Repair systems with exchangeable items and the longest queue mechanism (Q1945442)

The authors consider a repair facility with one server and two arrival streams of failed items. Arrivals and service times are modelled classically: the arrival processes are independent Poisson processes, and the service times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The queueing policy is the longest queue rule: At the completion of a service, the repaired item is delivered to the base that has the largest number of failed items. The authors explain a correspondence between their model and the classical longer queue model. The authors obtain formulae for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. They also provide sojourn time distributions.