introduction to csim 19 for c++ programmers

INTRODUCTION TO CSIM 19 FOR C++ PROGRAMMERS

Mesquite Corporation

http://www.mesquite.com/documentation/index.htm#startcpp

What is CSIM? Simulation language developed by

Mesquite Software in Austin, TX C/C++ based

Has now a Java-based version Allows user to create process-

oriented, discrete-event simulation models

Implemented as a library No need to learn a new language

OUR FIRST CSIM PROGRAM

A very simple example (I) M/M/1 server with a FCFS queue Input parameters are

Time intervals between arrivals Service times

Server

A very simple example (II) We want to know

Average customer response time:time of arrival to time of departure

Customer throughput rate:customers served per unit time

Server utilization:Fraction of elapsed time the server is busy

Average queue length:number of customers at the facility

The sim process

#include <cpp.h> // CSIM C++ header filefacility *f; // the service center

extern "C" void sim() { // sim process create("sim"); // make this a processf = new facility("f"); // create service center fwhile (simtime() < 5000.0) { hold(exponential(1.0)); // delay

customer(); // generate new customer} // while loopreport(); // output results

}// sim

The customer process

void customer() {create("customer"); // make this a processf->use(exponential(0.5)); // get service

} // customer

Advantages of the approach

• We can describe system through actions taken by each customer

• Facility f manages its own queue

Output

CSIM Simulation Report (Version 19 for MSVC++) Mon May 13 13:42:39 1996

Ending simulation time:10001.909 Elapsed simulation time:10001.909CPU time used (seconds):0.490 FACILITY SUMMARYfacility service service queue response complname disc time util through-put length time countf fcfs 1.00954 0.512 0.506801. 019832.01229 5069

This is the default output.We can request much more specific data

Program analysis: processes Two processes

sim: the main process customer: describes customer

behavior A CSIM process is a C++ function which

executes the "create" statement Establishes the procedure as an

independent, ready-to-run process, Returns control to the calling process

Program analysis: facilities One facility

f: the service center A facility is

Declared with a “facility" declaration Initialized by the "facility()" function

To request service from a facility f, process can call “f->use(Delta_t)”where “Delta_t” is the request duration

Program analysis: simtime() A global “clock” variable keeps track of

the simulated time Double-precision floating point

variable Value can be accessed through

“simtime()” function

Program analysis: hold() “hold()” function causes time to pass for

the process that calls it Deals with simulated time Do not use “sleep()”

Program analysis: exponential() “exponential(Delta_t)” function returns

a value for a exponential random variable with mean “Delta_t” Many other functions of this type

CSIM PROCESSES

Processes Model the active elements of a system Created through a call to “create()” Can have multiple instances of the

same process:

while (simtime() < 5000.0) { hold(exponential(1.0)); // delaycustomer(); // generate new customer

} // while

Process attributes Each instance of a CSIM process has:

Its own internal state A unique process id A process priority One of the following external states:

Executing Waiting-to-execute Holding (for some time interval) Waiting (for some event to occur)

Warning CSIM processes look very much like

conventional OS processes They are different:

One OS process per CSIM simulation CSIM processes run within that

process CSIM processes use simulated time

Not physical time

CSIM process creation When a function calls create()

CSIM creates a process control block (pcb) for the new process and puts it on the “next event list”

Control is returned immediately to the process which invoked the function

CSIM process scheduling Non-preemptive

A new process will execute only after the currently running process leaves the running state by

Executing a hold() Going through a wait Terminating

CSIM FACILITIES

Facilities We can define

Single server facilities:Can service one process at a time

Multi-server facilities:Can service several processes at a time and have a single queue

Arrays of single server facilities:each with its own queue

Facility scheduling By default, a facility services processes

in priority order Where several processes have the same

priority, they will be served on FCFS basis

Other service disciplines can be specified

Example:single-server facility (I)

facility *ss; // declare facility...ss = new facility("sngle srvr");

// initialize ...ss->use(Delta_t);

// use ss for duration Delta_t

Example:single-server facility (II)

s->reserve(); // reserve facility...hold(Delta_t);...s->release(); // release facility...

