Analysis of M/M/1/N Queueing System with Encouraged Arrivals, Feedback, Catastrophe and Retention of Reneged Customers Roman

M. Akhdar Akhdar; A. Alsileeni Alsileeni

المؤلفون

M. Akhdar Akhdar aDepartment of Statistics and Econometrics, Faculty of Economics and Political Science, Tripoli University, Tripoli, Libya
A. Alsileeni Alsileeni bCollaborator, Department of Statistics, Faculty of Science, Al-Asmari University, Zliten ,Libya

الملخص

This paper aims to derive the analytical solution of the truncated single-channel queue: M/M/1/N at the steady state by adding the concepts of encouraging arrivals, feedback strategy, catastrophe, and retention of reneged customers. Using the iterative method obtain the probability that there are n customers in the system, the possibility of a vacuous system, and some performance effectiveness measures. Some important queueing models are exceptional cases of this system. Some numerical values are given for the additional concepts to show the effect of the (arrival rate, and catastrophe rate) on the model so that the companies implementing this model work to reduce the harmful ones.

المراجع

Sharma, O. and A. Tarabia, A simple transient analysis of an M/M/1/N queue. Sankhyā: The Indian Journal of Statistics, Series A, 2000: p. 273-281.

Kumar, R., N.K. Jain, and B.K. Som, Optimization of an M/M/1/N feedback queue with retention of reneged customers. Operations Research and Decisions, 2014. 24(3): p. 45--58.

Kalidass, K., et al., Time dependent analysis of an M/M/1/N queue with catastrophes and a repairable server. Opsearch, 2012. 49(1): p. 39-61.

Garg, D. and N. Jain, Distribution of the Number of Times M/M/2/N Queuing System Reaches its Capacity in Time t under Catastrophic Effects.

Kumar, R. and B.K. Som, An M/M/1/N feedback queuing system with reverse balking, reverse reneging and retention of reneged customers. Indian Journal of Industrial and Applied Mathematics, 2015. 6(2): p. 173-183.

Som, B.K., Cost-profit Anslysis of Stochastic Heterogeneous Queue with Reverse Balking, Feedback and Retention of Impatient Customers. Reliability: Theory & Applications, 2019. 14(1).

Som, B.K. and S. Seth, An M/M/1/N Queuing system with Encouraged Arrivals. Global Journal of Pure and Applied Mathematics, 2017. 17: p. 3443-3453.

Som, B.K. and S. Seth, M/M/c/N queuing systems with encouraged arrivals, reneging, retention and feedback customers. Yugoslav Journal of Operations Research, 2018. 28(3): p. 333-344.

Awasthi, B., Performance Analysis of M/M/1/K Finite Capacity Queueing Model with Reverse Balking and Reverse Reneging. Journal of Computer and Mathematical Sciences, 2018. 9(7): p. 850-855.

Bouchentouf, A.A., M. Cherfaoui, and M. Boualem, Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers. Opsearch, 2019. 56(1): p. 300-323.

Fazlollahtabar, H. and H. Gholizadeh, Economic Analysis of the M/M/1/N Queuing System Cost Model in a Vague Environment. International Journal of Fuzzy Logic and Intelligent Systems, 2019. 19(3): p. 192-203.

Awasthi, B., M/M/1/C QUEUING MODEL WITH REVERSE BALKING AND FEEDBACK CUSTOMERS. Annals of the Faculty of Engineering Hunedoara, 2018. 16(4): p. 93-96.

Awasthi, B., Application of Queueing Theory in Decision Making in Presence of Uncertain Environment. Mathematics Today, 2018. 34: p. 35-41.

Som, B.K., A Markovian feedback queuing model with encouraged arrivals and customers impatience. EVIDENCE BASED MANAGEMENT, 2017: p. 202.

RAO, S.H., V.V. KUMAR, and K.S. KUMAR, ENCOURAGED OR DISCOURSED ARRIVALS OF AN M/M/1/N QUEUEING SYSTEM WITH MODIFIED RENEGING.

Kumar, R., A single-server Markovian queuing system with discouraged arrivals and retention of reneged customers. Yugoslav journal of operations research, 2016. 24(1).

Som, B.K. and S. Seth, Queuing System with Encouraged Arrivals, Impatient Customers and Retention of Impatient Customers for Designing Effective Business Strategies.

Boxma, O., Stochastic performance modelling. 2009: Technische Universiteit Eindhoven.

.