44
Subject Name: System Modeling & Simulation Subject Code: 10CS82 Prepared By : Ms. Pramela Devi( ASCP) Department : Computer Science & Engineering Date : 12-02-2015 3/4/2015
Subject Name: System Modeling & Simulation
Subject Code: 10CS82
Prepared By : Ms. Pramela Devi( ASCP)
Department : Computer Science & Engineering
Date : 12-02-2015
3/4/2015
UNIT 2
General Principles and
Simulation Software
Client
So & So Software
Pvt. Ltd
Date
dd.mm.y
y
Descriptor
Lorem Ipsum Dolor Sit
Amet, Consectetuer
Adipiscing
Engineered for
Tomorrow
Topic Details
1) Concepts in Discrete-Event Simulation:
2) The Event-Scheduling / Time-Advance Algorithm,
3) World Views,
4) Manual simulation Using Event Scheduling;
5) List processing.
6) Simulation in Java;
7) Simulation in GPSS.
8) Self check Exercise
9) Summary
3/4/2015
Learning Outcome:
Students will understand:-
The basic concepts in Discrete-Event Simulation
The detailed description on the Event-Scheduling / Time-Advance
Algorithm
Basics of World Views
How to perform manual simulation Using Event Scheduling
Definition of list processing.
How to perform simulation in Java
How to perform Simulation in GPSS
3/4/2015
w
1.Concepts in Discrete Event Simulation
System - a collection of entities that act and interact toward the accomplishment of some logical end
Model – An abstract representation of a system , contains structural, logical and mathematical relationship and describe a system in term of state, entities, attributes, sets, process, events , activities and delays
System State- A collection of variable describe a system over a time
Entity- Object or component in the system that requires explicit representation
Attribute – Properties of a given entity
List – Collection of entities ordered in some logical fashion
Event – An instantaneous occurrence that change the state of a system
Event Notice – A record of an event to occur at random time
Event List – A list of event notices for future events known as FEL
1.Concepts in Discrete Event Simulation Continued
Activity – A duration of time of specified length , example service time or inter arrival time
Delay – A duration of time of unspecified indefinite length, which is not known until it ends (e.g. a customer’s delay in a last-in-first-out waiting line which, when it begins, depends on future arrivals).
Clock- Variable representing simulated time
Deterministic Model - a deterministic simulation model is one that contains no random variables. All variables are known with certainty, or in other words, no probability is associated with them.
1.Concepts in Discrete Event Simulation Continued
Stochastic Model - a stochastic simulation model contains random variables
Static Model - a static simulation model is a representation of a system at a particular point in time.
Dynamic Model - a dynamic simulation is a representation of a system as it evolves over time.
Event Scheduling/Time Advance Algorithm
Future Event List FEL: contains all the notices for events scheduled to occur at a future time
At any given time (t), the FEL contains all previously scheduled future events and their associated event times, e.g.: t1, t2, t3, …, etc. See Fig.
The FEL is ordered by event time, i.e. events are arranged chronologically so that the event time satisfies
t ≤ t1 ≤ t2 ≤ … ≤ tn
At time (t), i.e. CLOCK = t, the event associated with t1 is called the imminent event. That is, the event that will occur
Advancing Simulation Time and Updating System Image
Prototype System Snapshot at simulation time t
• Clock t
System state
Entities and Attribute
Set1 Set 2 …… Future Event List FEL
Cumulative statistics and Counters
t
(x,y,z,….)
(3,t1 ) – Type 3 event to occur at time t1
(1,t2 ) – Type 1 event to occur at time t2
Advancing Simulation Time and Updating System Image
Old System Snapshot at simulation time t
• Clock t System state
…… Future Event List FEL
….
t
(5,1,6) (3,t1 ) – Type 3 event to occur at time t1
(1,t2 ) – Type 1 event to occur at time t2
(1,t3 ) – Type 1 event to occur at time t3
…………… (1,t3 ) – Type 2 event to occur at time tn
Event Scheduling / time advance algorithm
Step 1. Remove the event notice for the imminent event (event 3,
time t1) from the FEL
Step 2. Advance CLOCK to imminent event time (i.e. advance
CLOCK from t to t1)
Step 3. Execute imminent event; update system state; change
entity attributes; and set membership as needed
Step 4. Generate future events (if necessary) and place their event
notices on the FEL, ranked by event time, e.g. event 4 to
occur at time t*, where t1 < t*< t1
Step 5. Update cumulative statistics and counters
Advancing Simulation Time and Updating System Image
New System Snapshot at simulation time t
• Clock t System state
…… Future Event List FEL
….
t
(5,1,5) (1,t2 ) – Type 1 event to occur at time t2
(4,t* ) – Type 4 event to occur at time t*
(1,t3 ) – Type 1 event to occur at time t3
…………… (2,tn ) – Type 2 event to occur at time tn
Generation of External
Arrival Stream by Bootsrapping
1 2 3 n n+1
3.7
4.1
7.4
t t*
…. ….
