Analysis of the BMAP/G/1 retrial system with search of customers from the orbit

Analysis of the BMAP/G/1 retrial system with search of customers from the orbit

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Article ID: iaor20052372
Country: Netherlands
Volume: 157
Issue: 1
Start Page Number: 169
End Page Number: 179
Publication Date: Aug 2004
Journal: European Journal of Operational Research
Authors: , , ,
Keywords: markov processes
Abstract:

We consider a single server retrial queuing model in which customers arrive according to a batch Markovian arrival process. Any arriving batch finding the server busy enters into an orbit. Otherwise one customer from the arriving batch enters into service immediately while the rest join the orbit. The customers from the orbit try to reach the service later and the inter-retrial times are exponentially distributed with intensity depending (generally speaking) on the number of customers on the orbit. Additionally, the search mechanism can be switched-on at the service completion epoch with a known probability (probably depending on the number of customers on the orbit). The duration of the search is random and also probably depending on the number of customers in the orbit. The customer, which is found as the result of the search, enters the service immediately if the server is still idle. Assuming that the service times of the primary and repeated customers are generally distributed (with possibly different distributions), we perform the steady state analysis of the queueing model.

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