculation of the waiting time distribution of a discrete time G/G/1-queueing system with batch arrivals

This paper presents an analytical method to calculate the waiting time distribution for the G/G/1-queueing system with batch arrivals. Using the discrete time scale, it is possible to calculate the distribution of the waiting times and the idle times of a G/G/1-queueing system based on the Wiener–Hopf factorization. The influence of batch arrivals on the waiting time distribution is analyzed. The waiting time distribution is calculated for batch arrivals with both constant and stochastic batch sizes. The effect of stochastic batch sizes on the waiting process is highlighted. With the developed methods, it is possible to obtain congestion measures of high precision for logistic systems. The analytical results are evaluated by simulation. Several numerical examples are presented to emphasize the quality of the introduced methods.