Using a reserve/release pair lets us keepseparate counts of time spent by customers(a) in queue and (b) being serviced

Example:facility with three servers All three servers share the same queue

const long NSERV = 3; // 3 servers...facility_ms *ms; // declare facilityms = new facility_ms("multi", NSERV);...ms->use(service_time);....

The post office problem revisited (I)

#include <cpp.h> // CSIM C++ header filefacility_ms *po; // the service center

extern "C" void sim() { // sim process create("sim"); // make it a processpo = new facility_ms(“po“, 2); // create powhile (simtime() < 5000.0) { hold(exponential(1.0)); // delay

customer(); // generate new customer} // while loopreport(); // output results

}// sim

The post office problem revisited (II)

void customer() {create("customer"); // make it a processpo->use(exponential(0.5)); // get service

} // customer

Example:array of single-server facilities Each facility now has its own queue

const long NFACS = 10;facility_set *fa; // declare array fa = new facility_set("facs", NFACS);...i = random(0, NFACS - 1); // pick one (*fa)[i].use(service_time);//use facility[i]

Note the (*fa)[i]. without “->”

Example:setting a maximum wait time

const double MAXWAIT = 5.0;

...

st = ss->timed_reserve(MAXWAIT);

if (st < MAXWAIT) { // success

hold(service_time); ss->release(); // done

} else { //request timed out

...

}

Example:allowing preemption

FACILITY cpu; // declare facility cpu

cpu = new facility("cpu");

// initialize facility

...

cpu->set_servicefunc(pre_res)

// set service protocol to preempt-resume

...

priority = 100; // raise process priority

cpu->use(service_time);

CSIM STORAGES

Storages Like facilities but designed to be shared

Each process gets some units of storage

Used to simulate main memory Must have a name

Only used to label report entries

Example: single storage

const long SIZE = 100; storage *mem; // declare storagemem = new storage("mem", SIZE); // initialize mem with 100 units...amt = random(1, SIZE); mem->allocate(amt); // get storage ...mem->deallocate(amt); // release it...

Example: storage arrayconst long NSTORES = 5;const long SIZE = 100;storage _set *mems; // declare array...mems = new storage_set("mem", SIZE,

NSTORES); //initialize...(*mems)[3].allocate(amt); ...(*mems)[3].deallocate(amt);

Example:setting a maximum wait time

const double MAXWAIT = 1.0;st = mem->timed_allocate(amt, MAXWAIT);// maximum wait is one time unitif (st < MAXWAIT) {

// success...mem->deallocate(amt); // release

} else {// failure...

}

More options Can also specify faculties and storages

that can only be allocated at regular points in time Clock ticks

Must invoke “synchronous()” method before invoking “allocate()” method “synchronous()” method specifies

phase and period of allocation policy

CSIM BUFFERS

Buffers A buffer consist of

a counter indicating the amount of available capacity

A queue for processes waiting to get some buffer space

A typical producer behavior A queue for processes waiting to

free some buffer space A typical consumer behavior

Example:creating and accessing a buffer

const long SIZE = 100;

buffer *buf;

buff = new buffer("buff", SIZE);

...

amt = random(1, SIZE);

buff->get(amt);

...

buff->put(amt);

Example:setting a maximum wait time

st = buff->timed_get(amt, 1.0);

if (st < TIMED_OUT) {

// success

...

buff->put(amt);

} else {

// failure

...

}

CSIM EVENTS

Events Used to synchronize and control

interactions between different processes Have two states

Occurred (OCC) Not occurred (NOT_OCC).

Processes and events

A process can Set an event:

mark it as occurred Wait for an event:

when event occurs all waiting processes can continue occurred state

Queue on an event:when event occurs one waiting processes can continue

More details (I) When a process waits for an event:

If the event is in the not-occurred state, the process is suspended and placed in a queue of processes waiting for the event to occur. When the event occur

All waiting processes are allowed to proceed

Event is changed to not occurred If the event is in the occurred state,

The process continues to execute Event state is changed to not

occurred

More details (II) When a process queues on an event:

If the event is in the not-occurred state, the process is suspended and placed in a queueof processes queued on the event. When the event occur

