An M/M/s Queuing Model for Selected Petroleum Tank Farms in Oghara, Delta State, Nigeria

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-2
Year of Publication : 2021
Authors : Tsetimi J, Orighoyegha, M. G.


MLA Style: Tsetimi J, Orighoyegha, M. G.. "An M/M/s Queuing Model for Selected Petroleum Tank Farms in Oghara, Delta State, Nigeria" International Journal of Mathematics Trends and Technology 67.2 (2021):29-35. 

APA Style: Tsetimi J, Orighoyegha, M. G.(2021). An M/M/s Queuing Model for Selected Petroleum Tank Farms in Oghara, Delta State, Nigeria. International Journal of Mathematics Trends and Technology, 29-35.

In this paper we apply the M/M/S queuing model to Rain oil and Nepal tank farms, Oghara Delta State, Nigeria. The queuing patterns of the tank farms were analyzed using an M/M/S queuing model. The average waiting time of trucks in the system and in the queue and utilization rate of the supply system were computed with a view to determining how best the queuing system can be optimized in both tank farms. Comparison was also carried out between both tank farms. Findings revealed that the utilization rate was very high at both tank farms This means that the system is busy most of the time. We considered also, the waiting time of trucks on queue and the time spent in the system, and provided scientific evidence that the excessive amount of time spent in the system and on the queue can be greatly reduced by increasing the number of service channels. The study concluded by re-iterating the relevance of queuing theory to the effective service delivery of the tank farm industry in Nigeria and recommends the expansion of existing service channels as a way of optimizing efficiency and quality service delivery to truck owners.


[1] Erlang, A. K. (1917). Solution of Some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges. Reprinted in Telektronikk. 91(213)(1995) 42-49.
[2] Cooper, R. B., Introduction to Queuing theory. New York: Macmillan., (1981).
[3] Gross, D. and Harris, C. M., Fundamentals of queuing theory. New York: Wiley, 3rd Edition.,(1998).
[4] Wu, L., Application of Queuing Theory with Monte Carlo Simulation to the Study of the Intake and adverse Effect of Ethanol. Alcohol and Alcoholism. 33(5)(1998) 519-527.
[5] Mcmanus, M. C., Long, M. C., Cooper A. B. and Lavak, E., Queuing theory Accurately models the Need for critical care resources. Anesthesiology. 100(5)(2004) 1271-1276.
[6] Kasum, A. S., Abdulraheem, A. and Olaniyi T. A., Queue Efficiency in Nigeria Banks: A comparative analyses of old and new generation banks. Illorin Journal of Sociology. 2(1)(2006) 162-172.
[7] Tian, H. and Tong, Y., Study on Queuing System Optimization of Bank Based on BPR. 3rd International Conference on Environmental Service and Information and Application Technology (ESIAT). Oyo. (2011) 640-649.
[8] Duckworth, W. E., Operational Research techniques. Methinen and co., London,(1962).
[9] Green, V. L., How Many Hospital Beds?. Inquiry. 37(4)(2002) 400-412.
[10] Schwarte, J. and Freedman, W., Stochastic Model in Queuing Theory. 2nd Edition. Academic Press, Amsterdam.,(2011).
[11] Nosek, A. R. and Wilson, P. J., Queuing Theory and Customer Satisfaction, A review of Terminology, Trend Application to Pharmacy Practice. Hospital Pharmacy. 3613. LASTEH, Lagos., (2010).
[12] Amos, H. (2008). Simulation of Restaurant Operations using the Restaurant Modeling Studies. Proceedings of the 2002 Winter Simulation Conference. IEEE Press. (2002) 144-1453.
[13] Tsetimi, J., A Survey of Some Queuing Models in Multistage Manufacturing Systems. Journal of Nigerian Institution of Production Engineers. (2013) 15:195-201.
[14] Sharma, J. K. (2013). Operations Research: Theory and Applications, 5TH Edition. Mcmillian Publishers Ltd, India.

Keywords : Multiiple Servers, Petroleum Tank Farms, Queuing Model, Utilization Rate, Waiting Line