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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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Modeling & Simulating Queuing
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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Modeling & Simulating Queuing
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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Modeling & Simulating Queuing
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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Modeling & Simulating Queuing
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)