On response time and cycle time distributions in a two-stage cyclic queue

Abstract

We consider a two-stage closed cyclic queueing model. For the case of an exponential server at each queue we derive the joint distribution of the successive response times of a custumer at both queues, using a reversibility argument. This joint distribution turns out to have a product form. The correlation coefficient is calculated and shown to be non-positive.

For the case of one general server and one exponential server we derive two approximations for the joint distribution of the response times. The numerical results based on these approximations are compared with simulation results. The first approximation which heavily relies on results for the M/G/1 queue with finite capacity, is somewhat complicated, but it yields exact marginal distributions and appears to be very accurate. The second one is less accurate, but very easily ???.