On One Approach to Study of Departure Process in Batch Arrival Queues with Multiple Vacations
نویسنده
چکیده
A batch arrival single-server queueing system of a general type is considered. At the end of each busy period the server begins a multiple vacation period when the service process is stopped. A new approach to the study of departure process in such a system is proposed. Using the formula of total probability and renewal theory we direct the analysis to that in the system without vacations. An explicit representation for the double transform of probability function of departure process is derived. The formula is written down by means of transforms of distributions describing the arrival and service processes, vacation times and components of a certain factorization identity of Wiener-Hopf type connected with these distributions.
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