The increase in land travel demand over the years which poses a challenge in managing the high influx of people and goods into urban centres and cities such as Abuja, Calabar, Lagos, Kano, and Kaduna, Nigeria has led to queues in security check points. This study determines a mathematical model for analysing queueing system performance measures using the data obtained from Kugbo check-point, Abuja Keffi Highway. The service time data and system settings are used to choose the M/M/1 queueing mathematical model for a single server queueing system. According to the study, an average queue includes 3751 cars and takes 1 hour and 11 minutes to complete. An hourly queueing graph showed that on the busiest days, queue length and waiting time rose. Based on the busiest days (Mondays), an hourly queueing graph revealed that customer queueing length and waiting time is at its highest in the morning hours from 7am to 11am, and then from 4pm to 7pm. For effective and economical system management, this length of time spent on queue should be taken into account, also artificial intelligent simulation models like Netsim, SimEvent in MATLAB models are recommended for comparative studies.
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