An M/g/1 Retrial Queue with Second Multi-optional Service, Feedback and Unreliable Server

An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained. Retrial queueing system is characterized by the feature that the arriving customers who find the server busy join the retrial queue (orbit) to try again for their requests or leave the service area immediately. It has been successfully used to model many problems in telephone switching systems, telecommunication networks and computer networks. Interested reader can refer to the survey papers [1-5]. Server breakdown is a remarkable and unavoidable phenomenon in the service facility of a queueing system. For related retrial queueing literature, we refer to [6] which analyzed M/G/1 retrial queue with server subject to repairs and breakdowns. Yang and Li have studied M/G/1 retrial queue with server subject to starting failures. Krishma Kumar, et al. gave a detailed analysis of M/G/1 retrial queue with feedback and starting failures, where the retrial times are assumed to be generally distributed and the blocked customers follow a FCFS discipline in the retrial orbit. Wang, et al. studied a repairableM/G/1 retrial queueing model from the viewpoint of reliability for the first time, both of the queueing indexes and reliability Received: 2005-09-09, Revised: 2006-02-20. MR Subject Classification:60K25.