Maximum entropy and the G/G/1/N queue
Acta Informatica
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
Control policies for the MX/g/1 queueing system
Management Science
A queue with service interruptions in an alternating random environment
Operations Research
Batch arrival queue with N-policy and single vacation
Computers and Operations Research
Optimal two-threshold policies in an M/G/1 queue with two vacation types
Performance Evaluation
Analysis of a bulk queue with N-policy multiple vacations and setup times
Computers and Operations Research
A comparison of numerical techniques in Markov modeling
Communications of the ACM
Computers and Industrial Engineering
Computers and Industrial Engineering
A statistical mechanical approach to systems analysis
IBM Journal of Research and Development
Hi-index | 7.30 |
We consider the M^[^x^]/G/1 queueing system, in which the server operates N policy and a single vacation. As soon as the system becomes empty the server leaves for a vacation of random length V. When he returns from the vacation and the system size is greater than or equal to a threshold value N, he starts to serve the waiting customers. If he finds fewer customers than N. he waits in the system until the system size reaches or exceeds N. The server is subject to breakdowns according to a Poisson process and his repair time obeys an arbitrary distribution. We use maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length. We perform a comparative analysis between the approximate results with established exact results for various batch size, vacation time, service time and repair time distributions. We demonstrate that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems.