Document Type : Original Article


1 Department of Industrial Engineering, Arak branch, Islamic Azad University, Arak, Iran.

2 Department of Mechanical Engineering, Arak University of Technology, Arak, Iran.


This paper includes a simulation model built in order to predict the performance indicessuch aswaiting time by analyzing queue’s components in the real world under uncertain and subjective situation. The objective of this paper is to predict the waiting time of each customer in an M/M/C queuing model. In this regard, to enable decision makers to obtain useful results with enough knowledge on the behavior of system, the queuing system is considered in fuzzy environment in which the arrival and service times are represented by fuzzy variables. The proposed approach for vague systems can represent the system more accurately, and more information is provided for designing queueing systems in real life. Furthermore, simulation method is applied successfully for modeling complex systems and understanding queuing behavior. Finally, a numerical example as a case study in a banking system is solved to show the validity of developed model in the real situation.


Abou-El-Ata and M., Hariri, A., (1992). “The M/M/C/N queue with balking and reneging”, Computers and Operations Research, Vol. 19, pp. 713-716.
Alves, F.S.Q., Yehia, H.C., Pedrosa, L.A.C. and Kerbache, L., (2011). “Upper bounds on Performance measures of Heterogeneous M/M/C queues”, Hindawi Publishing Corporation, Mathematical Problems in Engineering, Article ID 702834.
Barak, S. and Fallahnezhad, M. S., (2012). “Cost Analysis of Fuzzy Queuing Systems”, International Journal of Applied Operational Research, Vol. 2, No. 2, pp. 25-36.
Bouazzi, I., Bhar and J., Atri, M., (2017). “Priority-based queuing and transmission rate management using a fuzzy logic controller in WSNs”, ICT Express, Vol. 3, No. 2, pp. 101-105.
Bonissone, P. P., (1980). “A fuzzy sets based linguistic approach: theory and applications”, In Proceedings of the 12th conference on winter simulation, IEEE Press, pp. 99-111.
Buckley, J. J., (2005). “Simulating Fuzzy systems”, Springer Science & Business Media, Vol. 171.
Carson, I. I., Nicol, D. M., Nelson, B. L. and Banks, J., (2005). Discrete-event system simulation, Prentice-Hall, Fourth Edition.
Chen, SP. (2004). “Parametric nonlinear programming fuzzy queues with finite capacity”, European Journal of Operational Research, Vol. 157, pp. 429-438.
Chen, SP., (2007). “Solving Fuzzy queuing decision problems via parametric mixed integer nonlinear programming method”, European Journal of Operational Research, Vol. 117, pp. 445-457.
Cooper, R.B., (1981). Introduction to queueing theory, North Holland.
Deshpande Y. L., Roger Jenkins and Simon Taylor, (1996). "Use of Simulation to Test Client-Server Models", pp. 1210- 1217Enrique H., (2014). "Simulation of Fuzzy Queueing Systems with a Variable Number of Servers, Arrival and Service Rates", Ruspini, Life Fellow, IEEE.
Fathi-Vajargah B. and Ghasemalipour, (2016). "Simulation of a random fuzzy queuing system with multiple servers", Journal of Contemporary Mathematical Analysis, Vol. 51, No. 2, pp 103–110.
Gerald Liberman and Fredericks Hillier, (1967). Introduction to operations research, McGraw-Hill, New York.
Gou, X., Xu, Z. and Liao, H., (2017). “Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making”, Information Sciences, Vol. 388, pp. 225-246.
Gross, D., (2008). Fundamentals of queueing theory, John Wiley & Sons, USA.
Güneş, M., (2012). “Modeling and Performance Analysis with Discrete-Event Simulation”, Computer Science, Informatik 4 Communication and Distributed Systems, Chapter 1.
Hillier, F. and Lieberman, G., (2005). Introduction to Operations Research, McGraw-Hill, New York, USA.
Jolai, F., Asadzadeh, S.M., Ghodsi, R. and Bagheri-Marani, Sh., (2016). “A multi-objective fuzzy queuing priority assignment model”, Applied Mathematical Modelling, Vol. 40, No. 21, pp. 9500-9513.
Ke, J.Ch., Huang, H.I. and Lin, Ch.H., (2007). “On retrial queueing model with fuzzy parameters”, Physica A: Statistical Mechanics and its Applications, Vol. 374, No. 1, pp. 272-280.
Mageed A. Ghaleb, Umar S. Suryahatmaja and Ibrahim M. Alharkan, (2015). "Modeling and simulation of Queuing Systems using arena software: A case study, Industrial Engineering and Operations Management (IEOM)", International Conference on Dubai, United Arab Emirates.
Maragatha Sundari, S. and Srinivasan, S., (2011). “M/M/C Queueing Model for Waiting Time of Customers in Bank Sectors ", Int. J. of Mathematical Sciences and Applications, Vol. 1, No. 3.
Quintas, A., (2016). “A Case Based approach to assess Waiting Time Prediction at an Intensive Care Unity”, Springer International Publishing.
Pardo, M.J. and Fuente, D., (2007). “Optimizing a priority-discipline queueing model using fuzzy set theory”, Computers & Mathematics with Applications, Vol. 54, No. 2, pp. 267-281.
Pardo, M.J. and Fuente, D., (2010). “Fuzzy Markovian decision processes: Application to queueing systems”, Computers & Mathematics with Applications, Vol. 60, No. 9, pp. 2526-2535.
Prakash, M., Sathish and V., (2016). “Qespera: an adaptive framework for prediction of queue waiting times in supercomputer systems”, Concurrency and Computation: Practice and Experience, Vol. 28, No. 9, pp. 2685–2710.
Sadeghi, N., Robinson Fayek, A. and Gerami Seresht, N., (2015). “Queue performance measures in construction simulation models containing subjective uncertainty”, Automation in Construction, Vol. 60, pp. 1-11.
Sameer, S.S., (2014). “Analysis of Single Server Queuing Model”, International Journal on Information Theory (IJIT), Vol. 3, No. 3.
Shavandi, H., (2006). “Fuzzy set theory and its application in industrial engineering and management”, Ghostareshe Olompaye, Tehran, Iran.
Syski, R., Waiting-time prediction, Maryland, Md. USA.
Takeshi, Y., Yuko, K., Masao, O. and Takeo, Y., (2014). “Evaluation of Waiting Time Prediction using Data Collected from Prescriptio”, Japanese Journal of Social Pharmacy, Vol. 33, No. 2, pp. 61-66.
Wang, Y.B., Qian, C. and Cao, J.-D., (2010). “Optimized M/M/c model and simulation for bank queuing system”, Software Engineering and Service Sciences (ICSESS), 2010 IEEE International Conference on Beijing, China.
Yazdanbakhsh, O. and Dick, S. (2017). “A systematic review of complex fuzzy sets and logic”, Fuzzy Sets and Systems, in press,
Yingjie, F. and Puion, A., (2005). “Waiting time prediction: an enhancement for call admission control of mobile system using neural networks, Advanced Communication Technology”, ICACT 2005. The 7th International Conference on Phoenix Park, South Korea.
Zadeh, L.A., (1965). “Fuzzy sets”, Information and Control, Vol. 8, No. 3, pp. 338-353.
Zhang Laifu Joel, Ng Wen Wei, Jonathan Louis and Tay Seng Chuan, (2000). "Discrete–event simulation of queuing systems", Sixth Youth Science Conference, Ministry of Education, Singapore.
Zhu, D.M., Ching, W.K. and Guu, S.M., (2016). “Sufficient conditions for the ergodicity of fuzzy Markov chains”, Fuzzy Sets and Systems, Vol. 304, pp. 82-93.