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Queueing models with the server's vacations and/or priority-based scheduling can be used for the performance evaluation of many computer and communication systems. This book provides a comprehensive and accessible analysis of these queueing models in the framework of M/G/1 systems. The method of imbedded Markov chains, the delay cycle analysis, and the method of supplementary variables are extensively used to study the M/G/1, M/G/1 with vacations, and M/G/1 with priorities. Only a basic understanding of queueing systems is assumed. A comprehensive bibliography of books on queues and teletraffic engineering completes the volume.