,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Chapter 3General Principles,Banks,Carson,Nelson&Nicol,Discrete-Event System Simulation,2,Purpose,Develops a common framework for the modeling of complex systems.,Covers the basic blocks for all discrete-event simulation models.,Introduces and explains the fundamental concepts and methodologies underlying all discrete-event simulation packages.,These concepts and methodologies are not tied to any particular simulation package.,3,Outline,Deals exclusively with dynamic,stochastic systems.,Discrete-event models are appropriate for those systems for which changes in system state occur only at discrete points in time.,Covers general principles and concepts:,Event scheduling/time advance algorithm.,The three prevalent world views.,Introduces some of the notions of list processing.,4,Concepts in Discrete-Event Simulation,System:a collection of entities that interact together over time,e.g.,people and machines.,Model:an abstract representation of a system.,System state:a collection of variables that contain all the info necessary to describe the system at any time.,Entity:any object or component in the system,e.g.,a server,a customer,a machine.,Attributes:the properties of a given entity.,5,Concepts in Discrete-Event Simulation,Lists:a collection of associated entities,ordered in some logical fashion,a.k.a,sets,queues and chains.,Event:an instantaneous occurrence that changes the state of a system,e.g.,an arrival of a new customer.,Event list:a list of event notices for future events,ordered by time of occurrence,a.k.a.the future event list(FEL),Activity:a duration of time of specified length which is known when it begins,e.g.,a service time.,Clock:a variable representing simulated time.,Note:different simulation packages use different terminology for the same or similar concepts.,6,Concepts in Discrete-Event Simulation,An activity typically represents a service time,an interarrival time,or any processing time whose duration has been characterized/defined by the modeler.,An activitys duration may be specified:,Deterministic,Statistical,A function depending on system variables and/or entity attributes.,Duration is not affected by the occurrence of other events,hence,activity is also called an unconditional wait.,Completion of an activity is an event,often called a primary event.,For example,If the current simulated time is CLOCK=100 minutes,and an inspection time of exactly 5 minutes is just beginning,then an event notice is created that specified the type of event and the event time(100+5=105 min).,7,Concepts in Discrete-Event Simulation,A delays duration is determined by system conditions(not specified by the modeler ahead of time.),Also called a conditional wait.,For example,a customers delay in a waiting line may be dependent on the number and duration of service of other customers ahead in line and,whether a server has a failure during the delay.,Dynamic:Function of time and constantly changing over time.,System state,entity attributes,the number of active entities,the contents of sets,and the activities and delays currently in progress are all function of time.,8,Concepts in Discrete-Event Simulation,Example:Able-Baker Call Center System.A discrete-event model has the following components:,System state:,The number of callers waiting to be served at time,t,Indicator that Able is idle or busy at time,t,Indicator that Baker is idle or busy at time,t,Entities:neither the caller nor the servers need to be explicitly represented,except in terms of the state variables,unless certain caller averages are desired.,Events:,Arrival,Service completion by Able,Service completion by Baker,Activities:,Interarrival time.,Service time by Able,Service time by Baker,Delay:a callers wait in queue until Able or Baker becomes free.,9,Concepts in Discrete-Event Simulation,The definition of the model components provides a static description of the model.,A description of the dynamic relationships and interactions between the components is also needed.,e.g.,how does each event affect system state?What events mark the beginning or end of each activity?What is the system state at time 0?,A discrete-event simulation is:,The modeling over time of a system all of whose state changes occur at discrete points in time.,Proceeds by producing a sequence of system snapshots.,10,Event Scheduling/Time Advance Algorithm,The mechanism for advancing simulation time and guaranteeing that all events occur in correct chronological order.,At any given time,t,the future event list(FEL)contains all previously scheduled future events and their associated event times(,t,1,t,2,),FEL is ordered by event time,and the event time satisfy:,t,t,1,t,2,t,3,t,n,where t is the value of CLOCK,Update system snapshot,t,i,Remove event from FE