Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

We consider two models of M=G=1 and G=M=1 type queueing systems with restricted accessibility. Let (V (t))t¿0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let n be his arrival time. In both models there is a capacity bound v∗ ∈ (0;∞): In Model I the amount of service given to the nth customer is equal to min[Sn; v∗ − V ( n−)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected i the currently used workload V ( n−) exceeds v∗, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods. c © 2000 Elsevier Science B.V. All rights reserved.