Application of Queueing Theory to Customers Purchasing Premium Motor Spirit (PMS) at a Filling Station
The formation of waiting lines is a prevalence scenario that happens whenever the immediate demand for a service surpass the current capacity to provide that service. This discrepancy may be temporal, but a queue accumulates during the period. Formation of a line causes an increase of customers waiting time, over-utilization of the available servers and loss of customer goodwill. Application of Queueing theory determines the measures of performance of the service facility; this can be used to design the appropriate service facility. Data for this study was collected at Nigeria National Petroleum Corporation (NNPC) Mega Station Jos for seven consecutive days between the hours of 7am-6pm daily through observations, interviews, and records of customers purchasing PMS only. The multi-server model was adopted for the study of the existing structure has eight servers. The data was analyzed using descriptive analysis; Minitab-16 and TORA- 2.0 software. The arrival rate λ=2.7483 customers/min is greater than the service rate μ=0.4137 customer/min showing that queue exists. There are Poisson arrivals and exponential service distributions as validated by a Chisquare goodness of fit test. The calculated mean of utilization factors for five scenarios is 67.808%.The utilization factor of 66.432 % obtained for M/M/10: FCFS/∞/∞ is the closest to this mean value and hence selected as the average utilization factor. This model that yielded an average queue time of 0.12353 minute and an average queue length of 0.33948 customers was formulated. M/M/10 gave optimal results and were proposed for adoption and to be used for solving similar problems. Management should open up two more servers. Incentives should be given to creating over time that will increase or sustain the acceptable utilization factor. Any utilization factor value below 66.432 % is not encouraged for this system as it will increase idle time.
MM Kembe, Gbenimak CJ and Onoja AA
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