Single Server Bulk Queue with Service Interruption, Two Phase Repairs and State Dependent Rates

author

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

This paper reports a study on a single server queue with bulk arrival and bulk service patterns wherein the incoming traffic depends on the state of the server which may be in operating or breakdown state. The repair of the breakdown server is performed in two phases. The operating duration of server, repair duration of both phases of repairing as well as job's inter-arrival times and service times are exponentially distributed. By using generating function approach, the transient analysis for the queue size distribution has been carried out. For steady state, the stability condition and average queue length for various states have been derived. By taking a numerical illustration, the effect of various parameters on the average queue length has been depicted graphically.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Analysis of a Single Server Queue with Working Vacation and Vacation Interruption

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...

full text

FINITE POPULATION SINGLE SERVER BATCH SERVICE QUEUE WITH COMPULSORY SERVER VACATION

A single server finite population queueing model with compulsory server vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also given.  

full text

Working Vacation Queue with Second Optional Service and Unreliable Server

An M/M/1 queueing system with second optional service and unreliable server is studied. We consider that the server works at different rate rather than being idle during the vacation period. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server’s status. All customers demand the first essential service whereas only some of them dema...

full text

A SINGLE SERVER BERNOULLI VACATION QUEUE WITH TWO TYPE OF SERVICES AND WITH RESTRICTED ADMISSIBILITY

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures are calculated. Some ...

full text

A Study on State Dependent Accessible and Second Optional Service Queue with Impatient and Feedback Customers

In this paper, we study a single server Markovian queue with state dependent accessible services, reneging and feedback of customers. The server can accommodate at the most $d$ customers in the service station, after which the new arrivals have to wait in the primary queue of infinite waiting space. All arrivals demand First Essential Service (FES), after completing FES, customers decide to joi...

full text

Analysis of a single server queue with semi-Markovian service interruption

In this paper we analyze a discrete time single server queue where the service time equals one slot The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables The service process is interrupted by a semi Markov process namely in certain states the server is available for service while the server is not available in other states We analyze bot...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 12  issue 1

pages  21- 28

publication date 1999-02-01

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