Abstract

We consider a discrete-time G e o / G / 1 retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. We also obtain two stochastic decomposition laws regarding the probability generating function of the system size. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.