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In this work, we suggest an analytic technique with triangular fuzzy and triangular intuitionistic fuzzy numbers to compute the membership functions of considerable state-executing proportion in Erlang service models. The inter-entry rate, which is Poisson, and the admin (service) rate, which is Erlang, are both fuzzy-natured in this case, with FEk designating the Erlang probabilistic deviation with k exponentially phase. The numeric antecedents are shown to validate the model's plausibility, FM/FEk/1. A contextual inquiry is also carried out, comparing individual fuzzy figures. Intuitionistic fuzzy queueing models that are comprehensible are more categorical than fuzzy queueing models. Expanding the fuzzy queuing model to an intuitionistic fuzzy environment can boost the implementation of the queuing model. The purpose of this study is to assess the performance of a single server Erlang queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. The fuzzy queuing theory model's performance evaluations are reported as a range of outcomes, but the intuitionistic fuzzy queuing theory model provides a myriad of values. In this context, the arrival and the service rate are both triangular and intuitionistic triangular fuzzy numbers. An assessment is made to find evaluation criteria using a design protocol in which fuzzy values are kept as they are and not made into crisp values, and two statistical problems are solved to understand the existence of the method.


Queuing theory Triangular fuzzy numbers Triangular intuitionistic fuzzy numbers Erlang service Performance measures Infinite capacity

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How to Cite
S, A., & Shanmugasundari, M. (2023). Comparison of Infinite Capacity FM/FEk/1 Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Erlang Service Rates. Pakistan Journal of Statistics and Operation Research, 19(1), 187-202.


  1. Ashok Kumar, V. (2011). A membership function solution approach to fuzzy queue with Erlang service model. International Journal of Mathematical Sciences and Applications, 1(2):881-891.
  2. Atanassov, K. (1999). Intuitionistic Fuzzy set: Theory and Applications. Springer Physica-Verlag, Berlin.
  3. Atanassov, K., and Gargor, G. (1989). Interval valued intuitionistic fuzzy set. Fuzzy Sets and Systems, 31(3): 343-349.
  4. Barak, S., and Fallahnezhad, M. (2012). Cost Analysis of Fuzzy Queuing Systems. International Journal of Applied Operational Research, 2(2):25-36.
  5. Buckley, J. (1990). Elementary queuing theory based on possibility theory. Fuzzy Sets and Systems, 37(1):43-52.
  6. Buckley, J. J., Feuring, T., and Hayashi, Y. (2001). Fuzzy queuing theory revisited. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(05):527-537.
  7. Chen, G., Liu, Z., and Zhang, J. (2020). Analysis of strategic customer behavior in fuzzy queuing systems. Journal of Industrial and Management Optimization, 16(1):371-386.
  8. Chen, S. P. (2005). Parametric nonlinear programming approach to fuzzy queues with bulk service. European Journal of Operational Research, 163(2):434-444.
  9. Chen, S. P. (2006). A bulk arrival queuing model with fuzzy parameters and varying batch sizes. Applied Mathematical Modelling, 30(9):920-929.
  10. Ferdowsi, F., Maleki, H. R., and Niroomand, S. (2019). Refueling problem of alternative fuel vehicles under intuitionistic fuzzy refueling waiting times: A fuzzy approach. Iranian Journal of Fuzzy Systems, 16(3):47-62.
  11. Giacomo Ascione, Nikolai Leonenko, and Enrica Pirozzi. (2020). Fractional Erlang queues. Stochastic Processes and their Applications, 130(6):3249-3276.
  12. Hanumantha Rao Sama, Vasanta Kumar Vemuri, and Venkata Siva Nageswara Hari Prasad Boppana. (2021). Optimal control policy for a two-phase M/M/1 unreliable gated queue under N-policy with a fuzzy environment. Ingénierie des Systèmes d’Information, 26(4):357-364.
  13. Hanumantha Rao, S., Vasanta Kumar, V., and Sathish Kumar, K. (2020). Encouraged or discouraged arrivals of an m/m/1/n queuing system with modified reneging. Advances in Mathematics: Scientific Journal, 9(9):6641-6647.
  14. Hanumantha Rao, S., Vasanta Kumar, V., Srinivasa Rao, T., and Srinivasa Kumar, B. (2016). A two-phase unreliable M/E_k/1 queuing system with server start up, N-policy, delayed repair and state dependent arrival rates. Global Journal of Pure and Applied Mathematics, 12(6):5387-5399.
  15. Kao, C., Li, C.C., and Chen, S.P. (1999). Parametric programming to the analysis of fuzzy queues. Fuzzy Sets and Systems, 107(1):93-100.
  16. Konstantin Kogan, Yael Perlman, and Galit Kelner. (2023). Software portfolio optimization: access rejection versus underutilization. Applied Sciences, 13(4):2314.
  17. Li, R. J., and Lee, E. (1989). Analysis of fuzzy queues. Computers & Mathematics with Applications, 17(7): 1143- 1147.
  18. Ming Ma., Menahem Friedman., and Abraham Kandel. (1999). A new fuzzy arithmetic. Fuzzy sets and systems, 108(1):83-90.
  19. Mohamed Bisher Zeina. (2020). Erlang Service Queuing Model with neutrosophic parameters. International Journal of Neutrosophic Science, 6(2):106-112.
  20. Mohammed Shapique, A. (2016). Fuzzy queue with Erlang service model using DSW algorithm. International Journal of Engineering Sciences and Research Technology, 5(1):50-54.
  21. Narayanamoorthy, S., Anuja, A., Brainy., J.V., Daekook Kang., and Maheshwari, S. (2020). Analyzation of fuzzy queuing performance measures by the L-R method with Erlang service model. AIP Conference Proceedings, 2261(030055):1-11.
  22. Narayanamoorthy, S., Anuja, A., Murugesan, V., and Daekook Kang. (2020). A distinctive analyzation of intuitionistic fuzzy queuing system using Erlang service model. AIP Conference Proceedings, 2261(030040):1-10.
  23. Negi, D., and Lee, E. (1992). Analysis and simulation of fuzzy queues. Fuzzy Sets and Systems, 46(3):321- 330.
  24. Prade, H. M. (1980). An outline of fuzzy or possibilistic models for queuing systems. Fuzzy Sets, 147-153.
  25. Revathi, S., Selvakumari, K. (2020). Performance measurements of an unsignalized traffic flow using fuzzy queuing theory. Advances in Mathematics: Scientific Journal, 9(11):9973-9981.
  26. Ritha, W., and Menon, B. S. (2011). Fuzzy N Policy Queues with Infinite Capacity. Journal of Physical Sciences, 15:73-82.
  27. Shaw, A. K., and Roy, T. K., (2012). Some Arithmetic Operations on Triangular Intuitionistic Fuzzy Number and its Application on reliability evaluation. International Journal of Fuzzy Mathematics and Systems, 2(4):363-382.
  28. Usha Prameela, K., and Pavan Kumar. (2019). FM/FE_k/1 queuing model with Erlang service under various types of fuzzy numbers. International Journal of Recent Technology and Engineering, 8(1):942-946.
  29. Usha Prameela, K., and Pavan Kumar. (2021). An Interpretation of non-preemptive priority fuzzy queuing model with asymmetrical service rates. Pakistan Journal of Statistics and Operation Research, 17(4):791-797.
  30. Zverkina, G. A. (2021). On some extended Erlang-Sevastyanov queuing system and its convergence rate. Journal of Mathematical Sciences, 254(4):485-503.