Matrix-geometric solution of multi-server queueing systems with Bernoulli scheduled modified vacation and retention of reneged customers: A meta-heuristic approach

ABSTRACT

In the present article, we deal with the multi-server finite capacity queueing system with Bernoulli’s scheduled modified vacation policy and the realistic retaining policy of reneged customers. After completion of the service of any customer, the server decides whether to go for the vacation of random duration or to continue facilitating the service to the waiting customer, if any, present in the queue. All servers, homogeneous in nature, provide the state-dependent service following the threshold policy to reduce the overload of the system. The impatience behavior of customers like balking and reneging is also considered in the stochastic modeling of the studied problem. The matrix analytic approach is employed to obtain the steady-state probabilities with which various system performance measures are also developed with practical justification. Finally, the expected cost minimization problem is formulated and dealt with the meta-heuristic approach: particle swarm optimization (PSO). All results of numerical simulation and optimal analysis are summarized in tables and graphs to provide quick insight. The concluding remarks and future scopes have also been discussed.

KEYWORDS:

• Bernoulli modified vacation policy
• retention of the reneged customer
• state-dependent service rate
• emergency vacation
• particle swarm optimization

Acknowledgments

The authors would like to thank the editorial board and anonymous referees for the valuable, constructive comments and suggestions for the earlier version of this paper.

Disclosure statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Funding

The author (SV) extends his sincere thanks to funding agency Council of Scientific and Industrial Research, New Delhi, India, for the financial support [SRF/Net (09/719(0068)/2015-EMR-1)]. Also, all authors are supported by DST FIST (India) grant [SR/FST/MSI-090/2013(C)].

Notes on contributors

Chandra Shekhar

Chandra Shekhar, the faculty at BITS Pilani, India, is actively involved in research in the area of queueing theory, computer and communication system, machine repair problem, reliability and maintainability, stochastic process, evolutionary computation, statistical analysis, fuzzy set & logic. Besides attending, presenting scientific papers and delivering invited talk, he has a number of research articles in these fields in journals of repute. He is also a member of the editorial board and reviewer of many reputed journals, academic societies, and Doctoral Research Committee & Advisory board of many universities. Authorship of the textbook on Differential Equation is also to his credit.

Shreekant Varshney

Shreekant Varshney has completed his Ph.D. from the Department of Mathematics, BITS Pilani, Pilani. He is CSIR SRF/NET qualified. He has presented many research papers at national and international conferences of repute. Many research articles in the journal of repute belong to his credit. His research interest is Queueing Theory, Stochastic Modelling, and Operations Research.

Amit Kumar

Amit Kumar is Assistant Professor at SGT University, India. He is TIFR qualified in 2011 and UGC-BSR fellow. He has presented many research papers at national and international conferences of repute. He has many published research articles in the journal of repute. His research interest is Queueing Theory, Reliability Theory, and Operations Research.