International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Transient Solution of a Single Server Queuing Model with Correlated Reneging Using Runge-Kutta Method

Rakesh Kumar
School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, Pin-182320, India.

Bhavneet Singh Soodan
School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, Pin-182320, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.5.068

Received on September 06, 2019
  ;
Accepted on April 16, 2020

Abstract

In this paper, the concept of correlated reneging is introduced in queuing theory. The reneging considered so far is dependent on system size, but there are many real life situations where customers may renege due to exogenous factors other than the state of the system. Further, the reneging of customer may induce the other customers to renege at two successive time points. Such reneging is called correlated reneging. An M/M/1/K queuing model with correlated reneging is studied. Runge-Kutta method of fourth order is presented to obtain the transient solution of the model. Some performance measures like expected system size and expected waiting time in the system are studied.

Keywords- Queuing model, Correlated reneging, Transient solution, Runge-Kutta method, Transition marks.

Citation

Kumar, R., & Soodan, B. S. (2020). Transient Solution of a Single Server Queuing Model with Correlated Reneging Using Runge-Kutta Method. International Journal of Mathematical, Engineering and Management Sciences, 5(5), 886-896. https://doi.org/10.33889/IJMEMS.2020.5.5.068.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.

Acknowledgements

The authors would like to thank the editor-in-chief and the anonymous referees for their comments and suggestions which helped us to bring this manuscript in the current form.

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