Simulation of Priority Queuing at TOTAL Petrol Filling Station in Makurdi Town Using SimEvents Toolkit

Document Type: Original Article


1 Department of Civil Engineering College of Engineering, University of Agriculture Makurdi, Nigeria

2 Department of Civil Engineering College of Engineering, University of Agriculture Makurdi, Nigeria


The incessant flash fuel scarcity leading to long queues and prolong waiting time at the TOTAL petrol station along Kashim Ibrahim road in Makurdi town has called for an efficient operational management policy. This study carried out simulation of priority queuing process at the station using SimEvent toolkit in MATLAB software. Field work at the station involved manual count of arriving vehicles and duration of service time of the pumps. It was used for estimating inter-arrival rates (veh/h) and service rate (veh/h) per server. Simulation model was developed using SimEvent toolkit which was simulated for experimental period of 6 hours (360 minutes) for the Do-Nothing Scenario on the Normal Queue (NQ) and demand split to a proposed Priority Queue (PQ) at 3%, 5%, 10%, 15%, 20% 25% and 30% of total demand. The split was based on assumed utility maximisation of motorist who may be willing to pay extra fare to be served earlier through the PQ in order to reduce waiting time and eliminate risk of waiting on queue by roadside and the stress of staying on long queues for long period. Results indicated significant reduction in waiting time on queue and queue length on the NQ as compared to the PQ. The optimised service delivery of the system was achieved at 80 – 85% demand on the NQ and 15 – 20% demand on the PQ. Adoption of the built model was therefore recommended for managers of the TOTAL petrol filling stations for optimum system performance and service delivery.


[1]     Schiller PL, Bruun EC, Kenworthy JR. An introduction to sustainable transportation: Policy, planning and implementation. Earthscan; 2010.
[2]     Balaji N. Optimal resource model using matlab/simulink controlled queuing system using multiserver at major fuel stations. Int J Pure Appl Math 2017;113:221–9.
[3]     Adeke PT. Mathematical Modelling of Priority Queues, M.Sc. Dissertation, Institute for Transport Studies, University of Leeds, United Kingdom 2015.
[4]     Adeke PT. Modelling of queuing process at airport check-in system: a case study of Manchester and Leeds-Bradford airports. Niger J Technol 2018;37:35. doi:10.4314/njt.v37i1.5.
[5]     Balaji N, Siva EP, Chandrasekaran AD, Tamilazhagan V. Optimal service using Matlab - simulink controlled Queuing system at call centers. J Phys Conf Ser 2018;1000:012167. doi:10.1088/1742-6596/1000/1/012167.
[6]     [Saidi S, de Barros A. Assessing Airport Passenger Screening Processing Systems. 13th World Conf Transp Res 2013.
[7]     Udo, B. It’s Official: Nigeria has no Authentic Data on Petrol Consumption. Premium Times Nigeria. Retrieved from 2018.
[8]     Hess S, Rose JM. Some lessons in stated choice survey design. Eur. Transp. Conf., vol. 2009, Citeseer; 2009.
[9]     Sanko N, Hess S, Dumont J, Daly A. Contrasting imputation with a latent variable approach to dealing with missing income in choice models. J Choice Model 2014;12:47–57. doi:10.1016/j.jocm.2014.10.001.
[10]   Kouwenhoven M. The Role of Accessibility in Passengers’ Choice of Airports, 2009, p. 129–63. doi:10.1787/9789282102466-5-en.
[11]   Osogami T, Wierman A, Harchol-Balter M, Scheller-Wolf A. How many servers are best in a dual-priority FCFS system. C Techical Rep C 2003.
[12]   Miller R. Priority Queues. Annals of Mathematical Statistics 2004;31:86–103.
[13]   Ha AY. Incentive-Compatible Pricing for a Service Facility with Joint Production and Congestion Externalities. Manage Sci 1998;44:1623–36. doi:10.1287/mnsc.44.12.1623.
[14]   Ben-Akiva M, Lerman SR. Discrete choice analysis: theory and application to travel demand. Transportation Studies; 1960.
[15]   Train K. Discrete Choice Methods with Simulation, Cambridge University Press 2020.
[16]   Hess S, Polak JW. Mixed logit modelling of airport choice in multi-airport regions. J Air Transp Manag 2005;11:59–68. doi:10.1016/j.jairtraman.2004.09.001.
[17]   Hess S, Rose JM. Some lessons in stated choice survey Design. European Transport Conference, 2009 proceedings, London, England 2009.
[18]   Kendall DG. Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann Math Stat 1953:338–54.
[19]   Coffman EG, Denning PJ. Operating systems theory. vol. 973. prentice-Hall Englewood Cliffs, NJ; 1973.
[20]   Bastani PA. Queueing Model of Hospital Congestion. MSc. Thesis submitted to Department of Mathematics Simon Fraser University 2009.
[21]   Sztrik J. Basic Queueing Theory, University of Debrecen, Faculty of Informatics 2012.
[22]   Bunday BD. Mathematical Modelling of Queues, the Mathematical Association. Math Gaz 1995;79:499–512.
[23]   Jain JL, Mohanty SG, Bohm W. A Course on Queueing Models, Statistics: A Series of Textbooks and Monographs. Chapman Hall/CRC, Taylor Fr Gr 2007.
[24]   Stephan FF. Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates. Oper Res 1958;6:399–418. doi:10.1287/opre.6.3.399.
[25]   Ross S. Stochastic Processes. New York, John Wiley and Sons 1983.
[26]   Ilin V, Simić D, Saulić N. Simulation Model of A Queuing System: The Case Study of A Fair Trade Manifestation in Novi Sad. 2nd Logist. Int. Conf., 2015.
[27]   MATLAB User Guide Manual. Mathworks Inc. USA 2015.
[28]   Google. Google Maps Inc., 2018 n.d.
[29]   NPC. National Population Commission. Federal Republic of Nigeria Official Gazzette. 94, No. 24 2006.