Optimization of an M/M/1/N feedback queue with retention of reneged customers

• Authors: Rakesh KUMAR , Narendra Kumar JAIN , Bhupernder Kumar SOM
• Languages of publication: EN

Abstracts

EN

Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.

Keywords

EN

reneging; retention of reneged customers revenue; queuing system; optimization

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2014
• Volume: 24
• Issue: 3
• Pages: 45-58

Contributors

author

Rakesh KUMAR

• School of Mathematics, Shri Mata Vaishno Devi University, Katra, J&K, India-182 320

author

Narendra Kumar JAIN

• Department of Statistics and Operational Research, Kurukshetra University, Kurukshetra, Haryana, India-136 119

author

Bhupernder Kumar SOM

• Department of Statistics and Operational Research, Kurukshetra University, Kurukshetra, Haryana, India-136 119

References

• ALTMAN E., YECHIALI U., Analysis of customers’ impatience in queues with server vacations, Queuing Systems, 2006, 52 (4), 261–279.
• CHOUDHURY A., MEDHI P., A simple analysis of customers impatience in multi-server queues, Journal of Applied Quantitative Methods, 2010, 5 (2), 182–198.
• DUDIN S.A., DUDINA S.O., Call center operation model as a MAP/PH/N/R-N system with impatient customers, Problems of Information Transmission, 2011, 47 (4), 364–377.
• JAIN M., SINGH P., M/M/m queue with balking, reneging and additional servers, IJE Transactions, 2002, 15 (2), 169–178.
• KAPODISTRIA S., The M/M/1 Queue with Synchronized Abandonments, Queuing Systems, 2011, 68, 79–109.
• KE J.C., WANG K.H., Cost analysis of the M/M/R machine repair problem with balking, reneging and server breakdowns, Journal of the Operational Research Society, 1999, 50, 275–282.
• KUMAR R., SHARMA S., A Markovian feedback queue with retention of reneged customers, 2012, AMO – Advanced Modeling and Optimization, 14, 3, 681–668.
• KUMAR R., SOM B.K., Revenue optimization in insurance business facing customer impatience – Queuing modeling approach, American Journal of Operational Research, 2013, 3, 2A, 44–47.
• KUMAR R., SOM B.K., JAIN S., Optimization and performance analysis of insurance business. A queuing modeling approach, International Journal of Mathematical Sciences and Engineering Applications, 2013, 7 (2), 327–340.
• MISHRA S.S., MISHRA V., The cost analysis of machine interference model with balking, reneging and spares, Opsearch, 2004, 41 (3), 188–199.
• PAN Q., The research and application of M/M/1/N queuing model with variable input rates, variable service rates and impatient customers, International Journal of Engineering and Natural Sciences, 2010, 4 (4), 217–219.
• TADJ L., ZANG G.Z., TADJ C., A queuing analysis of multi-purpose facility’s operations, Journal of Industrial and Management Optimization, 2011, 7 (1), 19–30.
• WANG H., CHANG Y.C., Cost analysis of finite M/M/R queuing system with balking, reneging and server breakdown, Mathematics Methods Operations Research, 2002, 56, 169–180.
• WU X., BRILL P., HLYNKA M., WANG J., An M/G/1 Retrial Queue with Balking and Retrials during Service, International Journal of Operational Research, 2005, 1 (1/2), 30–51.
• WU H.C., WANG H.K., KE C.J., KE B.J., A heuristic algorithm for the optimization of M/M/S queue with multiple working vacations, Journal of Industrial and Management Optimization, 2012, 8 (1), 1–17.
• YUE D., YUE W., Block-partitioning matrix solution of M/M/R/N queuing system with balking, reneging and server breakdowns, Journal of Industrial Management and Optimization, 2009, 5 (3), 417–430.
• YUE D., YUE W., SUN Y., Performance analysis of an M/M/c/N queuing system with balking, reneging and synchronous vacations of partial servers, The Sixth International Symposium on Operations Research and Its Applications, 2006, 128–143.

Identifiers

DOI

10.5277/ord140303