Operating characteristics ofqueuing system

• FCFS (First-Come-First-Served)
• LCFS (Last-Come-First-Served)
• Service in random order
• Priority service

1. operating characteristics of
queuing system
Aminul Islam Tanvin
ID: 11509015
Department Of ICT

2. Queuing Theory
•Queuing theory is the mathematics of waiting lines.

•It is extremely useful in predicting and
evaluating system performance.

•Queuing theory has been used for operations research,
manufacturing and systems analysis. Traditional
queuing theory problems refer to customers visiting a
store, analogous to requests arriving at a device.

3. Queuing problems arises because either
There is too less demand
(Much idle facility time or too Many
facilities
The problem is to either schedule arrivals or provide extra facilities or
both so as to obtain an optimum balance between costs associated with waiting
time and idle time .
There is too much demand on
the facilities

4. Basic elements of Queuing System
•Entries or customers
•Queue (waiting lines)
•Service channels or service facility

5. Basic Structure

6. Service process
Arrival process


Customer’s
Behavior
Queue Discipline


Number of
servers

System capacity
characteristics of
queuing system
Operating Characteristics Of Queue

7. Arrival pattern
•Customers arrive in
scheduled or random
fashion.
•The time duration
between each
customers’ arrival is
known as inter arrival
time. We assume it to
follow Poisson
Distribution
Poisson Distribution
probability
Arrival per unit time(λ)

8. Exponential Distribution
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.
It is represented by
Exponential
Distribution
probability
Customer served
per unit time (μ)
Assumption:
λ<μ

9. Service Channels
Single channel queuing system
Multi channel queuing system
Single channel multi phase system
Multi channel multi phase system

10. Service Discipline
•FCFS (First-Come-First-Served)
•LCFS (Last-Come-First-Served)
•Service in random order
•Priority service

11. System Capacity

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

12. Customer’s Behavior

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

13. Service Facility Behavior
•Failure: A server may fail while
serving a customer, thereby
interrupting service untill a repair
can be made.
•Changing service rate: A server
may speed up or slow down,
depending on the number of
customers in the queue.
•Batch processing: A server may
service several customers
simultaneously.

14. Waiting and Idle time
costs
Cost of waiting customers Cost of idle service facility
•Indirect cost of business loss
•Direct cost of idle equipment
or person.
•Payment to be made to the
servers(engaged at the
facilities),for the period for
which they remain idle.
The optimum balance of costs
can be made by scheduling
the flow of units or providing
proper number of service
facilities .

15. Total expected cost
Cost of providing
service
s
Increased service
Total expected cost = waiting time cost + cost of providing service
Let Cw = expected
waiting cost/unit time
Ls= expected no. of units
Cf = cost of servicing one unit
This will be minimum if d/dμ
(C)=0 Or if
-Cw.[λ/(μ-λ)²]+Cf=0 ,
Which gives ..
μ=λ±sqrt(Cw .λ/Cf)Total expected cost of
operating facility

16. Transient & Steady State of
the system
•When the operating characteristics are
dependent on time, it is said to be a
transient state.
•When the operating characteristics are
independent of time, it is said to be a
steady state.

17. Traffic intensity
The ratio λ/μ is called the traffic intensity or the
utilization factor and it determines the degree
to which the capacity of service station is
utilized.

18. Applications of Queuing Model

•Telecommunications
•Traffic control
•Determining the sequence of computer
operations.
•Predicting computer performance
•Health services (e.g.. control of hospital
bed assignments)
•Airport traffic, airline ticket sales
•Layoutof manufacturing systems.