State dependent bulk service queue with delayed vacations

الملخص EN

This investigation is concerned with the study of M/M (a, d, b)/1 queueing system with multiple vacations wherein finding (a-1) customers waiting in the queue, the server will wait in the system for some time (changeover time), instead of going for vacation immediately.

The server starts service on finding an arrival during the changeover time otherwise the server will go for a vacation.

There is provision to entertain late arriving customers in the ongoing service batch if the size of the batch being served is less than a threshold integer d (a ≤ d ≤ b) .

The steady state queue size distribution is established which is further employed to determine average queue length.

In order to match our investigation with the earlier existing results, we discuss some particular cases.

Tables and graphs to demonstrate the effect of traffic intensity on expected queue length for both vacation and non-vacation models are provided.