Introduction and Features of Queuing System and Application of Queuing Theory

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Theory of Queue in Queuing System

A queue is a waiting line of customers, animate or inanimate for some kind of service. It is formed when the number of customers arriving is greater than the number of the customer being served during a period of time. 

Number of Customers in System at any time = number of customers in Queue + number of customers being served.

Queuing Theory deals with situations where service is demanded. Different  Characteristics of Queuing System are:

• Customers: Unit, animate or inanimate that demands some form of service. 
• Server: A make facility that provides service to customers. One or more servers can be used by the Queuing System. 
• Queue or Waiting line: Arriving customers who cannot be served immediately on arrival wait in Queue to get service. 
•  Queue Discipline: 
• FCFS/FIFO: First Come First Serve or First In First Out. 
• SIRO: Service in Random Order. 
• Size Of Waiting Room: It can limit the maximum Queue size. 
• Traffic Intensity: It is denoted by rho(ρ). It is the ratio of the average arrival rate to the average departure rate. It is also called the Utilization Factor. It gives the proportion of time server is busy. 

Symbols and Notations:

The most used Symbols and Notations in the queuing system are:

n = number of customers in the system, both waiting and in service.

λ = average number of customers arriving per unit of time.

 µ = average number of the customer being served per unit of time.

λ / µ = ρ = traffic intensity.

Ls = average number of customers in the system. Both waiting and in service.

Lq = average number of customers waiting in the queue.

Ws = average waiting time of a customer in the system, both waiting and in service.

Wq = average waiting time of a customer in the queue.

Little's Formula:

It helps to determine the average number of items in a stationary queuing system based on the average waiting time of an item within a system and the average number of items arriving at the system per unit of time.

L =  λW

• Ls =  λWs
• Lq = λWq
• Ls = Lq + λ / µ
• Ws = Wq + 1/µ
• Average rate of cost System earns ($) = λ * (average amount an arriving customer pays)

Application of Queuing Theory in Computer Science

Queuing Theory deals with the Queues or waiting lines. 

Some of the areas of its application fields are:

1. Traffic Control
2. Hospital management
3. Computer System Design
4. Banking System
5. ATM machines

These are some of the fields that are related to Computer Science where Queuing Theory plays a crucial role. 

Related Posts:

• Queuing Model [M/M/1:∞, FIFO] Single Server and Infinite Capacity with Solved Problems
• Queuing Model [M/M/S:∞, FIFO] Multi-Server and Infinite Capacity with Solved Problems
• Queuing Model [M/M/1: K, FIFO] Single Server and finite queuing Capacity with Solved Problems
• Queuing Model [M/M/S: K, FIFO] Multi-Server and finite Queuing Capacity with Solved Problems
• Erlang Queuing Model [M/Ek/1: infinity, FIFO] single server with infinite queuing capacity solved problems