The document discusses queuing theory, which involves constructing mathematical models of queuing systems. Queuing theory can be applied to situations like waiting lines. A queue occurs when demand exceeds service rate. Key aspects of queuing models include arrival and service patterns, queue discipline, customer behavior, system capacity, and transient vs steady states. Research in queuing theory started in 1903 and notation was established in 1953.

1. Trisha Gopalakrishna- 1RV09ME106

2.  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.

3.  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.

4.  Research started by Agner Krarup  Notation for describing the
Erlang of Denmark in 1903 when he characteristics of a queuing model
created models to describe the was first suggested by David.G
Copenhagen Telephone Exchange. Kendall in 1953.
 The A/B/C notation is used in all
standard modern works of queuing
theory.

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

6.  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 Inter arrival Mean
Arrival Rate Rate Customer
Arrival Rate

7.  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

8.  FIFO- First in First out
 FCFS- First Come First Serve
 LIFO-Last in First out
 SIRO- Service in Random order

9.  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.

10.  Maximum number of customers that can be
accommodated in the queue.
 Assumed to be of infinite capacity.

11.  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.