A Retrial Queueing System with Orbital Search of Customers Lost from an Offer Zone

Abstract

A tandem retrial queueing system with orbital search in which two self-service stations namely, the main station and the offer zone and an orbit for passive customers lost from the offer zone without joining the main station is considered. The main service station is of infinite capacity while the offer zone which works in a random environment and the orbit for passive customers are of finite capacities. Two types of customers arrive to the service stations according to a Marked Markovian Arrival Process (MMAP) with representation \((D_0,D_1,D_2).\) The service times in both stations are exponentially distributed. A virtual search mechanism associated with the main station will be working when the number of customers in the main station is below a pre-assigned level L. The duration of search is exponentially distributed. The condition for system stability is established. The system state distribution in the steady state is obtained. Several system performance characteristics are derived. An associated optimization problem is investigated.