Only the first queued processes is allowed to proceed

Event is changed to not occurred If the event is in the occurred state,

The process continues to execute Event state is changed to not occurred

CSIM events and semaphores

Like binary semaphores, CSIM events can have two values:

occurred/not-occurred Occurred correspond to value of 1 Not-occurred corresponds to value

of 0 Set() method corresponds to V() Queue() method corresponds to P() Wait() method does not correspond

to any semaphore operation

Example:declaring and using an event

event *ev; //declare event ev

ev = new event("ev"); //initialize it

...

ev->wait(); // wait for event

...

ev->queue(); // queue on event

...

ev->set(); // set event

Example:arrays of events

const long NEV = 25;

event_set *eva; // declare array

eva = new event_set("ev array", NEV);

// initialize it events*/

...

(*eva)[5].wait();

...

(*eva)[5].set();

Example: waiting/queuing forany event in an array

i = eva->wait_any();

// i is index of event that occurred

or

i = eva->queue_any();

// i is index of event that occurred

Example: setting a maximum wait time

...

t = ev->timed_wait(MAXWAIT);

//wait for up to MAXWAIT time units

if (st ! = MAXWAIT) {

// success

...

}

CSIM MAILBOXES

Mailboxes

Allow for the asynchronous exchange of data between CSIM processes Any process may send a message to

any mailbox Any process may attempt to receive a

message from any mailbox

More details

A mailbox has two FIFO queues: A queue of unreceived messages A queue of waiting processes

At least one of the queues will be empty at any time Can either have messages waiting to

be received or processes waiting for messages but not both

Sending messages

CSIM uses non-blocking sends: When a process sends a message

If there is a waiting process The message is given to that

process Else

The message is placed in the message queue.

Receiving messages

CSIM uses blocking receives: When a process attempts to receive a

message, If there is an unreceived message

The message is given to the process

Else The process is placed in the

process queue

Observations

Non-blocking sends and blocking receives are the norm in most message passing systems CSP is the counter-example

Since messages are sent to and retrieved from a mailbox, this is a case of indirect communication

Messages

A message can be either A single integer or A pointer to some other data object.

If a process sends a pointer, it is the responsibility of that process to maintain the integrity of the referenced data object until it is received and processed We are simulating message passing

Example: a single mailbox

long msg_r, msg_s; // message variables

mailbox *mb; // declare mailbox mb

mb = new mailbox("mb"); // instantiate mailbox

...

mb->receive(&msg_r); // receive msg

...

mb->send(msg_s); // send msg

Example:setting a maximum wait time

...

st = mb->timed_receive(&msg_r, MAXWAIT);

// wait for up to MAXWAIT time units

if (st < MAXWAIT) {

//success

...

} // if

Example:arrays of mailboxes

const long NBOXES = 25;

mailbox_set *mba;

. . .

mba = new mailbox_set("mbox set", NBOXES);

Example: getting a message from any mailbox in an array

i = mba->receive_any(&msg);

// i is index of non-empty mailbox

Example: sending a message to a given mailbox in an array

(*mba)[3].send(msg);

Example:

st = mba->timed_receive_any(&msg, MAXWAIT);

if(st < MAXWAIT) {

// process message

...

} else {

// handle time out

...

} // if

MANAGING QUEUES

Queues

Each CSIM resource (facility, storage, buffer, mailbox, …) consists of One or more queues containing

waiting processes (suspended processes in CSIM lingo)

Resource-specific data structures CSIM allows programmer to manipulate

the contents of these queues

Example For facilities, the programmer can Find the process at the head of the

queue: pptr = f->first_process();

Find the process at the tail of the queue: pptr = f->last_process();

Remove a process from a facility queue : pptr = f->remove_process(pptr);

Insert a process in a facility queue: f->insert_process(pptr);

For more details

Check online documentation

GATHERING MORE STATISTICS

Tools

SIM provides four general-purpose statistics gathering tools: Tables Qtables Meters Boxes

Supplement standard statistics gathered by facilities and storages

Usage To obtain statistics other than mean

values for facilities and storages To obtain statistics for other model

components, such as mailboxes and events

To obtain statistics for selected submodels or for the model considered as a whole

