Modeling Queuing Operational Characteristics at Automated Teller Machine Points

Chaku Shammah Emmanuel., Sandra Cordelia Suleiman and Awhigbo Ezekiel Bulus
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Chaku Shammah Emmanuel.: Department of Statistics, Nasarawa State University, Keffi
Sandra Cordelia Suleiman: Department of Statistics, Nasarawa State University, Keffi
Awhigbo Ezekiel Bulus: Department of Statistics, Nasarawa State University, Keffi

International Journal of Research and Innovation in Applied Science, 2024, vol. 9, issue 6, 446-461

Abstract: The study was designed to obtain the queuing behavior of the queuing system at a bank. The data on queuing behavior was gathered for a period of seven (7) weeks; which comprises of four (4) hours daily from 14th August to 30th September, 2023. Four (4) ATM machines were observed as the service discipline for the period of seven (7) weeks in the bank. Plots reveals a consistent pattern throughout the month, with Sundays and Mondays experiencing double the average customer volume compared to weekdays and Saturdays. Moving on to the operating characteristics of the system, it was observed that the average customer arrival rate is approximately 12 customers per hour, with an average service rate of 30 customers per hour. The traffic intensity (Ï ) is calculated as 0.1202, indicating that, on average, 12.02% of customers keep the ATM busy per hour. The system utilization rate is 87.98%, implying that nearly 88% of customers are in the queue per hour. Additionally, the average time a customer spends in the system, considering additional transaction time, is 8.32 minutes. The probability of the system being empty is calculated as 0.389, indicating that the system is idle for 38.2% of the time and busy with customers for 61.1% of the time. Further analysis explores customer behavior, considering the probability that an arriving customer enters the system or reneges based on encountering a certain number of customers. On less busy days, an arriving customer enters the queue at 43.74% of the time, while on busy days, they enter the system at 99.97% of the time. The probability of an arriving customer reneging on less busy days is 56.26%, and on busy days, it is only 0.028%. Regarding unfairness characteristics, the system is shown to be highly discriminative.

Date: 2024
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