The M/G/1 Queue with Finite Workload Capacity

Authors:
D. Perry;W. Stadje;S. Zacks
Affiliations:
Department of Statistics, University of Haifa, 31905 Haifa, Israel;Fachbereich Mathematik/Informatik, University of Osnabrück, 49069 Osnabrück, Germany;Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

We consider the M/G/1 queueing system in which customers whose admission to the system would increase the workload beyond a prespecified finite capacity limit are not accepted. Various results on the distribution of the workload are derived; in particular, we give explicit formulas for its stationary distribution for M/M/1 and in the general case, under the preemptive LIFO discipline, for the joint stationary distribution of the number of customers in the system and their residual service times. Furthermore, the Laplace transform of the length of a busy period is determined. Finally, for M/D/1 the busy period distribution is derived in closed form.