Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
An MX/G/1 queueing system with a setup period and a vacation period
Queueing Systems: Theory and Applications
A batch arrival queue with a vacation time under single vacation policy
Computers and Operations Research
Application of the Superposition of Renewal Processes to the Study of Batch Arrival Queues
Queueing Systems: Theory and Applications
Vacation Queueing Models: Theory and Applications (International Series in Operations Research & Management Science)
The virtual waiting time in a finite-buffer queue with a single vacation policy
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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A single-server queueing system of MX/G/1 type with unlimited buffer size is considered. Whenever the system becomes empty, the server takes a single compulsory vacation that is independent of the arrival process. The service of the first customer after the vacation is preceded by a random setup time. We distinguish two cases of the evolution of the system: when the setup time begins after the vacation only, or if it begins at once when the first group of customers enters. In the paper we investigate the departure process h(t) that at any fixed moment t takes on a random value equal to the number of customers completely served before t. An explicit representation for Laplace Transform of probability generating function of departure process is derived and written down by means of transforms of four crucial "input" distributions of the system and factors of a certain factorization identity connected with them. The results are obtained using the method consisting of two main stages: first we study departure process on a single vacation cycle for an auxiliary system and direct the analysis to the case of the system without vacations, applying the formula of total probability; next we use the renewal-theory approach to obtain a general formula.