A matrix geometric approach to the M/M/1 two-phase multi optional retrial queue with Bernoulli feedback, impatient customers and a server subject to breakdown and repair

• Published in: Opsearch Vol. 51; no. 1; pp. 36 - 49
• Main Authors: Lakshmi, K., Ramanath, Kasturi
• Format: Journal Article
• Language: English
• Published: India Springer India 01.03.2014; Springer Nature B.V
• Subjects: Application Article; Breakdown; Breakdowns; Business and Management; Call centers; Customer services; Customers; Feedback; Interactive; Management; Mathematical models; Mathematics; Operations research; Operations Research/Decision Theory; Queues; Repair; Servers; Studies; Voice response technology; Two-phases of service; Retrial queues; Level dependent QBD; Bernoulli feedback; Impatient customer; Neuts and Rao truncation method; Server breakdown and repair
• ISSN: 0030-3887; 0975-0320
• DOI: 10.1007/s12597-013-0131-8

In this paper, we use the matrix geometric approach to analyze the behaviour of an Interactive Voice Response System (IVRS). We model the system as an M/M/1 retrial queue with two phases of service (the second service is multi optional), Bernoulli feedback, impatient customers and the possibility of server breakdown and repair. We study the stability of the system by employing the Neuts and Rao (Queueing Syst. 7 , 169–190 ( 1990 )) truncation method and then we study the level dependent QBD (Quasi-Birth Death) model obtained by the above truncation method to obtain expressions for the performance measures of the system. Numerical illustrations are provided to study the sensitivity of the performance measures of the system to the changes in various parameters of the system.