Study on the Queue-Length Distribution in G e o G ( M W V )‎ 1 N Queue with Working Vacations

Abstract EN

This paper analyzes a finite buffer size discrete-time G e o / G / 1 / N queue with multiple working vacations and different input rate.

Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained.

Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution.

Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae.

Finally, a state-dependent operating cost function is constructed to model an express logistics service center.

Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method.