01 Feb Estimated profit per car served is $6.

Modelling And Simulation

Q1. The following diagram shows an analog version of a system realized over SIMULINK workspace. Identify the system as projected here using an appropriate differential equation

Assume the initial values of the integrators marked x-int and y-int are 10.0 and 20.0, respectively. Choosing appropriate values of the gain parameters a,b,c,d simulate the system. Next, show how to send the simulated output values you generated to MATLAB work-space, and what kind of output this generates in terms of an algebraic function.

Q2. A dynamic system is defined by the following equation of motion y(t) as below

(d^2 y)/(dt^2 )= dy/dt+y+3 with the initial conditions y(0)=1,(dy/dt)_0=-1

Using SIMULINK obtain the profiles of y(t),dy/dt, and (d^2 y)/(dt^2 ) over a simulated time period of 20 secs. How would you change the solution framework if the problem now changes to

(d^2 y)/(dt^2 )= dy/dt+y^2+3 with the same initial conditions as before?

Q3. Using SIMULINK, design the solution workspace for the following system

(d^2 y)/(dt^2 )+y dy/dt+sin?(√t sin?(t))+3=0 with initial conditions y(0)=1,(dy/dt)_0=-1. Obtain the output as an algebraic expression.

Q4. What is the difference between a TEST block and a GATE block in GPSS? Show by a GPSS example how these two blocks work on GPSS processes.

Q5. Using Lecture Notes on GPSS, and other sources on the web, briefly describe the following terms and show their usage using a GPSS process using at least these blocks

MATCH and ASSSEMBLE

LINK and UNLINK

Q6. Using GPSS system simulation package, simulate the following scenario, and report your conclusion.

Cars arrive at a gas station with an interarrival time distributed as shown in Table A.

Interarrival time Cumulative frequency

< 0 0.0 <100 0.25 <200 0.48 <300 0.53 <400 0.67 <500 0.81 <600 0.95 <700 1.00 TABLE A Service time received by a car follows the distribution shown in Table B Service time (secs) Cumulative frequency <100 0.0 200 0.1 300 0.25 400 0.38 500 0.56 600 0.78 700 0.93 800 1.00 TABLE B A car stops for service only if the number of cars waiting for service is less than or equal to the number of cars of currently being served. Otherwise, it leaves, and it means revenue loss for the company. The gas station works from 7:00 AM till 7:00 PM. At the close of the day, any car still in the queue would be served by the attendants. Estimated profit per car served is $6.00 after paying for everything except attendant’s wage. An attendant is paid $15.00 per hour of service, and is paid at most 12 hours a day even if he has to stay beyond 7:00 PM. The gas station owner wants to find out how many attendants he needs to hire to keep the business profitable.