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Section B

On the multi-server retrial queue with geometric loss and feedback: computational algorithm and parameter optimization

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Pages 1083-1101 | Received 27 Nov 2009, Accepted 01 Jun 2010, Published online: 25 Jan 2011
 

Abstract

We consider an M/M/c retrial queue with geometric loss and feedback. An arriving customer finding a free server enters into service immediately; otherwise the customer either enters into an orbit to try again after a random amount of time or leave the system without service. After the completion of service, he decides either to join the retrial orbit or to leave the system. The retrial system is modelled by a quasi-birth-and-death process, and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of matrix-analytical approach. A cost model is derived to determine the optimal values of the number of servers and service rate simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures.

2010 AMS Subject Classifications :

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