**SIMULATION SOFTWARE$**

Computer implementation of simulation is costly because of the following reasons : (i) a large number of also are required in order to arrive at a reliable result, (ii) the requirements of storage is large and (iii) complexity of program development is considerable.

The program development cost is greatly reduced if special purpose simulation languages are used for program development. These languages are simple to use.

Simulation languages are application oriented. Continuous systems are usually described by systems of differential equations. Languages like DYNAMO and CSMP are equipped to describe continuous state transition and have tools to solve differential equations. For discrete systems where the state changes occur in single discontinuous steps, languages like GPSS, GASP, SIMSCRIPT and SIMULA are appropriately used.

GPSS is a popular simulation language well suited for queueing system. Since its inception in 1962 by G. Gordon, GPSS bas gone through many changes to increase its power and simplicity.

A classification of simulation languages is given below :

**PROBLEMS**

l . Give a scheme to generate random observations from (a) binomial distribution, (b) Poisson distribution

2. Simulate the value of the integral ʃ^{2}_{1} dx /1+√ x by taking 20 random numbers from (0, 1)

3. Consider gamma (3, 2) and the following random numbers

0.35, 0.36, 0.77, 0.89, 0.39, 0.79, 0.52, 0.64, 0.75.

Generate the first three random observations.

4. Rework the Example 3 with the following set of random numbers

RN for X 0.91 0.78 0.35 0.16 0.23 0.81 0.66

RN for Y 0.21 0.39 0.71 0.61 0.82 059 0.22

5. A company is evaluating an investment proposal wh1ch has uncertainty associated w1th the three important aspects : the original cost, the useful life and the annual net cash flows. The three

probability distributions for these variables are shown below :

Original Useful life Annual net cash inflows

Value Probability Period Probability Value Probability

$ 60000 0.6 6 yr. 0.3 $ 10000 0.1

$. 70000 0.3 7 yr. 0.4 $ 20000 0.2

$ 80000 0.1 8 yr. 0.3 $ 30000 0.3

$ 40000 0.4

The firm wants to perform five simulation runs of this projects life. To simulate, use the following sets of random numbers : 09, 84, 4 I , 92, 65; 24, 38, 74, 1 7, 45; 06, 48, 67, 54, 73 respectively.

6. People arrive at a bus stop with inter-arrival times 3 ± 1 minutes. A bus arrives with inter- arrival times of ± 5 minutes. The bus has a capacity of 30 people and number of seats occupied when the 'bus arrives is equally likely to be any number from 0 to 30. The bus takes on board as many passengers as it can seat and passengers that cannot be seated walk away. Write a flow chart to simulate the arrival of 1 00 buses and count how many people do not get on board.

**Network Scheduling by CPM/PERT**

**. INTRODUCTION**

Let us define 'Project'.

A project can be considered to be any series of activities and tasks that

(i) have a specific objective to be completed within certain specifications.

(ii) have defined start and end dates.

(iii) have funding limits and consume resources.

A number of techniques have been developed to assist in planning, scheduling and control of projects. The most popular methods are the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT). These techniques decompose the project into a number of activities, represent the precedence relationships among activities through a network and then determine a critical path through the network.

The basic concepts are described below :

**(a) Activity**

An activity is an item of work to be done that consumes time, effort, money or other resources. It is represented by an arrow. Tail represents start and head represents end of that activity.

** **

**(b) Event/Node**

It represents a point time signifying the completion of an activity and the beginning of another new activity. Here beginning of an activity represents tail event and end of an activity represents head event

**(c) Dummy Activity**

This shows only precedence relationship and they do not represent any real act1v1ty and is represented by a dashed line arrow or dotted line arrow and does not consume any time. e.g., c

**(d) Rules for Construction of a Network**

(1) Each activity is shown b y one and only one arrow.

(2) There will be only one beginning node/event and only one end node/event.

(3) No two activities can be identified by the same head and tail events.

( 4) All events/node should be numbered distinctly.

(5) Time flows from left to right.

**(e) Common Errors in Network**

(1) Loops :