Basic Definitions of Queuing Theory

Trisha Gopalakrishna- 1RV09ME106

Waiting lines at a self service fast food joint, buying tickets at the theatre, long lines at the bank are all instances to which the queuing theory can be applied.

A queue is said to occur when the rate at which the demand arises exceeds the rate at which service is being provided.

Definition

It is the quantitative technique which consists of constructing mathematical models for various types of queuing systems.

Mathematical models are constructed so that queue lengths and waiting times can be predicted which helps in balancing the cost of service and the cost associated with customers waiting for service.

History

Research started by Agner Krarup Erlang of Denmark in 1903 when he created models to describe the Copenhagen Telephone Exchange.

Notation for describing the characteristics of a queuing model was first suggested by David.G Kendall in 1953.

The A/B/C notation is used in all standard modern works of queuing theory.

Characteristics Input Process or Arrival Pattern Service Mechanism or Service Pattern Queue Discipline Customer’s Behaviour System Capacity Transient and Steady States

Arrival Pattern Customers arrive in random fashion. The time duration between each

customers’ arrival is known as inter arrival time. We assume it to follow Poisson Distribution.

Customer Arrival Rate

Inter arrival Rate

Mean Customer

Arrival Rate

Service Pattern Number of servers and speed of

service to be considered. The time taken by a server to service

a customer is known as Service Time.

Service Rate

Mean Service Rate

Queue Discipline FIFO- First in First out FCFS- First Come First Serve LIFO-Last in First out SIRO- Service in Random order

Customers’ Behaviour

Balking- When a customer leaves the queue because it is too long, has no time to wait, no space to stand etc.

Reneging- When a customer leaves the queue because of his impatience.

Priorities- When a customer is served based on priority and not time of arrival.

Jockeying- When a customer shifts from one queue to another.

System Capacity Maximum number of customers that

can be accommodated in the queue. Assumed to be of infinite capacity.

Transient and Steady States

When the operating characteristics are dependent on time, it is said to be a transient system.

When the operating characteristics are independent of time, it is said to be a steady state.

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