Mathematical Modelling and Automation of Real-time Queues

Abstract

The traditional Queue System followed today is quite certainly failing in managing huge crowds, especially in urban populated areas. There are even instances where the customers (users) have to wait for hours to get simple tasks done. It is important to manage these systems effectively by the Organizations in order to improve customer experience. While the Token Queue System provides a fairly acceptable solution, it has many problems of its own. In a token system, waiting physically in the building premises is inevitable. The design discussed in this paper holds the prime idea of completely automating the Token System, where users’ waiting time is almost negligible. Using the classical Queue Theory and Poisson’s Probability Distribution, it is possible to predict the arrival of the users and the average service time, for a particular service. It uses minimal resources and is cost effective. This paper discusses a model that uses these ideas to build a system that automates the traditional queuing system. It aims not only to minimize the customer wait time, but also reduce the crowds at the service area.