Queuing Theory - Operation Research, Queuing Theory discussed with expected short answer question and expected long answer questions

1. M.S.Ramaiah Management Institute, Bangalore | MBA PRIST(A) 2009-11

2. Presented By
Danny Singh
Karthikey Yamdagini
Krishna Kumar
Kumar Shubham
Monalisa Ghosh
Man Mohan Anand

3. Introduction
 Developed by A.K.Erling in
1903
 It analyze the shared facility
needs to be accessed for
service by a large number of
jobs or customers
 Examples:
Waiting lines in cafeterias,
hospitals, banks, theaters,
airports etc.

4. Expected Short Answer Questions

5. Discussion Slide -1
Define Queuing Model or Queuing Theory
Queuing theory is the mathematical study of waiting lines (or
queues) that enables mathematical analysis of several related
processes, including arriving at the (back of the) queue, waiting in
the queue, and being served by the Service Channels at the front of
the queue.
What do you mean by Traffic Intensity?
The ratio ‫/ג‬µ is called the traffic intensity or the utilization factor and
it determines the degree to which the capacity of service station is
utilize
Mean Rate of Arrival in the Queue( )

Mean Service Rate (  )

6. Discussion Slide -2
What do you mean by Balking, Reneging, Jockeying?
Balking
If a customer decides not to enter the queue since it is too long is
called Balking
Reneging
If a customer enters the queue but after sometimes loses patience
and leaves it is called Reneging
Jockeying
When there are 2 or more parallel queues and the customers move
from one queue to another is called Jockeying

7. Discussion Slide -3
What is Waiting Time Cost & Idle Time Cost?
 The cost of waiting customers include either the indirect cost of lost
business or direct cost of idle equipment and persons.
 The cost of idle service facilities is the payment to be made to the
servers for the period for which they remain idle.
What is Transient & Steady State of the system?
 Queuing analysis involves the system’s behavior over time. If the
operating characteristics vary with time then it is said to be transient
state of the system.
 If the behavior becomes independent of its initial conditions (no. of
customers in the system) and of the elapsed time is called Steady
State condition of the system

8. Expected Long Answer Questions

9. Applications of QM
Queuing Model can be applied to various situations :
 Where customers are involved such as restaurants, café,
super market, airports etc.
 Very useful in Manufacturing units
 Applicable for the problem of machine breakdown & repairs
 Applicable for the scheduling of jobs in production control
 Applicable for the minimization of traffic congestion at
tollbooth
 Provide solution of inventory control problems

10. Characteristics of Queuing
The basic characteristics of
queuing phenomenon are:
Customer
Arriving 1
 Service Center
 Service Channel
2
Major Constituents of a Waiting Line
3
Queuing System
Service Facility Customer
 Customer Leaving
 Queue
 Service Channel System

11. Elements of Queuing System
Arrival Distribution
Service Distribution
Service Channel
Elements of Queuing
Service Discipline
Models
Max. No. of
Customer allowed
Calling Source
Customer’s
Behavior

12. Operating Characteristics of QM
Operating
Characteristics
of Queuing
Models
Waiting Time in Total Time in Utilization
Queue Length System Length
the queue the system Factor

13. Assumption in Queuing Model
 The customer arrive for service at a single service facility at
random according to Poisson distribution with mean arrival rate ‫.ג‬
 The service time has exponential distribution with mean service
rate µ.
 The service discipline followed is First Come First Served.
 Customer Behavior is Normal
 Service facility behavior is Normal
 The calling source has infinite size
 The mean arrival rate is less than the mean service rate
 The waiting space available for customer in the queue is infinite

14. Limitations of Queuing Model
 The waiting space for the customer is usually limited
 The arrival rate may be state dependent
 The arrival process may not be stationary
 The population of customers may not be infinite and the
queuing discipline may not be First Come First Serve
 Services may not be rendered continuously
 The Queuing system may not have reached the steady state. It
may be, instead, in transient state

15. References
Books
– Operation Research – D.S.Hira
Websites
– http://en.wikipedia.org
– http://www.google.co.in
– http://www.answers.com

16. Thank You