QUEUING THEORY

1. BY
VIDHYA.K

2. QUEUING THEORY

3. INTRODUCTION:
 A flow of customers from finite/infinite population
towards the service facility forms a queue on account
of lack of capability to serve them all at a time.
 Queues (or) waiting lines are very common in
everyday life.
 In the absence of a perfect balance between the service
facilities and the customers, waiting time is required
either for the service facilities (or) for the customer’s
arrival.

4. EXAMPLE:
 We often face the problem of long queues for a bus, a
movie ticket, etc...
 We generally see long queues in front of railway
booking offices, bank counters, post offices, etc.. In
those days.
 We also find automobiles waiting at service stations,
likewise Patients waiting for doctors, etc..

5. COMMONLY USED TERMS IN
QUEUING THEORY:
 CUSTOMER: customers may either be a person or a
machine or other items which is arrived to avail some
service.
 SERVICE STATIONS: it is a point where service is
provided. It can be one or more service stations.
 WAITING TIME: the time that the customer spends in
the queue before being serviced.
 TIME SPENT BY A CUSTOMER IN THE SYSTEM:
It is equal to the waiting time of customer plus the
service time.

6. CONTINUED.....
 NUMBER OF CUSTOMERS IN THE SYSTEM:
It is equal to the sum of number of customers in queue
and the number of customers being served.
 QUEUE LENGTH: number of customers waiting in the
queue comprises the queue length.
 JOCKEYING: joining the other queue and leaving the
first queue.
 RENEGING: joining the queue and leaving it
afterwards.

7. Continued...
 BALKING: customers decides not to join the queue.
 QUEUEING SYSTEM: it is the system consisting of
arrival of customers, waiting in queue, picking up for
service according to a certain discipline, being serviced
and departure of customers.

8. ELEMENTS OF QUEUING SYSTEM:
The input(arrival pattern),
The service mechanism(service
pattern),
The queue discipline and
Output of the queue.

9. The input(arrival pattern):
The input describes the way in which the customers
arrive and join the system.
We cannot predict the arrival time of customers
randomly.
It is characterised by its:
size, arrival time distribution of customers, mean time
between intervals, attitude of the customers.
Mean time is often represented by Greek letter λ known
as LAMBDA. Mean time between arrivals is
represented by 1/λ .

10. SERVICE MECHANISM:
 This means the arrangement of service facility to serve the
customers. If there is infinite number of servers then all
the customers are served instantaneously on arrival, and
there will be no queue.
 If the number of servers are finite then the customers are
served according to the specific order with service time a
constant or a random variable.
 The average number of customers being served in one unit
of time at a service station is often denoted by the Greek
letter μ.
 Average time taken to service a customer is represented by
1/μ.

11. QUEUE DISCIPLINE:
 It is a rule according to which the customers are
selected for the service when a queue has been formed.
The common disciplines are:
 FIRST COME FIRST SERVED (FCFS)
 FIRST IN FIRST OUT (FIFO)
 LAST IN FIRST OUT (LIFO)
 SELECTION FOR SERVICE IN RANDOM ORDER
(SIRO).

12. OUTPUT OF THE QUEUE:
 Generally this factor is not important but in some
cases it may influence the service/arrival rate.
 For example: if there is only one door to service point
through which people enter and leave after being
served, it is possible that people leaving could affect
the rate of arrival.

13. THANK YOU