CLOCK =
a*
Between successive arrival
events, other types of events may
occur, causing system state to
change
0
Arrival
Time
Arrival
Time
At simulated time t, assumed to be the
instant of the nth arrival, generate
interarrival time a*, compute t*= t + a*
and schedule future arrival on FEL to
occur at future time t*
Stopping a Simulation
At time 0, schedule a stop simulation event at a specified future time TE. The simulation will run over the time interval [0, TE]
Example: Simulate a shop for 8 hours
Run length TE is determined by the simulation itself. TE is the time of occurrence of some event E.
- Example: TE = time of the 100th service completion
3 World Views
• When using a simulation package or even when doing hand simulation, a modeler adopts a world view or orientation for developing a model.
• The most prevalent world views are
1. the event-scheduling world view
2. the process-interaction world view
3. the activity-scanning world view.
• Particular simulation packages (e.g. Arena) usually support one of these world views.
Engineered for
Tomorrow
Event Scheduling World Views
Concentrates on events and their effects on system state
It makes use of the Future Event List and variable time increments
This is the approach we have just discussed
It is a very flexible approach using which any system can be simulated
It requires lots of mechanisms (e.g. FEL handling) to be coded, which may slow down the development of the simulation model for very simple systems.
This is the world view that is usually used when the simulation program is directly coded on a general-purpose programming language such as Java.
Engineered for
Tomorrow
Process Interaction World View
• Models the system in terms of processes
• Concentrates on entities, and their life cycles as they flow through the system, demanding resources and queueing to wait for resources.
• A process is a time-sequenced list of events, activities and delays that define the life cycle of one entity as it moves through a system.
• Some activities might require resources that are limited, which may cause delays in the process
En for Tomorrow
Process Interaction World View
• This approach is easier for the modeler since people usually perceive the systems in terms of the processes the entities experience
• But this approach is usually harder to implement directly, especially when the systems to be simulated are complex
• Thus, many simulation packages (including ARENA) use this view for the modeler to describe the system (user-interface), but an event-scheduling approach is used operationally to perform the simulation run, hidden from the user.
Activity Scanning World View
Concentrates on activities and conditions that allow them to begin
It uses fixed time increments
At each clock advance, the conditions for each activity are checked, and if the conditions hold, then the corresponding activity starts.
The (M,N) inventory system simulation we used last week used activity-scanning approach. The time increment used was a day.
Simple in concept and leads to modular models that are easier to maintain, understand and modify.
The repeated scanning (at each time increment) results in slow runtime on computers
3.1.3. Manual Simulation Using Event Scheduling (1)
Entities : The server and customers Events : Arrival (A), Departure (D)
Stopping event (E), scheduled to occur at time 60.
System state (LQ(t), LS(t)) :
LQ(t) is the number of customers in the waiting line
LS(t) is the number being served (0 or 1) at time t
(A, t ), representing an arrival event to occur at future time t
(D, t ), representing a customer departure at future time t
(E, 60), representing the simulation-stop event at future time 60.
Activities : Interarrival time Service time
Delay : Customer time spent in waiting line.
Manual Simulation Using Event Scheduling
The interarrival times and service
Initial conditions
The system snapshot at time zero (CLOCK = 0)
LQ(0) = 0, LS(0) = 1
both a departure event and arrival event on the FEL.
The simulation is scheduled to stop at time 60.
Server utilization : total server busy time (B) / total time (TE).
a* : the generated interarrival time
s* : the generated service times
3.1.3. Manual Simulation Using Event Scheduling (4)
Manual Simulation Using Event Scheduling
• Example 3.5 (The Dump Truck Problem)
Traveling
Loading
Scale Weighing
queue
Loader
queue
First-Come
First-Served
First-Come
First-Served
The distributions of loading time, weighing time, and travel time are given in
Tables
The purpose of the simulation is to estimate the loader and scale utilizations
(percentage of time busy).
3.1.3. Manual Simulation Using Event Scheduling (9)
– The activity times are taken from the following list as needed:
3.1.3. Manual Simulation Using Event Scheduling (10)
System state [LQ(t), L(t), WQ(t), W(t)]
LQ(t) = number of trucks in loader queue
L(t) = number of trucks (0, 1, or 2) being loaded
WQ(t) = number of trucks in weigh queue
W(t) = number of trucks (0 or 1) being weighed, all at simulation time t
Event notices :(ALQ, t, DTi ), dump truck i arrives at loader queue (ALQ) at time t
(EL, t, DTi), dump truck i ends loading (EL) at time t
(EW, t, DTi), dump truck i ends weighing (EW) at time t
Entities : The six dump trucks (DT 1, … , DT 6)
3.1.3. Manual Simulation Using Event Scheduling (11)
Loader queue : all trucks waiting to begin loading, ordered on
a first come, first served basis
Weigh queue : all trucks waiting to be weighed, ordered on a first come, first served basis
Activities : Loading time, weighing time, and travel time
Delays : Delay at loader queue, and delay at scale
It has been assumed that five of the trucks are at the loaders and one is at the scale at time 0.