To employ the CSIM run length control algorithms Stop the simulation once collected data

satisfy user’s accuracy requirements

Steps to be taken

Identify statistics of interest and which statistics gathering tools are appropriate

Declare a global pointer (variable) for each statistics gathering tool that will be used

Initialize each statistics gathering tool Add instrumentation (i.e., function calls) to

the model to feed data to the tools Generate reports

TABLES

Purpose To gather statistics about a sequence of

discrete entities such as Interarrival times Service times Response times

Tables do not store anywhere the recorded values They simply update their statistics

each time a value is included

Standard statistics

Minimum Maximum Range Mean Variance Standard deviation Coefficient of variation No quantiles (median, …)

Optional features Creation of a histogram Calculation of confidence intervals Computation of statistics for values in

a moving window

Types of tables

Tables can be Dynamic

Should be used by default Permanent

Not cleared when the reset function is called

Not deleted when rerun is called Used to gather data across multiple

runs of a model

Declaring and initializinga dynamic table

table *td;

td = new table("response times");

Declaring and initializinga permanent table

permanent_table *td;

td = new permanent_table("response times");

Using a table

To “insert” a value, use either td->tabulate(1.0);or td->record(1.0);

To generate reports For a specific table, use

td->report(); For all existing tables, use

report_tables();

Specifying a histogram

Prototype:void table::add_histogram(long nbucket,double min,double max)

Example:td->add_histogram(10, 0.0, 10.0); Will divide range from 0 to 10 into 10

classes or buckets

Confidence Intervals

CSIM can automatically compute confidence intervals for the mean value of any table td->confidence();

Must invoke method immediately after table has been initialized

We get 90, 95 and 98 percent confidence intervals

Moving window

Can specify that only the last n values are used in computing the statistics n is called the window size

Example: td->moving_window(1000);

Usually specified immediately after the table is initialized Can do it later but table must be

empty Can be used to remove initial bias

Other options

Can rename a table: td->set_name("elapsed time");

Can clear and reinitialize a table td->reset_table();

Can delete a dynamic table delete td;

The post office problem revisited (I)

#include <cpp.h> // header filefacility_ms *po; // the service centertable *tqueue, *tservice, *ttotal;const long nclerks = 2;

void customer();

The post office problem revisited (II)

extern "C" void sim() { // sim process create("sim"); // make it a process po = new facility_ms(“po", nclerks); tqueue = new table("Waiting times"); tservice = new table("Service

times"); ttotal = new table("Total times"); while (simtime() < 5000.0) { hold(exponential(1.0)); // delay customer(); // new customer } // while loop report(); // output results}// sim

The post office problem revisited (III) void customer() { double t0, t1, t2; create("customer"); t0 = simtime(); po->reserve(); t1 = simtime(); tqueue->record(t1 – t0); hold(exponential(1.0)); po->release(); t2 = simtime(); tservice->record(t2 – t1); ttotal->record(t2 – t0);} // customer

The post office problem revisited (IV)

void customer() { double t0, t2; create("customer"); t0 = simtime(); po->use(exponential(1.0)); t2 = simtime(); ttotal->record(t2 – t0);} // customer

Observations

If we use a use statement in the customer process, we can only have collected total times

QTABLES

Purpose To gather statistics about on an integer

function of time such as Queue length Population of a subsystem Number of available resources ...

Qtables record and gather statistics about time-averaged values

Qtables and Tables

Entering a value into a table is done through a tabulate() method

Updating a qtable is a two-step process:

qtbl->note_entry();...qtbl->note_exit();

Think of qtables as special tables for queues

Declaring and Initializing Dynamic Qtables A pointer to a dynamic qtable is declared

in a CSIM program as follows: qtable *qtd;

Before a qtable can be used, it must be initialized qtd = new qtable("queue length");

Initializing Permanent Qtables A qtable can be initialized as a

permanent qtable qtd = new

permanent_qtable("queue length");

Noting a Change in Value

Most common way for the value of a qtable to change is for it to increase or decrease by one. Customer joins/leaves a queue A resource is allocated/released

Use qtd -> note_entry();

...qtd->note_exit();

