Study of a Four-Server Feedback Queuing Model with Finite Chances of Customer Returns to Any Server
Keywords:
Feedback, Queuing System, Poisson Process, Four Server, Mean Queue Length of the system
Abstract
A queuing model has been created for a system with four servers, allowing customers to return to any server. Each customer can revisit upto finie number of times and may need services from one or all servers. If a customer requires assistance from multiple servers, they will first go to the first server and then can choose to visit either of the other three. After receiving service from any server, the customer can either return to another server or exit the system based on their satisfaction. The likelihood of a customer leaving a server changes with each visit, differing from their previous departure probability. The Mean Queue Length of the system is calculated from the steady state equations developed from the model.
References
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[7] Saikia G, Medhi P and Choudhury A. Analyzing Impatience in Multiserver Markovian Queues ; International Journal of Supply and Operations Management. 2020 ;7(4) , 310-321.
[8] Som BK and Seth S. An M/M/c/N Feedback Queuing System with Encouraged Arrivals, Reverse Reneging and Retention of Reneged Customers; Lloyd Business Review.2021 ; 1(1) , 26-30.
[9] Singla N and Kaur H. A Two-State Retrial Queueing Model with Feedback having Two Identical Parallel Servers; Indian Journal Of Science And Technology.2021 ;14(11) , 915-931.
[10] Saini V and Gupta D. Analysis of a Complex Feedback Queue Network; Turkish Online Journal of Qualitative Inquiry (TOJQI) . 2021 ;12(7) , 2377-2383
[11] Elalouf A and Wachtel G. Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies; Operations Research Forum.2022;3(2) doi: 10.1007/s43069-021-00114-8
[12] Gupta P, Kumar N and Gupta R. (R1971) Analysis of Feedback Queueing Model with Differentiated Vacations under Classical Retrial Policy; Applications and Applied Mathematics. 2022 ; 17(2) , 290-307.
[13] Laxmi PV, Qrewi H A.B.D and George A A. Analysis Of Markovian Batch Service Queue With Feedback And Second Optional Service ; RT&A .2022 ;17(68) , 507-518.
[14] Kamal. Mathematical modeling of some feedback queueing systems. Ph. D. Thesis. Baba Mastnath University, Asthal Bohar, Rohtak, Haryana. 2023.¬¬¬¬¬¬¬¬
[2]. Kumar, S. and Taneja, G. Analysis of a hierarchical structured queuing system with three service channels and chances of repetition of service with feedback. International Journal of Pure and Applied Mathematics. 2017; 115 (2), 383-363.
[3] Kumar R and Som BK. A Multi-Server Queue With Reverse Balking and Impatient Customers. Pak. J. Statist. 2020 ; 36(2), 91-101.
[4] Liu P, Jiang T ,and Chai X. Performance Analysis of Queueing Systems with a Particular Service Interruption Discipline. Discrete Dynamics in Nature and Society; 2020, https://doi.org/10.1155/2020/1847512.
[5] Kotba K.A.M , El-Ashkara H.A. Quality Control for Feedback M/M/1/N Queue with Balking and Retention of Reneged Customers; Filomat. 2020 ; 34(1), 167-174.
[6] Melikov A, Aliyeva S and Sztrik J. Analysis of Instantaneous Feedback Queue with Heterogeneous Servers;2020.8(12), 2186; https://doi.org/10.3390/math8122186.
[7] Saikia G, Medhi P and Choudhury A. Analyzing Impatience in Multiserver Markovian Queues ; International Journal of Supply and Operations Management. 2020 ;7(4) , 310-321.
[8] Som BK and Seth S. An M/M/c/N Feedback Queuing System with Encouraged Arrivals, Reverse Reneging and Retention of Reneged Customers; Lloyd Business Review.2021 ; 1(1) , 26-30.
[9] Singla N and Kaur H. A Two-State Retrial Queueing Model with Feedback having Two Identical Parallel Servers; Indian Journal Of Science And Technology.2021 ;14(11) , 915-931.
[10] Saini V and Gupta D. Analysis of a Complex Feedback Queue Network; Turkish Online Journal of Qualitative Inquiry (TOJQI) . 2021 ;12(7) , 2377-2383
[11] Elalouf A and Wachtel G. Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies; Operations Research Forum.2022;3(2) doi: 10.1007/s43069-021-00114-8
[12] Gupta P, Kumar N and Gupta R. (R1971) Analysis of Feedback Queueing Model with Differentiated Vacations under Classical Retrial Policy; Applications and Applied Mathematics. 2022 ; 17(2) , 290-307.
[13] Laxmi PV, Qrewi H A.B.D and George A A. Analysis Of Markovian Batch Service Queue With Feedback And Second Optional Service ; RT&A .2022 ;17(68) , 507-518.
[14] Kamal. Mathematical modeling of some feedback queueing systems. Ph. D. Thesis. Baba Mastnath University, Asthal Bohar, Rohtak, Haryana. 2023.¬¬¬¬¬¬¬¬
Published
2023-12-28
How to Cite
Surender Kumar, & Nidhi Sharma. (2023). Study of a Four-Server Feedback Queuing Model with Finite Chances of Customer Returns to Any Server. Revista Electronica De Veterinaria, 24(4), 678-686. https://doi.org/10.69980/redvet.v24i4.1920
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