Mario Luis Chew Hernández, Leopoldo Viveros Rosas, Verónica Velázquez Romero


This paper shows a management model for a queuing system operating two shifts and where client reneging is present. The model provides the optimal active server policy considering lost clients and cost. Using influence diagrams and decision trees, the proposed model implements a Bayesian scheme to update the initial knowledge in response to the observed number of lost customers in the first shift. In addition, a utility function is used to represent the preferences of the decision-maker and simulation to determine the consequences and probabilities of the trees. The results are displayed as the number of active servers recommended for each shift, according to the preferences of the decision-maker and the clients lost in the first shift. For the case study, it is found that if the weight for the number of lost clients in the utility function (kNL) is less than 0.63, a single server should be used in both shifts, while when kNL is greater than said value, the first shift opens one server, while a second one is activated for the next shift depending on the number of lost clients in the first shift.


Queue Theory; Simulation; Decision analysis; Influence Diagram, Customer Reneging

Full Text:



H.M. Taha, Introduction to operations research. USA: McGraw-Hill, 2011.

R. T. Clemen, Making Hard Decisions: An introduction to Decision Analysis. USA: Duxbury Press, 1996.

K.A. Alnowibet, A. Khireldin, M. Abdelawwad, and A.W. Mohamed, “Airport terminal building capacity evaluation using queuing system,” Alexandria Engineering Journal, vol. 61, no. 12, pp. 10109-10118, 2022, doi:10.1016/j.aej.2022.03.055

R. Shone, K. Glazebrook, and K.G. Zografos, “Applications of stochastic modeling in air traffic management: Methods, challenges and opportunities for solving air traffic problems under uncertainty,” European Journal of Operational Research, vol. 292, no. 1, pp. 1-26, 2021, doi:10.1016/j.ejor.2020.10.039

H. Tarakci, Z. Ozdemir, and M. Sharafali, “On the staffing policy and technology investment in a specialty hospital offering telemedicine,” Decision Support Systems, vol. 46, no. 2, pp. 468-480, 2009, doi:10.1016/j.dss.2008.08.001

L. Kerbache and J. MacGregor Smith, “Multi-objective routing within large scale facilities using open finite queueing networks,” European Journal of Operational Research, vol. 121, no. 1, pp. 105-123, 2000, doi:10.1016/S0377-2217(99)00018-1

A. Pala and J. Zhuang, “Security screening queues with impatient applicants: A new model with a case study,” European Journal of Operational Research, vol. 265, no. 3, pp. 919-930, 2018, doi:10.1016/j.ejor.2017.08.038

X. Wang and J. Zhuang, “Balancing congestion and security in the presence of strategic applicants with private information,” European Journal of Operational Research, vol. 212, no. 1, pp. 100-111, 2011, doi:10.1016/j.ejor.2011.01.019

F. Trigos, A.R. Vazquez, and L.E. Cárdenas-Barrón, “A simulation-based heuristic that promotes business profit while increasing the perceived quality of service industries,” International Journal of Production Economics, vol. 211, pp. 60-70, 2019, doi:10.1016/j.ijpe.2019.01.009

Q. Wang and Z. Bin, “Analysis of a busy period queuing system with balking, reneging and motivating,” Applied Mathematical Modelling, vol. 64, pp. 480-488, 2018, doi:10.1016/j.apm.2018.07.053

K. Sasanuma and A. Scheller-Wolf, “Approximate performance measures for a single station two-stage reneging queue,” Operations Research Letters, vol. 49, no. 2, pp. 212-217, 2021, doi:10.1016/j.orl.2021.01.004

W.F. Nasrallah, “How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging,” European Journal of Operational Research, vol. 193, no. 1, pp. 317-320, 2009, doi:10.1016/j.ejor.2007.11.055

S.I. Ammar, M.M. Helan, and F.T. Al Amri, “The busy period of an M/M/1 queue with balking and reneging,” Applied Mathematical Modelling, vol. 37, no. 22, pp. 9223-9229, 2013, doi:10.1016/j.apm.2013.04.023

W. Xiong, D. Jagerman, and T. Altiok, “M/G/1 queue with deterministic reneging times,” Performance Evaluation, vol. 65, no. 3–4, pp. 308-316, 2008, doi:10.1016/j.peva.2007.07.003

C.-H. Wu and J.-C. Ke, “Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers,” Journal of Computational and Applied Mathematics, vol. 235, no. 3, pp. 547-562, 2010, doi:10.1016/j.cam.2010.06.005

S. Dimou, A. Economou, and D. Fakinos, “The single server vacation queueing model with geometric abandonments,” Journal of Statistical Planning and Inference, vol. 141, no. 8, pp. 2863-2877, 2011, doi:10.1016/j.jspi.2011.03.010

A. Economou, D. Logothetis, and A. Manou, “The value of reneging for strategic customers in queueing systems with server vacations/failures,” European Journal of Operational Research, vol. 299, no. 3, pp. 960-976, 2022, doi:10.1016/j.ejor.2022.01.010

A.I. Pazgal and S. Radas, “Comparison of customer balking and reneging behavior to queueing theory predictions: An experimental study,” Computers and Operations Research, vol. 35, no. 8, pp. 2537-2548, 2008, doi:10.1016/j.cor.2006.12.027

R.A. Howard, “Decision Analysis: Practice and Promise,” Management Science, vol. 34, no.6, pp. 679-695, 1988.

M.D. Resnik, Choices: An introduction to Decision Theory. USA: The University of Minnesota Press, 2008.

S. Ross, Simulation. USA: Academic Press, 2012.

R. Keeney, Value-Focused Thinking. USA: Duxury Press, 1992.

R.A. Howard and A.E. Abbas, Foundations of Decision Analysis. USA: Pearson Education, 2016.

DOI: https://doi.org/10.21776/ub.jemis.2023.011.02.6


  • There are currently no refbacks.

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