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Simulation
Waiting Line
Introduction
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Definition (informal)
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A model is a simplified description of an
entity (an object, a system of objects)
such that it preserves
some defining components of the entity
 the relations between these components
that are of current interest.
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Introduction
Definition (more formal) A model is a
construct invented as an aid to understand
the system under study.
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A model is a formal statement of:
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assumptions
conceptualizations
experimental design
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The purpose of a model
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to help
 understand,
 describe, or
 predict
how things work in the real world
by exploring a simplified
representation of a particular entity or
phenomenon.
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Examples of models
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a city map,
a house floor plan,
a photo of a house,
an equation,
a square,
etc.
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Types of models
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Static - a snapshot of the object/system at a
particular time
Dynamic - model of changes in the
object/system
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Continuous
Discrete - changes occur at some time intervals
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Computational models
Simulate a set of processes observed in the
natural world
in order to gain an understanding of these
processes and to predict the outcome of natural
processes
given a specific set of input parameters.
Conceptual and theoretical modeling constructs
are expressed as sets of algorithms and
implemented as software packages.
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Simulation
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An experiment performed on a model
Experiment: observing and studying the
behavior of a system
Reasons for using simulation as a problemsolving tool.
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The physical system is not available.
The experiment may be dangerous.
The cost of experimentation is too high.
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Discrete simulation
Components
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Entities: objects that interact
Attributes: properties of entities
Activities: processes that change the
system
Events: occurrence of activities
Statistics: measures of the performance of
the system
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Approaches
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Time driven
Event driven
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Time driven discrete simulation
Initialize time  initialTime
While time < stopTime
• Execute all events to be done at this time
• Increment time
Output measures
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Event driven discrete simulation
Initialize time  initialTime
While more events to be done
• Advance time to the time
of the earliest event
• Execute the earliest event
Output measures
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Waiting line simulation
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Objects
Waiting Line
 Service providers (Cashiers)
 Clock
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Waiting Line
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Attributes:
Input
 probability of arrival
 line capacity
 processing time
Output
 average waiting time
 number of transactions
 maximum length of the waiting line
 unprocessed requests due to exceeding the
line capacity
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Waiting Line
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Events:
Arrival:
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record time in queue
increment line length
Exit line:
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record waiting time: now – arrival
increment transactions
decrement line length
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Cashiers (service providers)
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Attributes:
Input
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Number of cashiers
Output
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Status of each cashier
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Idle
Busy, remaining processing time
Total idle time per cashier
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Cashiers (service providers)
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Events:
Get a customer to be served
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Assign an available cashier to a customer
Update cashier status
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If idle, increment idle time
If busy, decrement processing time
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Clock
Records the time in increments of 1
 Returns time
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Simulator
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Initialize
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Simulation time
Processing time
Probability of arrival
Line capacity
Number of cashiers
S
PT
P
L
C
Attributes:
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Current time elapsed, init 0
Available cashier
CT
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Algorithm
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While CT (current time elapsed) is less
than S (simulation time)
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Record arrival with probability P
If available cashier and line not empty
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exit line
assign cashier to do the service
Update cashiers’ status
Increment CT
Prepare report
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Reports
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average waiting time
number of transactions
maximum length of line
average idle time
maximum idle time
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