Special case

The value of a qtable can be changed To an arbitrary number

qtd->note_value(12); To an arbitrary floating (double)

qtd->note_value(1.75); The value of a qtable can be initialized

to an arbitrary floating (double) number qtd->set_initial_value(-1.0);

Producing reports

To generate a report for a specific qtable use qtd->report();

To generate reports for all existing qtables use report_qtables();

Report for a qtable will include the qtable name and all statistics

Histograms

To specify a histogram use qtd->add_histogram(

nbuckets, // number of bucketsmin, // minimum valuemax // maximum value);

Caution: The min and max parameters of add_histogram are of type long, not double as for tables

Confidence Intervals

CSIM can automatically compute confidence intervals for the mean value of any qtable

qtd->confidence();

Must invoke method immediately after qtable has been initialized

We get 90, 95 and 98 percent confidence intervals

Moving window

Specifying a moving window forces the qtable to use only the last n changes a computing the statistics n is called the window size (long int)

Use qtd->moving_window (n);

It is an error to specify a moving window for a qtable that is not empty.

More

Can rename, reset and delete qtables

qtd-> set_name ("number in queue");

qtd->reset_qtable (); delete qtd;

Reset does not clear qtable optional features like histogram, confidence intervals and moving window

The post office problem revisited (I)

#include <cpp.h> // header filefacility_ms *po; // the service centerqtable *tqueue, *tclerks, *tpo;const long nclerks = 2;

void customer();

The post office problem revisited (II)

extern "C" void sim() { // sim process create("sim"); // make it a process po = new facility_ms("po", nclerks); tqueue = new qtable("Queue"); tclerks = new qtable("Clerks"); tpo = new qtable("Post Office"); while (simtime() < 5000.0) { hold(exponential(1.0)); //

delay customer(); // new customer } // while loop report(); // output results}// sim

The post office problem revisited (III) void customer() { create("customer"); tqueue->note_entry(); tpo->note_entry(); po->reserve(); tqueue->note_exit(); tclerks->note_entry(); hold(exponential(1.0)); po->release(); tclerks->note_exit(); tpo-> note_exit();} // customer

The post office problem revisited (IV)

void customer() { create("customer"); tpo->note_entry(); po->use(exponential(1.0)); tpo->note_exit();} // customer

METERS

Meters

Used to gather statistics on the flow of entities past a specific point in a model

Can measure arrival rates completion rates allocation rates

Declaring and InitializingDynamic Meters To declare a dynamic meter,use

meter *md; To initialize the meter use

md = new meter(" completions");

Measuring passages at a meter Use

md-> note_passage();

For the statistics to be accurate, every entity of interest must Note its passage Do so at the correct time

Producing Reports

Can generate a report for a specified meter at any time md->report();

Can generate reports for all existing meters by calling the report_meters function report_meters();

Standard Report Options

Can request meters to produce histograms md ->add_histogram(

nbuckets, // longmin, // doublemax // double)

Can request meters to compute confidence intervals md ->confidence();

Other Options

Can rename, reset and delete meters md ->set_name(" departures"); md->reset(); delete md;

BOXES

Boxes

Conceptually enclose part or all of a mode

Gather statistics on The number of entities in the box The amount of time entities spend in

the box (i.e., the elapsed time).

Boxes, Tables and Qtables

Each box combines a table and a qtable Statistics on elapsed times are kept in

the table Statistics on number of entities in the

box are kept in the qtable Simplifies the programmer's task

Declaring and Initializing Dynamic Boxes To declare a dynamic box, use

box *bd; To initialize a dynamic box, use

bd = new box("system"); To make the box permanent, use

bd = new permanent_box("system");

Instrumenting the model

An entity enters a box by calling the enter method timestamp = bd->enter();

timestamp must be saved by the entity that entered the box

The entity exits the box by calling the exit method and passing to it the timestamp that it received upon entry bd->exit(timestamp);

Producing Reports

To generate a report for a specified box, use bd->report();

To generate reportsd for all existing boxes, use report_boxes();

Histograms

Can specify histograms For the elapsed times in a box;

bd->add_time_histogram(10, 0.0, 10.0);

