Finite MX/M/C Queue with State Dependent Service, Two-Class Arrivals and Impatient Customers

P Mahendra Varma; Rajyalakshmi Kottapalli  lowast; V N Rama Devi

doi:10.17485/IJST/v17i28.1611

Article

Finite MX/M/C Queue with State Dependent Service, Two-Class Arrivals and Impatient Customers

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i28.1611

Year: 2024, Volume: 17, Issue: 28, Pages: 2897-2902

Original Article

Finite MX/M/C Queue with State Dependent Service, Two-Class Arrivals and Impatient Customers

P Mahendra Varma¹, Rajyalakshmi Kottapalli^2∗, V N Rama Devi³

¹Research Scholar, Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, 522302, Andhra Pradesh, India
²Assistant Professor, Department of Department of Engineering Mathematics, College of Engineering, KoneruLakshmaiah Education Foundation, Green fields, Vad-deswaram, Guntur, 522303, Andhra Pradesh, India
³Professor, Department of Mathematics, GRIET, Hyderabad, Telangana, India

*Corresponding Author
Email: [email protected]

Received Date:12 May 2024, Accepted Date:25 June 2024, Published Date:22 July 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: 1. To compute the transition probabilities for the queueing system to be in different states. 2. To calculate the average system length and mean waiting time under the specified parameters. 3. To investigate and test the impact of system characteristics on the anticipated system length as well as mean waiting times. Method: MATLAB software is used for the Runge-Kutta method to calculate probabilities and system constants. Findings: An increase in Type-I arrival rate λ1 and Type-II arrival rate λ2 will cause both mean waiting times and queue length to increase, and they are reduced with an increase in service rates µ1 and µ2 of Type-I and Type-II classes. A rise in parameters such as special service rate µ3, probability of balking and reneging will result in a reduction in both mean waiting times and queue length. Novelty: This article covers a batch arrival finite Markovian queueing system with multi-server support and consumer impatience. In real time, all arrivals need not enter the queue at the same arrival rates, as it is based on the needs of the customer. In view of this, we have assumed two types of customers along with two different rates of arrival and state-dependent service. We did our work in transient mode, as time can influence the waiting lines. Also determined the system's performance indices and demonstrated the impact of the input parameters on the system's constants.

Keywords: Batch Arrival, Customer Impatience, Two Class Customers, State Dependent Service, Multi Server Facility

References

Kumar K, Jain M, Shekhar C. Machine Repair System with F-Policy, Two Unreliable Servers, and Warm Standbys. Journal of Testing and Evaluation. 2019;47(1). Available from: https://doi.org/10.1520/JTE20160595
Dissa S, Ushakumari PV. Two commodity queueing inventory system with random com-mon lifetime, two demand classes and pool of customers. Available from: https://doi.org/10.1016/j.heliyon.2023.e21478
Barakim J, O. On-preemptive priority M/M/m queue with serv-ers’ vacations. Computers & Industrial Engineering. 2021;160. Available from: https://doi.org/10.1016/j.cie.2021.107390
Gil-Borras S, EPG, Alonso-Ayuso A, Duarte A. A heuristic approach for the online order batching problem with multiple pickers. Computers & Industrial Engineering. 2021;160:107517. Available from: https://doi.org/10.1016/j.cie.2021.107517
Xudongchai T, Jiang, Linhongli, Weixu L, Liu. On a many-to-many matched queueing system with flexible matching mechanism and impatient customers. Journal of Computational and Applied Mathematics. . Available from: https://doi.org/10.1016/j.cam.2022.114573
Das RR, Devi R, Rathore VNA, Chandan K. Transient analysis of M/M/1 queue with server failures, N-policy, second optional service and customer impatience. AIP Conference Proceedings. 2022;2516(1):360007. Available from: https://doi.org/10.1063/5.0110050
Sridhar R, Devi VN, Chandan K. Performance analysis of M/M/1 queue with working vacation, N-policy and customer impatience in transient mode. AIP Conference Proceedings. 2022;2516. Available from: https://doi.org/10.1063/5.0108662
Devi VR. Queueing System with Two-Phase, N-Policy, Server Failure and Second Optional Batch Service with Customers impatient Behavior. IOP Conf. Series: Journal of Physics: Conf. Series. 2019;1344:12015. Available from: https://doi.org/10.1088/1742-6596/1344/1/012015
Franco C, Nilsonherazo , Padilla JA, Castaneda. A queueing Network approach for capacity planning and patient Scheduling: A case study for the COVID-19 vaccination process in Colombia. National Library of Medicine. 2022;40(49). Available from: https://doi.org/10.1016/j.vaccine.2022.09.079
Sun W, Xumengxie Z, Zhang S, Li. Equilibrium balking behavior of customers and regulation measures in a multi-server queue with threshold policy. Available from: https://doi.org/10.1080/16843703.2024.2358613

Copyright

© 2024 Varma et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)