Server unavailability reduces mean waiting time in some batch service queuing systems

This article shows that in some queuing systems server unavailability is sometimes beneficial both to the system owner and to the customers. To be more specific, mean queue size and mean waiting time may decrease even in the presence of server vacations. To this end, we first derive the probability generating function of the batch service M/G^B/1 system with multiple vacations. We, then, consider the case of exponential service and vacation times and show that under some parameter combinations, mean queue size decreases even in the presence of server vacations. We discuss the implications of this phenomenon.