For the population of a box bd->add_number_histogram(10, 0, 10);

Confidence intervals

Can specify confidence intervals For the elapsed times in a box

bd->time_confidence(); For the population of a box

bd->_number_confidence();

The post office problem revisited (I)

// Uses boxes

#include <cpp.h> // header filefacility_ms *po; // the service centerbox *bqueue, *bclerks, *bpo;const long nclerks = 2;

void customer();

The post office problem revisited (II)

extern "C" void sim() { // sim process create("sim"); // make it a process po = new facility_ms("po", nclerks); bqueue = new box("Queue"); bclerks = new box("Clerks"); bpo = new box("Post Office"); while (simtime() < 5000.0) { hold(exponential(1.0)); // delay customer(); // new customer } // while loop report(); // output results}// sim

The post office problem revisited (III) void customer() { double t0, t1; create("customer"); t0 = bqueue->enter(); t0 = bpo->enter(); po->reserve(); bqueue->exit(t0); t1 = bclerks->enter(); hold(exponential(1.0)); po->release(); bclerks->exit(t1); bpo->exit(t0);} // customer

The post office problem revisited (IV)

void customer() { double t0; create("customer"); t0 = bpo->enter(); po->use(exponential(1.0)); bpo->exit(t0);} // customer

STATISTICS GATHERING

Statistics gathering

Will show how to combine boxes and meters to gather statistics

Example

Want to instrument a service center and get

Arrival rates Departure rates Statistics about the whole service center Statistics about the server alone

Use Meters for both rates Boxes to isolate subsystems

The service center

Server

Will use two meters and two boxes One box around queue and server One box around server alone

MeterMeter

Declarations

facility *f;

meter *arrivals;

meter *departures;

box *queue_box;

box *service_box;

All entities are dynamic

Initialization

f = new facility("center");

arrivals = new meter("arrivals");

departures = new meter("completions");

queue_box = new box("queue");

service_box = new box("in service");

Instrumentation

arrivals->note_passage(); timestamp1 = queue_box->enter(); f->reserve(); timestamp2 = service_box-

>enter(); hold (exponential(0.8)); f ->release(); service_box->exit(timestamp2); queue_box->exit(timestamp1); departures->note_passage();}

Notes

The time at which the customer process enters the queue is the current time immediately before it issues the request() for the facility

The time at which the customer process enters the server is the current time immediately after it issues the request() for the facility

Every box requires each process using it to keep track of entry timestamps Timestamps must be local to the process

RUNNING A CSIM PROGRAM

Your program should run on one of the four Linux machines (linux01 to linux04) of our department.

Do not forget to add to your program:

#include <cpp.h> To compile your program with g++, you

should useg++ -DCPP program1.cpp –o program1 /usr/lib/libcsimcpp.a –lm

The basics

How to simplify your life

Create a file named csim containing g++ -DCPP $* /usr/lib/libcsimcpp.a –

lm Make it executable You can now write

csim program1.cpp –o program1

First example:A camper rental service

Hill Country Camper Rental Service has four campers available for rent to walk-in customers.

Rental times are uniformly distributed between three and seven days

Walk-in customers arrive randomly every two days, on the average.

If a camper is not available, the customer will go elsewhere.

Quantities of interest

Fraction of arriving customers that will be lost because no camper is available

Mean number of rented campers

Median number of rented campers

Fraction of arriving customers that will be lost if one of the four campers is in the shop for repairs

Basic entities

Two basic entities Customers Campers

We will use Processes to represent customers A multi-server facility to represent the

campers

How it will look

Campers

YesFree campers?

