Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates
Queueing Systems: Theory and Applications
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Analysis of customers' impatience in queues with server vacations
Queueing Systems: Theory and Applications
Vacation Queueing Models: Theory and Applications (International Series in Operations Research & Management Science)
Synchronized reneging in queueing systems with vacations
Queueing Systems: Theory and Applications
The M/M/1 queue with synchronized abandonments
Queueing Systems: Theory and Applications
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We consider a single-server Markovian queue with synchronized services and setup times. The customers arrive according to a Poisson process and are served simultaneously. The service times are independent and exponentially distributed. At a service completion epoch, every customer remains satisfied with probability p (independently of the others) and departs from the system; otherwise, he stays for a new service. Moreover, the server takes multiple vacations whenever the system is empty. Some of the transition rates of the underlying two-dimensional Markov chain involve binomial coefficients dependent on the number of customers. Indeed, at each service completion epoch, the number of customers n is reduced according to a binomial (n, p) distribution. We show that the model can be efficiently studied using the framework of q-hypergeometric series and we carry out an extensive analysis including the stationary, the busy period, and the sojourn time distributions. Exact formulas and numerical results show the effect of the level of synchronization to the performance of such systems.