TITLE:
A Multi-Stage Queue Approach to Solving Customer Congestion Problem in a Restaurant
AUTHORS:
Adegoke S. Ajiboye, Kayode A. Saminu
KEYWORDS:
Multistage Queues, Customer Congestion, What-If Scenario Analysis, Queue Network
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.2,
April
13,
2018
ABSTRACT: 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.