Performance Analysis and Cost Optimization of Non-Markovian Bulk Queue with 'p'- Entering Discipline during Multiple Adaptive Vacations

S. Jeyakumar ； E. Rameshkumar

《International Journal of Information and Management Sciences》 28卷2期 (2017/06) Pp. 99-111

https://doi.org/10.6186/IJIMS.2017.28.2.3

摘要

The steady state analysis of M^x/G/1 queue with Multiple Adaptive Vacation (MAV), where the customers enter during the server vacations with probability 'p' (0 ≤ p ≤ 1) is considered. The server provides service to all the entering customers with service follows general distribution. Upon the system being found to be empty, the server immediately takes a vacation of random period. When the server returns to system after a vacation, if the queue length is still empty, he avails another vacation and so on until he completes M number of vacations in successions and the server remains idle and starts service when the server finds a customer in the queue. The probability generating function at an arbitrary time epoch is obtained using Supplementary variable technique. Basic system characteristics such as expected value of the length of the queue, busy period, idle time and expected value of the waiting time are obtained. Cost model is presented and algorithm for finding optimum cost is also presented for the proposed model. Numerical illustration is also provided.

關鍵字

Bulk arrival ； general service ； multiple adaptive vacations ； supplementary variable ； dormant period ； 'p'- entering discipline

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