The Efficient Way for Operating the Queuing System

In our daily life, we often have to wait for paying for groceries, ordering food, or any others activities involving customers and servers. Queuing theory is a study of waiting and its formation as well as function using a mathematical model. The model represents a queueing system that indicates the characteristics and patterns of the queue such as average waiting time, average serving time, etc. These models could help determine the efficient way for operating the queuing system.

According to Operations Research: Applications and Algorithms (Winston,1987), the queuing system uses Kendall notation to describe the characteristics or attributes of the queue. This notation (1/2/3/4/5/6) describes a queuing system with six characteristics: (1) arrival time distribution, (2) service time distribution, (3) a number of servers, (4) queue discipline, (5) a maximum number of customers in the system, and (6) customers’ population size.

Arrival time and service time distribution has four possibilities:

1. M means the distribution is independent, identically distributed (iid) random variables having an exponential distribution.

2. D means the distribution is iid and deterministic.

3. Ek means the distribution is iid Erlangs distribution with parameter k.

4. GI means the distribution follows some general distribution.

Moreover, the queue discipline also has four variations: FCFS (First come, first served), LCFS (Last come, first served), SIRO (Service in random order), and GD (General queue discipline). For instance, the notation M/M/2/FCFS/10/∞ could represent a drive-thru at a restaurant with two lanes, exponential arrival time, and serving time, using the first-come-first-serve discipline with a total capacity of 10 cars.

Queues are an essential way to managing customers’ flow with limited resources; However, longer queue time may result to customer dissatisfaction and may risk losing revenue. Through queuing theory, organizations may apply more efficient queueing systems that could not only improve customer satisfaction but also provide information for other managerial operations such as, scheduling and pricing.