Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the first queue and arbitrarily distributed service times, which for any customer are identical in both queues. For this tandem queue, we relate the tail behaviour of the sojourn time...

AMS classifications: 60K25, 90B22.

In this note a conjecture of Balachandran and Tijms [Balachandran, K. R., H. C. Tijms. 1975. On the D-policy for the M/G/1 queue. Management Sci. 21 1073-1076.] concerning the optimality of the D-policy over the N-policy in an M/G/1 queueing system is proved, using an inequality for renewal...

This paper considers the supremum m of the service times of the customers served in a busy period of the M[+45 degree rule]G[+45 degree rule]1 queueing system. An implicit expression for the distribution m(w) of m is derived. This expression leads to some bounds for m(w), while it can also be...

We consider a series of queues with Poisson input. Each queueing system contains an infinite number of service channels. The service times in each channel have a general distribution. For this M/G[infinity] tandem model we obtain the joint time-dependent distribution of queue length and residual...