In this paper we study the busy period in GI/G/1 work-conserving queues. We give the exact asymptotics of the tail distribution of the busy period under the light-tailed assumptions. We also study the workload process in the M/G/1 system conditioned to stay positive.

We consider an M/G/1 queue with subexponential service times. We give a simple derivation of the global and local asymptotics for the busy period. This analysis relies on the explicit formula for the joint distribution for the number of customers and the length of the busy period of the M/G/1 queue. 2000 Mathematics Subject Classification: 60K25, 60G50, 60F10.

This paper investigates a discrete-time impatient customer queue with Bernoulli-schedule vacation interruption. The  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. Cost analysi...

this paper investigates a discrete-time impatient customer queue with bernoulli-schedule vacation interruption. the  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. we obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. cost an...