Retrial tandem queue with controllable strategy of repeated attempts

Abstract

We consider a tandem retrial queueing system with single-server first station (Station 1) and multi-server second station (Station 2). The input flow at Station 1 is described by a Batch Markovian Arrival Process. If arriving customers meet a busy server of Station 1, they go to the orbit and repeat their attempts to get service in a random time interval. The system has two operation modes which are distinguished by a strategy of repeated attempts. The mode changes dynamically depending on the number of customers in the orbit according to the threshold control policy. We calculate the stationary distribution of the system content at the embedded epochs and at an arbitrary time and derive formulas for the main performance measures. Using these formulas, we are able to calculate the value of the cost criterion which evaluates the quality of service in the system as a function of the threshold level. Numerical results illustrate the behavior of performance measures and the cost criterion as functions of the threshold.

Keywords:

• Tandem queue
• batch Markovian arrival process
• controlled strategy of repeated attempts
• centralized strategy
• decentralized strategy

Notes

No potential conflict of interest was reported by the authors.