Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Poisson input queueing system with startup time and under control-operating policy
Computers and Operations Research
Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
M(n)/G/1/N queues with generalized vacations
Computers and Operations Research
A comparison of numerical techniques in Markov modeling
Communications of the ACM
An MX/G/1 queueing system with a setup period and a vacation period
Queueing Systems: Theory and Applications
A statistical mechanical approach to systems analysis
IBM Journal of Research and Development
On the Mx/G /1 queue with vacation time
Operations Research Letters
Computers and Industrial Engineering
Journal of Computational and Applied Mathematics
Maintenance of deteriorating single server queues with random shocks
Computers and Industrial Engineering
Journal of Computational and Applied Mathematics
Computers and Industrial Engineering
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We consider a single unreliable sever in an M^[^x^]/M/1 queueing system with multiple vacations. As soon as the system becomes empty, the server leaves the system for a vacation of exponential length. When he returns from the vacation, if there are customers waiting in the queue, he begins to serve the customers; otherwise, another vacation is taken. Breakdown times and repair times of the server are assumed to obey a negative exponential distribution. Arrival rate varies according to the server's status: vacation, busy, or breakdown. Using the maximum entropy principle, we develop the approximate formulae for the probability distributions of the number of customers in the system which is used to obtain various system performance measures. We perform a comparative analysis between the exact results and the maximum entropy results. We demonstrate, through the maximum entropy results, that the maximum entropy principle approach is accurate enough for practical purposes.