Objects in a Simulation Model

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Objects in a Simulation Model

• Activate objects, which are instances of the
  classes that inherit the library class Process
• Passive objects, which are instances of any other
  class, including some of the library classes
  (e.g., queue classes)

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Single-Server Models

• There is only one server object that provides
  service to customer objects
• Arriving customer objects join a queue to wait
  for service
• The random events are
• customer arrival
• start service
• service completion

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Simple Queue

• A waiting line for arriving customers (or other
  objects). A passive entity in the model, used as
  global shared resource.
• An arriving customer can only enter the queue at
  the tail
• The server removes the customer at the head of
  the queue
• The usual order of customers is FIFO.

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A Simple (FIFO) Queue
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The Car-Wash Model

• Arriving cars join a line (queue) to wait for
  service
• There is only one car-wash machine that can
  service one car at a time
• After the service for a car is complete, the car
  leaves the system

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Components in the Model

• A set of customer processes, the cars
• One server process, the wash-machine
• One process represents the environment that
  generates arrivals
• One global shared resource, the queue

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Events

• customer arrival
• start of service
• end of service and departure of a customer

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Single Server System Model
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Modeling Diagrams

• The UML diagram shows the main entities in the
  model
• The UML static modeling diagrams show the basic
  structure of the classes and their relationships
• The dynamic modeling diagrams show all the
  process interactions and the use of resources for
  every model.

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UML class diagrams
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UML Class Diagram
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UML Collaboration Diagram
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UML Sequence Diagram
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UML State Diagram Car Object
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Results of a Simulation Run

• The trace, which is a sequence of all relevant
  events with time of occurrence
• The summary statistics with the values of the
  performance metrics of the model for the current
  run

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Performance Measures to be Computed

• The average number of customers in the system
• The average number of customers in the queue(s)
  (i.e., that are waiting)
• The average time that a customer spends in the
  system
• The average time that a customer spends in the
  queue(s)
• The server (wash-machine) utilization.

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Performance and Workload Characterization

• The usual objective for determining the
  performance measures in a queuing system is to
  achieve the following criteria
• Reduce the customer waiting periods
• Improve the server utilization
• Maximize throughput (the number of customers
  served) for a given workload.

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Workload Parameters

• The performance of the system depends on the
  workload submitted, and for this queuing model it
  consists of the following parameters
• The average customer arrival rate, ?
• The average customer service rate, ?
• The resource demand for the customers

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System Parameters

• The queue size
• The resource capacity of the system
• The speed of the server

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Performance Measures Depend on Workload

• The performance metrics computed in the
  single-server model, depend on the workload
  submitted, and on the system parameters.
• Modifying the workload on a model and/or the
  system parameters changes the behavior of the
  model.

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Examples of Performance and Workload

• To compare two models with different servers, is
  equivalent to changing the workload by providing
  two different values for the average service time
  demands of the customers.
• If the system workload increases, the server
  utilization will also increase

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Bottleneck

• The bottleneck of the system at capacity will be
  localized in the server or resource with a
  utilization of 1, while the other servers or
  resources each have utilization significantly
  below 1.
• The bottleneck can be localized at the server,
  the queue, or at the resources.

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Studying System Behavior

• All the changes that occur in the system are
  analyzed
• In the model of the simple car-wash system, the
  system changes state when a customer arrives,
  when a customer starts service, when a customer
  completes service, etc.
• These changes are instantaneous occurrences and
  are called events.

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Random Variables in the Model

• In the Car-wash model, the following random
  variables are defined
• The inter-arrival period for the car objects
• The service period for each car object.

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Generation of Random Variables

• To facilitate the simulation of random events,
  PsimJ provides random number generators using
  several probability distributions
• Some of the distributions return an integer
  (long) value, others return a real (double) value

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Probability Distributions in PsimJ

• Uniform
• Exponential
• Poisson
• Normal
• Erlang
• Geometric
• Hyper-exponential

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Random Events in the Carwash Model

• Two random events
• customer arrivals
• end of a customer service
• Two random variables are modeled
• inter-arrival periods
• service periods
• Both random variables follow an exponential
  distribution.

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Distributions Provided by PsimJ

• The sample models included in the Psim Web page
• http//science.kennesaw.edu/jgarrido/psim.html

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Using PsimJ with Java

• All processes (active objects) are created from a
  user-defined class that inherits the library
  class Process.
• All non-process objects (passive objects) are
  created directly from the corresponding library
  class (e.g., class Squeue), or other classes.

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The Structure of a Model in Java

• Define all classes for the models processes, and
  inherit from the library class Process.
• Define one class (main class) that includes
  method main.
• In method Main_body of the main class, start the
  simulation by invoking method start_sim, then
  calculate summary statistics.

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Method main

• In method main
• Define a simulation object of the library class
  Simulation give a name to the model.
• Create all the objects used in the model.
• Start the active objects.