3.1.3. Manual Simulation Using Event Scheduling (13)
The utilizations are estimated as follows:
32.076
2/49
average loader utilization
00.176
76 average scale utilization
These estimates cannot be regarded as accurate estimates of the long-run “steady-state” utilizations of the loader and scale.
3.2 List Processing
• List : a set of ordered or ranked records.
• Record : one entity or one event notice.
3.2.1 List : Basic Properties and Operations (1)
Event type
Event time
Any data
Next pointer
Event type
Event time
Any data
Next pointer
Event type
Event time
Any data
Next pointer
Head Pointer
Tail Pointer
Event type
Event time
Any data
Next pointer
Record Record Record
Field : an entity identifier and its attributes
: the event type, event time, and any other event
related data
How to store record in a physical location in computer memory in arrays : successive records in contiguous locations by pointers to a record : structures in C, classes in C++
The main operations on a list :
Removing a record from the top of the list.
when time is advanced and the imminent event is due to be executed.
by adjusting the head pointer on the FEL by removing the event at the top of the FEL.
Removing a record from any location on the list.
3.2.1 List : Basic Properties and
Operations (2)
The main operations on a list (Cont.)
Adding an entity record to the top or bottom of the list.
when an entity joins the back of a first-in first-out queue.
by adjusting the tail pointer on the FEL by adding an entity to the bottom of the FEL
Adding a record to an arbitrary position on the list, determined by the ranking rule.
if a queue has a ranking rule of earliest due date first (EDF).
by making a partial search through the list.
The goal of list-processing techniques
: to make second and fourth operations efficient
3.2.1 List : Basic Properties and Operations (3)
The notation R(i) : the ith record in the array
Advantage Any specified record, say the ith, can be retrieved quickly without searching, merely by referencing R(i ).
Disadvantage
When items are added to the middle of a list or the list must be rearranged.
Arrays typically have a fixed size, determined at compile time or upon initial allocation when a program first begins to execute.In simulation, the maximum number of records for any list may be difficult or impossible to determine ahead of time, while the current number in a list may vary widely over the course of the simulation run.
3.2.2 Using Arrays for List Processing (1)
3.2.2 Using Arrays for List Processing (2)
• Two methods for keeping track of the ranking of records in a list
• to store the first record in R(1), the second in R(2), and so on, and the last in R(tailptr), where tailptr is used to refer to the last item in the list.
• a variable called a head pointer, with name headptr, points to the record at the top of the list.
2 1 3 4 5 8 7 9 10
100 101 102 103 104 105 106 107 108 109 110 Memory address
2 1 3 4 5 8 7 9 10
100 101 102 103 104 105 106 107 108 109 110
6
6 adding
move move move move
3.2.3 Using Dynamic Allocation and Linked Lists (1)
• In procedural languages such as C and C++, and in most simulation languages, entity records are dynamically created when an entity is created and event notice records are dynamically created whenever an event is scheduled on the future event list.
• The languages themselves, or the operating systems on which they are running, maintain a linked list of free chunks of computer memory and allocate a chunk of desired size upon request to running programs.
• With dynamic allocation, a record is referenced by a pointer instead of an array index. A pointer to a record can be thought of as the physical or logical address in computer memory of the record.
Simulation in Java Single Channel Queue
Simulation in Java continued…
Self Check Exercise
Engineered for
Tomorrow
• What is discrete event simulation? Explain event scheduling algorithm by
generating system snapshots at clock time T and clock time T1 with
diagrams.
• Explain the concepts of discrete event simulation.
• Six dump trucks are used to have coal from entrance of a mine to a rail
road. Each truck is loaded by one of the two loaders. After loading, a truck
immediately moves to the scale, to be weighed as soon as possible. Both
loader and scale have first come first served waiting line for trucks. Travel
time from loader to scale is considered negligible. After being weighed, a
truck begins travel time and then afterwards returns to loader queue. The
activities of loading, weighing and travel time are given in below table:
End of simulation is 40 minutes of completion of weighing from scale. Depict
simulation table and estimate loader and scale utilizations. Assume that 5
trucks are at loaders and one truck is at scale at time 0.
• Draw the flowchart of the execution of the arrival event & departure event
for a single channel queue using event scheduling.
• What do you mean by world view? Briefly explain different types of
world view.
• Explain in detail about List Processing.
• Explain about simulation in GPSS.
• Explain in detail about the concepts of discrete event simulation
• Simulate the grocery counter problem using manual simulation using event
scheduling with the following data.
Summary
Engineered for
Tomorrow
The concepts in simulation are System, Model System state, Entity Attribute, List, Event, Event Notice etc.
Different types of simulation models are :
Stochastic Model - a stochastic simulation model contains random variables
Static Model - a static simulation model is a representation of a system at a particular point in time.
Dynamic Model - a dynamic simulation is a representation of a system as it evolves over time.
Future Event List FEL: contains all the notices for events scheduled to occur at a future time
At any given time (t), the FEL contains all previously scheduled future events and their associated event times, e.g.: t1, t2, t3, …, etc. See Fig.
The FEL is ordered by event time, i.e. events are arranged chronologically so that the event time satisfies
