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## Structure of a Waiting Line System

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### Structure of a Waiting Line System. Queuing theory is the study of waiting lines. Four characteristics of a queuing system: The manner in which customers arrive (bulk ... – PowerPoint PPT presentation

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Title: Structure of a Waiting Line System

1
Structure of a Waiting Line System
• Queuing theory is the study of waiting lines
• Four characteristics of a queuing system
• The manner in which customers arrive (bulk,
individual, by appointment or randomly)
• The time required for service
• The priority for determining order of service
• The number and configuration of servers in the
system

2
Structure of a Waiting Line System
• In general, arrival of customers into a system is
a random event. Frequently the arrival pattern
is modeled as a Poisson process.
• Service time is also usually a random variable.
It is often described by the exponential
distribution.
• The most common queue discipline is FIFO. An
elevator however would use LIFO and an emergency
room would use a highest cost criterion.

3
Queuing Systems
• A three part code A/B/s is used to describe
various queuing systems where
• A describes the arrival distribution assumed
• B describes the service distribution assumed
• s is the number of channels (servers) per line

4
Operating Characteristics of a Queuing System
• What is the average wait time of the customer in
the queue? In the system?
• What is the average number of customers in the
queue? In the system?
• What percent of time is the service facility
idle? What is the average amount of server free
time between customers?
• What is the probability that an arriving customer
will have to wait?

5
Example Wayne International Airport
• Whenever an international plane arrives at the
airport, two customs inspectors on duty set up
operations to process the passengers.
• Incoming passengers must first have their
passports and visas checked. This is handled by
one inspector. The time required to check a
passenger's passports and visas can be described
by the probability distribution on the next
slide.

6
Example Wayne International Airport
• Random Number Mapping
• Time Required to
• Check a Passenger's
Random
• Passport and Visa Probability
Numbers
• 20 seconds
.20 00 -19
• 40 seconds
.40 20 - 59
• 60 seconds
.30 60 - 89
• 80 seconds
.10 90 - 99

7
Example Wayne International Airport
• After having their passports and visas checked,
the passengers next proceed to the second customs
official who does baggage inspections.
Passengers form a single waiting line with the
official inspecting baggage on a first come,
first served basis.

8
Example Wayne International Airport
• Random Number Mapping
• Time Required For
Random
• Baggage Inspection Probability
Numbers
• No Time
.25 00 - 24
• 1 minute .60
25 - 84
• 2 minutes .10
85 - 94
• 3 minutes .05
95 - 99

9
Example Wayne International Airport
• Next-Event Simulation Records
• For each passenger the following information
must be recorded
• When his service begins at the passport control
inspection
• The length of time for this service
• When his service begins at the baggage inspection
• The length of time for this service

10
Example Wayne International Airport
• A chartered plane from abroad lands at Wayne
Airport with 80 passengers. Simulate the
processing of the first 10 passengers through
customs using the random numbers given on the
next slides.

11
Example Wayne International Airport
• Passport Control
Baggage Inspections
• Pass. Time Rand. Service Time Time
Rand. Service Time
• Num . Begin Num. Time End Begin
Num. Time End
• 1 000 93 120 120
120 13 000 120
• 2 120 63 100 220
220 08 000 220
• 3 220 26 40 300
300 60 100 400
• 4 300 16 20 320
400 13 000 400
• 5 320 21 40 400
400 68 100 500

12
Example Wayne International Airport
• Passport Control
Baggage Inspections
• Pass. Time Rand. Service Time Time
Rand. Service Time
• Num . Begin Num. Time End Begin
Num. Time End
• 6 400 26 40 440
500 40 100 600
• 7 440 70 100 540
600 40 100 700
• 8 540 55 40 620
700 27 100 800
• 9 620 72 100 720
800 23 000 800
• 10 720 89 100 820
820 64 100 920

13
Example Wayne International Airport
• Question
• How long will it take for the first 10
passengers to clear customs?
• Passenger 10 clears customs after 9 minutes and
20 seconds.

14
Example Wayne International Airport
• Question
• What is the average length of time a customer
waits before having his bags inspected after he
clears passport control? How is this estimate
biased?