Optimizing Resource Allocation in M/M/1/N Queues with Feedback, Discouraged Arrivals, and Reneging for Enhanced Service Delivery

Authors

  • Savita Department of Mathematics, Chandigarh University, Mohali, Punjab 140413, India
  • Amit Kumar Department of Mathematics, Chandigarh University, Mohali, Punjab 140413, India
  • Chandra Shekhar Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Pilani, Rajasthan, 333 031, India

DOI:

https://doi.org/10.13052/jrss0974-8024.1711

Keywords:

Queueing models, discouraged arrivals, reneging, resource allocation, feedback, service quality

Abstract

This article presents a novel computational approach for analyzing M/M/1/N queues with feedback, discouraged arrivals, and reneging, under the first-come, first-served (FCFS) discipline. We calculate explicit transient state probabilities and represent results using symmetric tridiagonal matrix eigenvalues. Through numerical simulations, we validate our method, providing practical insights for optimizing resource allocation. Our study contributes to both theory and application, advancing queueing theory and aiding decision-makers in improving service quality and resource management.

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Author Biographies

Savita, Department of Mathematics, Chandigarh University, Mohali, Punjab 140413, India

Savita is a research scholar in the Department of Mathematics at Chandigarh University. She earned her M.Sc. degree from GJU Hisar in 2006. Her primary research interests lie in the field of queueing theory and stochastic processes. She has actively participated in several national and international conferences.

Amit Kumar, Department of Mathematics, Chandigarh University, Mohali, Punjab 140413, India

Amit Kumar is an Assistant Professor at the University Institute of Science, Chandigarh University, India. He holds a Ph.D. from Birla Institute of Technology and Science, Pilani Campus, Rajasthan. His research interests encompass queueing theory, machine repair problem, optimal control, reliability and maintainability, stochastic modeling, sensitivity analysis, evolutionary computation, statistical analysis, and fuzzy set and logic. Kumar has published numerous research articles in reputable journals such as Reliability Engineering and System Safety, Journal of Computational and Applied Mathematics, Quality Technology and Quantitative Management, and Arabian Journal of Science and Engineering. He actively participates in conferences, Faculty Development Programs (FDPs), workshops, and symposiums as both a presenter and invited speaker. Kumar also serves as a reviewer for several prestigious journals and has professional experience visiting the irrigation department in Roorkee, India. (ORCID 0000-0001-5347-1808).

Chandra Shekhar, Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Pilani, Rajasthan, 333 031, India

Chandra Shekhar is a distinguished Professor and former Head of the Department of Mathematics at BITS Pilani, India. His research interests span queueing theory, computer and communication systems, machine repair problems, reliability and maintainability, stochastic processes, evolutionary computation, statistical analysis, and fuzzy set and logic. Professionally, he actively participates in academic events, presenting papers and delivering invited talks at national and international conferences and Faculty Development Programs (FDPs). He has organized multiple conferences, workshops, and symposiums and received recognition with the best research paper award at an international conference. He has authored over 50 research articles in prestigious journals, supervised three Ph.D. theses, and contributed to book chapters and textbooks. He serves as a member of editorial boards, a reviewer for reputable journals, and participates in various academic committees. He has professional experience working with esteemed organizations, including IIRS (ISRO), CSIR-IIP, NIH, WIHG, CPWD, NTPC, Bank of Maharashtra, and APS Lifetech. (ORCID: 0000-0002-2114-9096)

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Published

2024-06-05

How to Cite

Savita, Kumar, A., & Shekhar, C. (2024). Optimizing Resource Allocation in M/M/1/N Queues with Feedback, Discouraged Arrivals, and Reneging for Enhanced Service Delivery. Journal of Reliability and Statistical Studies, 17(01), 1–16. https://doi.org/10.13052/jrss0974-8024.1711

Issue

2024: Vol 17 Iss 1

Section

Advances in Reliability Studies