The multistage queue model was developed for a situation where parallel and\nunrelated queues exist at the first stage only. These queues merged into single\nqueues at the remaining stages. The parallel queues offer services that are different\nfrom one another and customers arrive to join the queue that offer services\nthat they need. The mathematical model was developed assuming an\nM/M/1 queue system and the measures of effectiveness were derived. The\nmodel was applied to solve the problem of customer congestion in a restaurant\nin the city of Ibadan, Nigeria that serves three different local delicacies.\nThe three local delicacies constitute three different queues at the first stage.\nThe second stage consists of only one queue which is for purchase of drinks\nand the third stage which is the last stage is for payment. Every customer in\nthe restaurant passes through the three stages. Utilization factors for the five\nqueues were determined and found to range from 70% to 97%. The average\ntime spent by customers in the system was found to be 543.04 minutes. A simulation\nstudy using what-if scenario analysis was performed to determine\nthe optimum service configuration for the system. The optimum configuration\nreduced average time for customers in the system from 543.04 minutes to\n13.47 minutes without hiring new servers.
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