Abstract
In this paper we consider a single server retrial queue with two orbits of which the first orbit is occupied by primary customers who on arrival find the server busy or interrupted. The other orbit has finite capacity and consists of customers whose service get interrupted due to server breakdown. Interrupted customers are picked up with probability p by the server at the epoch at which he/she becomes free either by the successful completion of a service or by completion of repair. Also there arises a competition between primary customers, retrial customers from the first and the second orbit to access the server. Failed retrials result in the customers returning to the respective orbits. The primary customers arrive according to a Markovian arrival process (MAP), the interruption occur according to a Poisson process. Fixing of interruption takes a random duration having phase type distribution. The service time follows phase type distribution. Stability condition of the system is established. Steady-state system size distribution is obtained. Performance characteristics of the system are evaluated.
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Acknowledgments
The work of the third author is supported by the Maulana Azad National fellowship \([F1-17.1/2015-16/MANF-2015-17-KER-65493]\) of University Grants commission, India.
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Babu, D., Krishnamoorthy, A., Joshua, V.C. (2018). Retrial Queue with Search of Interrupted Customers from the Finite Orbit. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM WRQ 2018 2018. Communications in Computer and Information Science, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-97595-5_28
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