Simulating Queuing Systems

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Simulation of Queuing System


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Queuing System

The analysis of waiting lines, called Queuing

Theory, applies to any situation in which customers

arrive at a system, wait, and receive service.

Queuing Theory was developed by a Danish

engineer,A. K. Erlangin 1908.

The main objectives of queuing theory are to

improve customer service and reduce operating

costs.


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Components of the Queuing System

Customer

Arrivals

Servers

Waiting Line

Servicing System

Exit

Queue or


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Customer Service Arrival Pattern(Waiting Line)

Arrival Pattern

Constant Variable

Example: A part

from an automatedmachine arrives

every 30 seconds.

Example:

Customersarriving in a bank.


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Waiting Line Attributes

Input or arrival time.

Output or service rate.

Service or queue discipline.

FIFO LIFO

Priority

Random


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Degree of Patience

No Way!

BALKING

No Way!

RENEGING


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Service Pattern or Service Facility

Service

Pattern

Constant Variable

Example: Each part

takes exactly 30seconds to make.

Example: People

spending timeshopping.


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Suggestions for Managing Queues

1. Determine an acceptable waiting time for your customers.

3. Try to divert your customers attention when waiting.

3. Inform your customers of what to expect.

4. Train your servers to be friendly.

5. Encourage customers to come during the slack periods.


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Single Queue Parallel Systems

Customers in a queue

Servers


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Workingwaiting room =

queue

potential customers

parallel servers

An arrival

a service

completion


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Parallel Queues Parallel Systems

Customers in parallel queues

Servers


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Modeling & Simulating Queuing

System

A queuing model provides measures ofsystem performance The quality of service provided to the customers

The efficiency of the service operation and the

cost of providing service


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System

The quality of the service provided can bemeasured by Waiting time in the queue

Time in the system (waiting time plus service

time) Completion by a deadline


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System

The efficiency of service operation is measured by Average queue length

Average number of customers in the system (queue pluscustomers in service)

Throughput the rate at which customers are served

Server utilization percentage of time servers are busy

Percentage of customers who balk or renege


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System

The waiting time of any customer is equal to the time

at which the customer begins service minus the timethe customer arrived.

The server is idle if the time at which customerarrives is greater than the time at which the previous

customer completed service. If a customer arrives at time t, then all prior

customers who have not yet completed service bytime tmust still be in the system.


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System

Some observations If a customer arrives at time t and the server is not busy,

then that customer can begin service immediately uponarrival.

If a customer arrives at time t and the server is busy, then

that customer will begin service at the time that the previous

customer completes service.

The time at which a customer completes service is

computed as the time that the customer begins service plus

the time it takes to perform the service.

Once completion times are known, we may find the length

of the queue.


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Kendalls Notation

V indicates the arrival pattern.

W indicates the service pattern.

B gives the number of servers.

Y represents the system capacity.

Z Indicates the queue discipline.


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Symbols used for inter arrival time, servicetimes & the queue disciplines

Queue Characteristic Symbol Meaning

Inter arrival time D Deterministic

Or Service time

M Exponential

Queue Discipline FIFO First in First out

LIFO Last in First out

SIRO Random order

PRI Priority orderingGD Any other spec-

-ified ordering


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Cont..

If Y (system capacity) is not specified then set it to infinite.

If Z (queue discipline) is not specified then set it to FIFO.

M/D/2/5/FIFO (Mathematical notation) is system having:

Exponential arrival times.

Deterministic service times.

Two servers. Capacity of 5 customers.

FIFO queue discipline.


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We welcome your queries!!

Presented by:

Nitin Kapoor

Richa Sharma

(MCA-III)

Simulating Queuing Systems

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