No

Customer process will start with a test

A narrative

Customer arrives at rental agency If there are no available campers,

he/she goes away Otherwise he/she

Reserves a camper Holds it for uniform (MAXRENTAL,

MINRENTAL) Releases the camper

Data gathering

Put a box around the multi-server facility representing them campers Use number_histogram to evaluate

the mean number of rented campers

Keep track of number of rented campers If all campers are rented out,

customer will be lost

Includes and defines

#include <cpp.h> // required

#define DURATION 360

#define NCAMPERS 4

#define MIART 2.0

#define MINRENTAL 3.0

#define MAXRENTAL 7.0

void customer();

Global declarations

facility_ms *campers; // service center

box *agency;

// other global variables

int nrented = 0; // no of rented campers

int ncust = 0; // no of customers

int nlost = 0; // no of lost customers

Sim process (I)

extern "C" void sim() { // sim process

create("sim"); // make this a process

campers = new facility_ms("campers", NCAMPERS); // create the facility

// initialize box

agency = new box("rental agency");

agency->add_number_histogram(5, 0, 4);

Sim process (II)

while(simtime() < DURATION) {

hold(exponential(MIART));

customer(); // generate next customer

} // while

Sim process (III)

report(); // produce statistics report

printf("\nNumber of customer arrivals: d\n", ncust);

printf("Number of lost customers: %d\n", nlost);

printf("Percentage of lost customers: %f percent\n", (nlost*100.0)/ncust);

} // sim

Customer process (I)

void customer() {

double time_in; // MUST BE LOCAL

create("customer"); // make this a process

ncust++; // note arrival

if (nrented == NCAMPERS) {

nlost++; // customer goes elsewhere

terminate (); // bye bye

} // if

Customer process (II)

// proceed with rental time_in = agency->enter(); //note entry campers->reserve(); // request service nrented++; // one more rented camper hold(uniform(MINRENTAL,

MAXRENTAL)); campers->release(); // return camper nrented--; // one less rented camper agency->exit(time_in); // note exit} // customer

Output (I) C++/CSIM Simulation Report (Version 19.0 for Linux x86)

Tue Apr 8 09:22:41 2008

Ending simulation time: 363.461

Elapsed simulation time: 363.461

CPU time used (seconds): 0.000

Output (II) FACILITY SUMMARY

facility service service through- queue response compl

name disc time util. put length time count

--------------------------------------------------------------------------------

campers fcfs 4.89966 2.022 0.41270 2.02209 4.89966 150

> server 0 4.77374 0.722 0.15132 55

> server 1 5.04442 0.597 0.11831 43

> server 2 4.60802 0.406 0.08804 32

> server 3 5.40136 0.297 0.05503 20

Output (III) BOX 1: camper rental agency

statistics on elapsed times

minimum 3.054523 mean 4.899663

maximum 6.959299 variance 1.309492

range 3.904776 standard deviation 1.144330

observations 150 coefficient of var 0.233553

statistics on population

initial 0 minimum 0 mean 2.043391

final 2 maximum 4 variance 1.265306

entries 152 range 4 standard deviation 1.124858

exits 150 coeff of variation 0.550486

Output (IV) cumulative

number total time proportion proportion

0 25.00858 0.068807 0.068807 *****

1 104.86629 0.288522 0.357328 ********************

2 105.44072 0.290102 0.647431 ********************

3 85.63595 0.235613 0.883043 ****************

>= 4 42.50915 0.116957 1.000000 ********

Total number of customer arrivals: 176

Number of lost customers: 24

Percentage of lost customers: 13.636364 percent

Estimating a median

• Median of number of rented campers isabove 1 but less than 2

• Assuming linearity, median is around 1.51

Observations

Could have decomposed sim process into three functions initialize() generateCustomers() displayResults()

Could have replaced request(), hold() and release() calls by campers->use(uniform(…);

Second Example:A RAID array

Have extra parity data P = A XOR B XOR C

A B C P

Second Example:A RAID array Can tolerate failure of one disk

Say disk A fails We can reconstitute its contents using

A = P XOR A XOR B XOR C

A B C P

X

Disk array reliability

Reliability R(t) of a system is the probability that will remain operational over a time interval [0. t ] given that it was operational at time t = 0 Not the same as availability Our focus is evaluating the risk of a

data loss during array lifetime

Limitations of Markov models

Require disk failures and disk repairs to be Poisson processes Disk repair times are not

exponentially distributed Disk failures are not independent

events A failing disk may overhead a disk

rack Disk failure rate vary over time

Disk failure rates

Disk MTTFs express failure rates over actual disk lifetime A disk with a MTTF of 1,000,000 hours

will not last an average of 114 years Disk MTTFs announced by

manufacturers are fairly optimistic Obtained by extrapolating stress tests Observed disk failure rates are much

larger

Quantities of interest (I)

