Optimization of M G 1 Queue with Vacation (TECHNICAL NOTE)

Authors

  • Madhu Jain Department Of Mathematics, IIT Roorkee,Roorkee,India
Abstract:

This paper reports on the minimization of the average waiting time of the customers in the M/G/1 queue with vacation. Explicit formula for the unknown service parameter of a particular customer has been obtained by considering the exhaustive service discipline in the case of multi-user with unlimited service system. Moreover, results in case of partially gated and gated service disciplines under limited/unlimited service systems have been provided. Some particular cases such as M/M/1 and M/D/1 models with and without vacation have also been discussed.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

An M/G/1 Retrial Queue with Single Working Vacation

We consider an M/G/1 retrial queue with general retrial times and single working vacation. During the working vacation period, customers can be served at a lower rate. Both service times in a vacation period and in a service period are generally distributed random variables. Using supplementary variable method we obtain the probability generating function for the number of customers and the ave...

full text

Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...

full text

AN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

full text

The Bm Ap=g=1 Vacation Queue with Queue–length Dependent Vacation Schedule

We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

full text

The M/M/1 Queue with Multiple Working Vacation

We study a batch arrival M/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtain...

full text

Performance analysis of M/G/1 queue with working vacations and vacation interruption

In this paper, we analyze a single-server vacation queue with a general arrival process. Two policies, working vacation and vacation interruption, are connected to model some practical problems. The GI/M/1 queue with such two policies is described and by the matrix analysis method, we obtain various performance measures such as mean queue length and waiting time. Finally, using some numerical e...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 15  issue 2

pages  157- 160

publication date 2002-06-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023