Clearing Models for M/G/1 Queues

Authors:
Onno J. Boxma;David Perry;Wolfgang Stadje
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;Department of Statistics, University of Haifa, 31905 Haifa, Israel;Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

We consider M/G/1-type queueing systems with ‘disasters’, occurring at certain random times and causing an instantaneous removal of the entire residual workload from the system. After such a clearing, the system is assumed to be ready to start working again immediately. We consider clearings at deterministic equidistant times, at random times and at crossings of some prespecified level, and derive the stationary distribution of the workload process for these clearing times and some of their combinations.