On a Retrial Queueing Model with Customer Induced Interruption
Varghese Jacob *
Department of Mathematics, Government College, Kottayam-686013, India.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a retrial queueing system with customer induced interruption while in service. We consider a single server queueing system of infinite capacity to which customers arrive according to a Poisson process and the service time follows an exponential distribution.
An arriving customer to an idle server obtains service immediately and customers who find server busy go directly to the orbit from where he retry for service. The inter-retrial time follows exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The customer whose service is got interrupted will enter into a finite buffer. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We analyse the steady-state behavior of this queuing system. Several performance measures are obtained. Numerical illustrations of the system behaviour are also provided with example.
Keywords: Quasi-birth-and-death process, Matrix analytic methods, Customer induced interruption, Retrial queues, Steady-state analysis.