A RETRIAL QUEUEING MODEL WITH MAP ARRIVALS, CATASTROPHIC FAILURES WITH REPAIRS, AND CUSTOMER IMPATIENCE

Srinivas R. Chakravarthy (), Alexander N. Dudin and Valentina I. Klimenok
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Srinivas R. Chakravarthy: Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;
Alexander N. Dudin: Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;
Valentina I. Klimenok: Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;

Asia-Pacific Journal of Operational Research (APJOR), 2010, vol. 27, issue 06, 727-752

Abstract: We consider a single server retrial queueing system in which arrivals occur according to a Markovian arrival process. An arriving customer finding an idle server will get service immediately; otherwise the customer enters into a retrial orbit. The system is subject to catastrophic failures at which time all customers in the system (the one in service as well as the customers, if any, in the orbit) are lost. The system undergoes a repair and after completion of a repair the server in the system will be available for service. The customers in the orbit try to reach the server by sending a signal at random times and get service if the server is idle at those times. While customers are waiting in the orbit, they may become impatient and leave the system after a random amount of time. Any arrival finding the server unavailable (due to busy or under repair) and cannot enter the orbit due to the buffer being full (in the case of finite buffer only) is considered lost. Under exponential assumption for all except for the arrivals, the queueing model (for both finite and infinite orbit sizes) is studied using matrix-analytic methods and the qualitative nature of the model is brought out through some illustrative numerical examples.

Keywords: Markovian arrival process; retrial; queueing; catastrophic failures; repairs; abandonment; impatience; algorithmic probability (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0217595910002971

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