This document discusses queuing systems and their key elements and characteristics. It describes queuing systems as having customers arriving for service, waiting if service is not immediate, and leaving after being served. The main elements of a queuing system are the input source (where customers come from), the service mechanism, the queue discipline (order of service), and the system's capacity. Characteristics of queuing systems include the expected number of customers in the system and queue, as well as the expected waiting and service times. Deterministic queuing systems have set customer inter-arrival and service times.

2. CONTENTS
INTRODUCTION1
STRUCTURE OF QUEUING SYSTEM2
ELEMENTS OF A QUEUING SYSTEM3
CHARACTERISTICS OF A QUEUING SYSTEM4

3. 01 02 03
I N T R O D U C T I O N
Queue or (waiting
line) is formed of
the customers
waiting to be
served.
The process or
system that performs
the service to the
customer is known as
the service channel or
service facility
Queues, in general,
build up as an
interaction between
customers arriving for
service and a service
facility.

4. Structure of Que uing Syste m
 T h e m e c h a n i s m o f Q u e u i n g p r o c e s s i s s i m p l e .
 C u s t o m e r s a r r i v e a t s e r v i c e c o u n t e r a n d a r e a t t e n d e d b y o n e o r m o r e o f t h e s e r v e r s .
 A s s o o n a s a c u s t o m e r i s s e r v e d , i t d e p a r t s f r o m t h e s y s t e m .
 T h u s , a q u e u i n g s y s t e m c a n b e d e s c r i b e d a s c o m p o s e d o f c u s t o m e r s a r r i v i n g f o r s e r v i c e ,
w a i t i n g f o r s e r v i c e , i f i t i s n o t i m m e d i a t e , a n d i f h a v i n g w a i t e d f o r s e r v i c e , l e a v i n g t h e
s y s t e m a f t e r b e i n g s e r v e d .

5. Q u e u i n g S y s t e m
C u s t o m e r s
A r r i v i n g
Waiting
Customers
Queue
Discipline
Queue Service
Mechanism
C u s t o m e r s
l e a v i n g
a f t e r
s e r v i c e

6. E l e m e n t s o f Q u e u i n g S y s t e m
Input Source
01
Service Mechanism
02
Queue Discipline
03
Capacity of the
Queuing Sytem04

7. I n p u t S o u r c e
Size of the Queue
a
Pattern of Arrivals
b
Customer's Behaviour
c

8. S e r v i c e M e c h a n i s m
Structure of the
Service System
a
Speed of Service
b

9. Q u e u e D i s c i p l i n e
FCFS
01
FIFO and LIFO
02
SIRO
03
PRIORITY
04

10. C a p a c i t y o f t h e Q u e u i n g S y s t e m
Finite Source Infinite Source

11. 01 02 03
D e t e r m i n i s t i c Q u e u i n g S y s t e m
A Queuing system wherin the
customers arrive at regular
intervals and the service time
for each customer is known
and constant , is known as
Deterministic Queuing System
When the service rate is
less than the arrival rate,
the service facility cannot
cope up with all the arrivals
and thus leads to explosive
situation.
Let the arrival rate be
λ customers per unit
time and the service
rate be µ customers
per unit time.

12. Operating Characteristics of Queuing System
 Expected number of customers in the system is denoted as E(n) or Ls is the average number of customers in
the system, both waiting and in service. Here, n stands for number of customers in the queuing system.
 Expected number of customers in the Queue is denoted as E(m) or Lq is the average number of customers
waiting in the queue. Here m =n-1 i.e excluding the customer being served.
 Expected waiting time in the system denoted by E(v) or Ws is the average total time spent by a customer in
the system.
 Expected waiting time in the Queue denoted by E(w) or Wq is the average time spent by a customer in the
Queue before the commencement of his service.
 The Service Utilization factor (Busy period) denoted by p (=λ/µ) is the proportion of time that a server actually
spends with the customers. Here, λ stands for the average number of customers arriving per unit of time and
µ stands for the average number of customers completing service per unit of time. The service Utilization
factor is also known as traffic intensity or the clearing ratio.

13. Thank You
Dr.Saradha A
Assistant Professor
Department of Economics
Ethiraj College for Women
Chennai