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Using GUI with Models

• Java facilitates the implementation of graphical
  interfaces for simulation models
• A general GUI framework is included with PsimJ.
  The package name is gui
• To run the carwash model with GUI, run the
  CarwashGUI class, instead of the Carwash class

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Carwash Simulation Run
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Carwash Simulation Run (2)
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Queuing Models

• Models that include at least one queue
• From the software point of view, the queue is a
  data structure that stores waiting customers
• The server removes from the queue the next
  customer to service

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Basic Categories of Queuing Models

• Single-server models
• Multi-server models
• Queuing networks

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Examples of Queuing Models

• Computer systems
• Communication systems, networks
• Teller facilities in a bank
• Production systems
• Transport and materials handling
• Repair and maintenance systems

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Service Stations

• A queuing model consists of a number of
  facilities and interconnecting queues. Each
  facility, or service station, consists of one or
  more servers.
• For these types of systems, it is very common in
  practice to use exponentially distribution for
  inter-arrival periods and for service periods.

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Types of Queuing Models

• Single-server, single-queue
• Multi-server, single-queue
• Multi-server, multi-queue
• Multi-server, multi-queue with priorities
• Multi-server, multi-queue with priorities and
  preemption.

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Multiple Servers Single Queue

• Any of the servers available can provide service
  demanded by a customer
• A server removes the next customer from the head
  of the customer queue
• One or more servers can be idle, waiting for
  customers to arrive

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Carwash Model With Multiple Machines
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General Description of the Model

• This model has K machines (servers)
• A customer can receive service from any machine
  (any server)
• A customer waits in the customer queue until it
  is at the head of the queue and a machine becomes
  available
• The machine removes the customer from the head of
  the queue and starts to service it

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Idle Servers

• Idle servers are organized in a server queue
• A server joins a queue of idle servers if there
  are no customers
• An arriving customer enters the input queue and
  reactivates the server at the head of the server
  queue. If there are no servers available, the
  customer just waits

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Models With Multiple Servers and Multiple Queues
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Multi-Server Multi-Queue Model

• Every server has its own queue of customers
• An arriving customer selects the server with the
  smallest queue
• Alternatively, an arriving customer randomly
  selects a server.

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Multi-Server Multi-Queue Model with Preemption

• Every customer has a priority
• An arriving customer can interrupt the service of
  another customer with a lower priority
• the interrupted customer is returned to the head
  of his queue, this customer is the one with the
  lowest priority and that started most recently.

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Performance Measures

• The average number of customers in the system
• The average number of customers in the queue(s)
  (i.e., that are waiting)
• The average period that a customer spends in the
  system
• The average period that a customer spends in the
  customer queue waiting
• The server utilization

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Queuing Networks

• Consists of two or more interconnected stations
• The output from a station are connected to input
  of another station
• Each station has one or more servers and its
  queues
• Each station provides a different service

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Service in a Queuing Network

• Customers enter the network at any of several
  entry stations
• Customers are routed through the network
  demanding service from different stations
• Customers can exit from any of several exit
  stations

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A Queuing Network
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Models With Priorities

• Customers are grouped into classes or types
• Each customer class has its own priority, and
  workload parameters (e.g., arrival rate and a
  service demand)
• The customers wait in a priority queue, with
  highest priority closest to the head
• A server removes the customer with the highest
  priority from the queue

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Examples

• Medical service systems
• Computer communication networks
• Operating systems
• Car-wash systems for different types of vehicles

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Priority Queue

• A queue that holds customers by priority
• The queue discipline is ordering of the customers
  by priority
• Customers with the highest priority are always at
  the head of the queue

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Model With Priorities
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Priority Queues in PsimJ

• To declare a priority queue, use class Pqueue
• public static Pqueue car_queue // for car
  objects
• To create object car_queue (passive object) with
  K different priorities
• car_queue new Pqueue (CarQ, K)
• In PsimJ, the highest priority is 0

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Priorities For the Car Objects

• There is an arrivals object for every customer
  class
• Each arrivals object creates car objects for the
  corresponding priority
• A car object gets its priority when created (in
  the constructor)
• A car object joins the corresponding priority
  queue to wait for service

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Defining and Using Car Priority
The constructor in class Car public Car(String
name, int type, double dur)
... int my_priority type // type (priority)
of car set_prio (my_priority) // assigns its
priority
In the Main_body of class Car // this object
joins the priority queue car_queue.into(this)
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Results of a Simulation Run

• The trace, which is the sequence of events that
  occur during the simulation run
• Performance measures for every priority
• Throughput
• Average wait period
• other measures

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Multi-Server Model with Priorities

• Every customer has a priority and joins the
  priority queue
• An server gets the customer from the queue with
  highest priority
• If there are no customers, and server joins a
  server queue and becomes idle

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Multiple Servers With Priority