Yutaka Baba

Analysis of a GI/M/1 queue with multiple working vacations

Consider a GI/M/1 queue with vacations such that the server works with different rates rather than completely stops during a vacation period. We derive the steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs, and for the sojourn time for an arbitrary customer.

On the Mx/G /1 queue with vacation time

We consider an M^x/G/1 queueing system in which the server takes a vacation each time that the system, becomes empty. Using supplementary variables, we derive the general queue length distribution at an arbitrary time. We also obtain the waiting time and busy period distributions.