Author(s)

Adegoke S. Ajiboye, Kayode A. Saminu

Department of Statistics, The Federal University of Technology, Akure, Nigeria.

The multistage queue model was developed for a situation where parallel and unrelated queues exist at the first stage only. These queues merged into single queues at the remaining stages. The parallel queues offer services that are different from one another and customers arrive to join the queue that offer services that they need. The mathematical model was developed assuming an M/M/1 queue system and the measures of effectiveness were derived. The model was applied to solve the problem of customer congestion in a restaurant in the city of Ibadan, Nigeria that serves three different local delicacies. The three local delicacies constitute three different queues at the first stage. The second stage consists of only one queue which is for purchase of drinks and the third stage which is the last stage is for payment. Every customer in the restaurant passes through the three stages. Utilization factors for the five queues were determined and found to range from 70% to 97%. The average time spent by customers in the system was found to be 543.04 minutes. A simulation study using what-if scenario analysis was performed to determine the optimum service configuration for the system. The optimum configuration reduced average time for customers in the system from 543.04 minutes to 13.47 minutes without hiring new servers.

Multistage Queues, Customer Congestion, What-If Scenario Analysis, Queue Network

Ajiboye, A. and Saminu, K. (2018) A Multi-Stage Queue Approach to Solving Customer Congestion Problem in a Restaurant. Open Journal of Statistics, 8, 302-316. doi: 10.4236/ojs.2018.82019.