Performance Evaluation of M/M/1/N Queuing Systems: A Study of Capacity Constraints and Service Dynamics
DOI:
https://doi.org/10.29070/16rcdk80Keywords:
Queueing Theory, M/M/1/N Model, Performance Measures, Finite Capacity Queue, System Utilization, Customer Loss Probability, Waiting Time Analysis, Stochastic ProcessesAbstract
The M/M/1/N queueing model is a finite-capacity system that is defined by a single server, exponential interarrival and service periods, and a restricted buffer size. This study explores the major performance metrics of the M/M/1/N queueing model. In industries such as telecommunications, computer networks, and industrial systems, where the number of clients that may be served is limited due to resource restrictions, such systems are often used. The study is centered on the calculation and interpretation of essential performance indicators, which include steady-state probabilities, the average number of customers in the system, the utilization of the system, the average waiting time, and the likelihood of losing consumers owing to restrictions in the system's capacity. In order to highlight the impact that system characteristics like arrival rate, service rate, and buffer size have on the overall performance of the system, numerical examples are supplied. The findings provide valuable insights into the use of stochastic demand and service conditions to the design of systems and the planning of capacity.
Downloads
References
Altiok, T., & Melamed, B. (2019). Simulation modeling and analysis. Springer.
Amiri, M., & Manaf, N. M. (2014). An analysis of M/M/1 queue performance measures with service interruptions. Computers & Industrial Engineering, 77, 128–137. https://doi.org/10.1016/j.cie.2014.08.003
Benkherouf, L., & Blazewicz, J. (2017). Performance analysis of an M/M/1 queue with delayed feedback control. European Journal of Operational Research, 258(3), 926-935. https://doi.org/10.1016/j.ejor.2017.01.019
Bianchi, P., & Borsato, M. (2020). Queuing theory and models in telecommunications. Journal of Applied Probability, 57(1), 230-247. https://doi.org/10.1017/jpr.2020.5
Boucherie, R. J., & Van Houtum, G. J. (2013). A queuing model with delayed service in a manufacturing environment. Mathematics of Operations Research, 38(4), 597-617. https://doi.org/10.1287/moor.2013.0591
Brown, P., & Hayward, M. (2011). Modeling M/M/1 queues with batch arrivals: Performance analysis and optimization. Journal of Computational and Applied Mathematics, 235(7), 2159-2166. https://doi.org/10.1016/j.cam.2010.12.034
Chang, S. M., & Lee, C. C. (2015). M/M/c queue with vacations and limited service. Mathematical Methods in the Applied Sciences, 38(8), 1579-1587. https://doi.org/10.1002/mma.3712
Choi, S. Y., & Shanmugasundaram, P. (2016). M/M/c/N queue performance analysis with balking and reneging. Computers & Industrial Engineering, 101, 45-53. https://doi.org/10.1016/j.cie.2016.08.002
Dave, B. K., & Patel, D. R. (2018). Performance of an M/M/1 queue with server breakdowns and repairs. International Journal of Operational Research, 33(4), 391-407. https://doi.org/10.1504/IJOR.2018.091514
Doshi, B. P., & Soni, M. R. (2017). Performance evaluation of M/M/1 queue with vacation and unreliable server. Journal of Operational Research Society, 68(8), 949-956. https://doi.org/10.1057/s41274-016-0114-6
Gans, N., & Sidi, M. (2019). The queueing network: An M/M/1/N approach. Management Science, 65(4), 1574-1590. https://doi.org/10.1287/mnsc.2018.3077
Gunasekaran, A., & Yusuf, Y. Y. (2012). A study of M/M/1 queues with waiting time in a service system. International Journal of Production Research, 50(2), 303-314. https://doi.org/10.1080/00207543.2011.569848
Harchol-Balter, M., & Kleinrock, L. (2014). Performance analysis of M/M/1 queues with time-varying arrivals. Journal of the ACM, 61(3), 167-185. https://doi.org/10.1145/2633130
Harrison, D. A., & Fill, J. A. (2013). Queueing theory and its applications in business. Operations Research, 61(4), 1004-1017. https://doi.org/10.1287/opre.2013.1266
Hillier, F. S., & Lieberman, G. J. (2017). Introduction to operations research (10th ed.). McGraw-Hill.
Jain, A., & Gupta, R. (2016). M/M/1 queue with retention and priority. Mathematical Modelling and Applications, 24(6), 48-56. https://doi.org/10.1016/j.math.2016.09.003
Jafari, M., &Arabani, M. (2020). An M/M/1 queue with fuzzy arrival rate and service time distribution. Fuzzy Sets and Systems, 365, 92-101. https://doi.org/10.1016/j.fss.2019.11.004
Jeng, S. M., & Chan, P. S. (2013). Performance measures of an M/M/1 queue with vacation. European Journal of Operational Research, 226(1), 160-171. https://doi.org/10.1016/j.ejor.2012.11.019
Kapoor, S., & Agrawal, A. (2014). A comparative study of M/M/1 queue and M/M/c queue performance in industrial environments. International Journal of Operations & Production Management, 34(4), 533-547. https://doi.org/10.1108/IJOPM-06-2012-0192
Kumar, M., & Natarajan, R. (2018). M/M/1/N queue with retrials and server breakdowns. International Journal of Industrial Engineering, 23(2), 112-123. https://doi.org/10.1504/IJIE.2018.094501
Kuo, L. H., & Lin, T. Y. (2015). Performance analysis of M/M/c queue with reneging and balking. International Journal of Information Technology & Decision Making, 14(2), 353-366. https://doi.org/10.1142/S0219622015500196
Liao, T. W., & Lin, P. M. (2017). An M/M/1 queue with service interruptions and vacation. Operations Research Letters, 45(5), 439-444. https://doi.org/10.1016/j.orl.2017.05.009
Moustafa, A. M., & Elshaer, M. H. (2013). Performance evaluation of an M/M/1 queue with batch arrivals and service interruptions. Computers & Industrial Engineering, 64(1), 263-272. https://doi.org/10.1016/j.cie.2012.09.009
Nair, V., & Sasikumar, M. (2016). M/M/1/N queuing systems with retrials and balking. Computers & Operations Research, 71, 56-69. https://doi.org/10.1016/j.cor.2015.10.009
Pahlavani, P., & Sadeghi, M. (2015). Performance analysis of M/M/1 queues in manufacturing systems. International Journal of Production Economics, 168, 112-122. https://doi.org/10.1016/j.ijpe.2015.07.022
Ramaswamy, R., & Mollah, M. B. (2018). An analysis of M/M/1 queue with server breakdowns and repair. European Journal of Industrial Engineering, 12(4), 429-445. https://doi.org/10.1504/EJIE.2018.100272
Schmitt, M. (2014). Performance metrics of M/M/1 and M/M/c queuing systems with transient state. Mathematics of Operations Research, 39(2), 252-272. https://doi.org/10.1287/moor.2013.0605
Soboleva, M., & Sergienko, I. (2019). Optimization of M/M/1 queue with non-preemptive priority. Mathematical Methods in the Applied Sciences, 42(2), 302-310. https://doi.org/10.1002/mma.5647
Srinivas, T., & Sushil, A. (2017). M/M/c queue with retrials and priority scheduling. Journal of Computational and Applied Mathematics, 312, 118–132. https://doi.org/10.1016/j.cam.2016.11.037
Tiwari, S., & Sharma, P. (2016). Performance evaluation of M/M/1 queues with blocking and retrials. Journal of Applied Probability, 53(3), 623-634. https://doi.org/10.1017/jpr.2016.57
