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The application of queuing theory in analyzing and simulating waiting lines and systems. The theory's history, elements, and various queuing disciplines are discussed. Examples include air traffic at an airport and networks. Queuing systems are used to describe and evaluate system performance.
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Simulation of Queuing Systems Introduction
Waiting line queues are one of the most important areas, wherethe technique of simulation has been extensively employed.
The waiting lines or queues are a common site in real life
The waiting lines or queues are a common site in real life.
People at railway ticket window, vehicles at a petrol pump or at atraffic signal, workers at a tool crib, products at a machiningcenter television sets at a repair shop are a few examples ofcenter, television sets at a repair shop are a few examples ofwaiting lines.
Simulation of Queuing Systems
The queuing theory its development to anThe
queuing theory its development to an
engineer A.K.Earlang, who in 1920, studiedwaiting line queues of telephone calls inC
h
D
k
Copenhagen, Denmark.
The problem was that during the busy period,t l
h
t
bl
t
h
dl
telephone operators were unable to handlethe calls, there was too much waiting time,which resulted in customer dissatisfactionwhich resulted in customer dissatisfaction.
State Variables
customer
queue
server
State:
InTheAir
: number of aircraft either landing or
waiting to land
OnTheGround
: number of landed aircraft
RunwayFree
: Boolean, true if runway available
Queuing System
Elements of Queuing Systems
Elements
of Queuing Systems
Queuing System
Population of Customers or calling source
can be
considered either limited (closed systems) or unlimitedconsidered either limited (closed systems) or unlimited(open systems).
Unlimited population represents a theoretical model of systems with a large number of possible customers (asystems with a large number of possible customers (abank on a busy street, a motorway petrol station).
Example of a limited population may be a number ofprocesses to be run (served) by a computer or a certainprocesses to be run (served) by a computer or a certainnumber of machines to be repaired by a service man.
It is necessary to take the term "customer" very generally. Customers may be people machines of various nature
Customers
may be people, machines of various nature,
computer processes, telephone calls, etc.
Queuing System
Queue or waiting line
represents a certain number
of customers waiting for service (of course thequeue may be empty).
Typically the customer being served is considered
yp
y
g
not to be in the queue. Sometimes the customersform a queue literally (people waiting in a line for abank teller).
Sometimes the queue is an abstraction (planeswaiting for a runway to land).
There are two important properties of a queue:
There are two important properties of a queue: Maximum Size
and
Queuing Discipline
Queuing System
Maximum Queue Size
(also called
System
Maximum
Queue Size
(also
called
System
capacity
) is the maximum number of customers that
may wait in the queue (plus the one(s) being
d)
served).
Queue is always limited, but some theoreticalmodels assume an unlimited queue lengthmodels assume an unlimited queue length.
If the queue length is limited, some customers are forced to renounce without being servedforced to renounce without being served
Example application of queuing theory
In many retail stores and banks
In
many retail stores and banks
multiple line/multiple checkout system
a
queuing system where customers wait for the nextq
g
y
available cashier
We can prove using queuing theory that :throughput improves increases when queues areused instead of separate lines
Example application of queuing theory
Model Queuing System
Queuing System
Queue
Server
Server System
Queuing System
Use Queuing models to
Describe the behavior of queuing systems
Evaluate system performance
System Configuration
Servers
CCustomers
Single Queue Configuration
Queuing System
Queuing Discipline
represents the way the queue is organized
(r les of inserting and remo ing c stomers to/from the q e e)(rules of inserting and removing customers to/from the queue).There are these ways:
1) FIFO (First In First Out) also called FCFS (First Come First
Serve) - orderly queue.
)
y q
2) LIFO (Last In First Out) also called LCFS (Last Come First Serve)
- stack.
3) SIRO (Serve In Random Order).4) Priority Queue, that may be viewed as a number of queues for
various priorities.
5) Many other more complex queuing methods that typically change
the customer’s position in the queue according to the time spentthe customer s position in the queue according to the time spentalready in the queue, expected service duration, and/or priority.These methods are typical for computer multi-access systems
Queuing System
Most quantitative parameters (like average queue
q
p
g
q
length, average time spent in the system) do notdepend on the queuing discipline.
That’s why most models either do not take the
That s why most models either do not take thequeuing discipline into account at all or assume thenormal FIFO queue.
In fact the only parameter that depends on thequeuing discipline is the variance (or standarddeviation) of the waiting time There is this importantdeviation) of the waiting time. There is this importantrule (that may be used for example to verify resultsof a simulation experiment):