Examples of Queuing Theory
Various real-life examples where Queuing theory is uses are:
Call Center Example: Consider a call center with a single server that receives calls according to a Poisson process with a rate of 10 calls per minute. The service time for each call follows an exponential distribution with a mean of 3 minutes. Using queuing theory, we can calculate the average number of calls waiting in the queue (Lq) and the average waiting time in the queue (Wq) as:
Lq = λ2 / (μ × (μ – λ))
= 102 / (1/3 × (1/3 – 10))
= 10 calls
Wq = Lq / λ
= 10 / 10 = 1 minute
Supermarket Checkout Example: A supermarket has two checkout counters, each with its own queue. Customers arrive according to a Poisson process with a rate of 20 customers per minute and are served in a first-come-first-served (FCFS) manner. The service time for each customer follows an exponential distribution with a mean of 2 minutes. Using queuing theory, we can calculate the average number of customers in the system (L) and the average waiting time in the queue (Wq) as:
L = (λ / μ) / (1 – (λ / (2 × μ)))
= (20 / 30) / (1 – (20 / (2 × 30)))
= 1.5 customers
Wq = L / λ – 1/μ
= 1.5 / 20 – 1/30
= 0.075 minutes
Queuing Theory
Queuing theory is a specific division of mathematics that focuses on studying waiting lines (queues) in cases where there is an excess of demand for a service as compared to the availability of the service. It gives a way of looking at and analyzing the behaviour of systems which encounter congestion as a normal occurrence: call centres, computer networks, transportation, etc.
By observing queue length, customers’ waiting time, and server utilization, queuing models can become immensely beneficial in resource management and enhancement of systems performance.
In this article, we have covered the basics of Queueing Theory.
Table of Content
- What Is Queuing Theory?
- How Queuing Theory Works
- Who Invented Queuing Theory?
- What Are Basic Elements of Queuing Theory?
- How Do You Use Queuing Theory?
- Examples of Queuing Theory
- Applications of Queuing Theory