The cyclic queue with one general and one exponential server

This is the authors' abstract. We don't add key points for this paper.

This paper considers the two-stage cyclic queueing model consisting of one general ( G ) and one exponential ( M ) server. The strong connection between the present model and the M/G/ 1 model (with finite waiting room) is exploited to yield the joint distribution of the successive response times of a customer at the G queue and the M queue. This result reveals a surprising phenomenon: in general there is a difference between the joint distribution of the two successive response times at (first) the G queue and (then) the M queue, and the joint distribution of the two successive response times at (first) the M queue and (then) the G queue. Another associated result is an expression for the cycle-time distribution. Special consideration is given to the case that the number of customers in the system tends to ∞, while the mean service times tend to 0 at an inversely proportional rate.