In this paper, we propose an algorithm to calculate the higher moments of the busy period length of a discretetime M/G/1 type queue with finite buffer. The queueing model has a level-dependent transition probability matrix. Our algorithm is given as a set of recursive formulas which are derived from the relationship among the generating function matrices of the fundamental period. As an example...

We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue ...

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous...