Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Stochastic petri net analysis of finite-population vacation queueing systems
Queueing Systems: Theory and Applications
Modelling with Generalized Stochastic Petri Nets
Modelling with Generalized Stochastic Petri Nets
Analysis on queueing systems with synchronous vacations of partial servers
Performance Evaluation
Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers
Queueing Systems: Theory and Applications
Analysis of multi-server queue with a single vacation (e, d)-policy
Performance Evaluation
Analytic and numerical aspects of batch service queues with single vacation
Computers and Operations Research
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Systems with vacations are usually modeled and analyzed by queueing theory, and almost all works assume that the customer source is infinite and the arrival process is Poisson. This paper aims to present an approach for modeling and analyzing finite-source multiserver systems with single and multiple vacations of servers or all stations, using the Generalized Stochastic Petri nets model. We show how this high level formalism, allows a simple construction of detailed and compact models for such systems and to obtain easily the underlying Markov chains. However, for real vacation systems, the models may have a huge state space. To overcome this problem, we give the algorithms for automatically computing the infinitesimal generator, for the different vacation policies. In addition, we develop the formulas of the main exact stationary performance indices. Through numerical examples, we discuss the effect of server number, vacation rate and vacation policy on the system's performances.