Mean Time to Data Loss (MTTDL): Used in many studies Assumes that long-term data loss rate

of an array can be sued to predict its data loss rate during its actual lifetime

MTTDLs are measured in decades, it not centuries

Array actual lifetimes are 5 to 7 years

Quantities of interest (II)

Failure rate over first n years; Probability that array will not lose any

data over n years Better performance index

Reflects actual usage conditions

Our model

Will investigate failure rates over first n years of operation of array

Will start the array and stop the simulation when A data loss occurs Array exceeds its operational lifetime

and repeat the process until we get good confidence intervals for failure rates

Possible extensions

Use variable disk failure rates High during burn-in period Much lower during first or second

year Increase as disk age

Model correlated failures

CSIM implications

Have one process per disk Wait until first of

Data loss Array reached the end of its useful

lifetime 5 to 7 years

Program will use a timed_wait() on a“data loss” event Other solutions are possible

Entities

The disk drives Assumed to fail independently of each

other Not always true

Overheating disks in disk racks Disks from the same defective

batch

Constants

#include <cpp.h> // required #include <math.h> #define NDISKS 5 // number of disks in

array#define NYEARS 5 // lifetime of array

(years)#define MTTF 300000.0 // disk MTTF

(hours)#define MTTR 8.0 // disk MTTR (hours)#define NRUNS 400000L // number of

runs

Other global declarations

int nfailed; // number of failed disksdouble lifetime = NYEARS * 365 * 24;// simulation duration

event *dataloss;

void disk(int i);

Sim process (I)

extern "C" void sim() { // sim process int i; create("sim"); // make this a process dataloss = new event(“data loss"); // create NDISKS disk processes for (i=0; i < NDISKS; i++){ disk(i); } // for

Sim process (II)

// wait for data loss or // end of useful lifetime

dataloss->timed_wait(lifetime); report(); // produce statistics report if (simtime() < lifetime) {

printf ("Array failed at %3.0f\n", simtime());

} else { printf ("Array did not fail\n”);

} // if-else} // sim

Disk process (I)

void disk(int i) { create("disk"); while(simtime() < lifetime) { // expect failure hold(failures->exponential(MTTF)); // disk failed nfailed++; if (nfailed == 2) { dataloss->set(); terminate(); // the process } // if

Disk process (II)

// start repair process hold(repairs-

>exponential(MTTR)); // disk is repaired/replaced nfailed--; } // while} // disk

MORE ABOUT REPORTS

Tables, Qtables, …

To generate a complete report use report();

We can also generate partial reports: report_hdr(); report_facilities(); …

(check the online CSIM documentation)

Printing model statistics

To generate a report on the model statistics, use mdlstat();

Can also get specific reports on the number of events processed events_processed();

States of system entities

Use dump_status(); Can also get partial reports

status_processes (); status_next_event_list(); status_events (); status_mailboxes (); status_facilities (); status_storages ();

DEBUGGING AND TRACING

Tracing all state changes

To generate trace messages for all state changes, use trace_on();

To turn off tracing, use trace_off ();

Can use logical tests to turn and off trace messages

Can also use run time option –T to turn on trace messages

Tracing processes

Can trace one type of processes: trace_process ("customer");

Can trace a specific process: trace_process ("customer.100"); Number in string specifies the

process sequence number

Tracing a specific object

Object can be a facility, storage, event, or mailbox.

Use trace_object ("memory");

where string specifies the object name

Writing your own trace messages

Can include in your program: trace_object (“Your own text");

Redirecting trace output

Use fp = fopen ("trace", "w");

set_trace_file (fp);

MISCELLEANOUS OPTIONS

Restarting the model (I) Use rerun(); It will

Clear all non-permanent tables structures Kill all processes Reinitialize all facilities, events, mailboxes,

process classes, storage units, tables and qtables established before the first create(); statement

Eliminate all remaining facilities, storage units, events, …

Reset the clock to zero

Restarting the model (II)

Use rerun(); It will not:

Reset the random number generator Clear the permanent table structures

A good reason to use permanent tables