Simulation and Modelling - Unit Wise Questions

1.  Describe different types of mathematical simulation models. Develop a mathematical model (differential equation) for any dynamic system.

1.  Differentiate between dynamic physical models and static physical models with example.

1.  Define simulation. What are the various steps in simulation study? Explain.

1.  Explain the steps in simulation study. What are the limitation of simulation?

1.  What is model? What are the different types of models? Give example for each.

1.  Differentiate between static and dynamic physical models in simulation. Describe dynamic physical model in detail with the help of suitable example.

2.  Define physical model. Explain the dynamic physical model with the help of suitable diagrams and expressions. [2+8]

3. Explain the analogy between Mechanical system and electrical system using Dynamic Physical Model. Explain Dynamic mathematical model and static mathematical model.

3. What do you understand by static mathematical model? Explain with example. Differentiate between stochastic and deterministic activities.

4.  Differentiate between static physical and dynamic physicals models.

4.  What are the advantages and disadvantages of simulation?

4.  When is simulation appropriate and when it is not?

4.  Differentiate between analytical models and numerical models.

4.  What are the types of simulation models?

4.  Define model. Describe different types of simulation models in brief.

4.  Define and describe different types of elements and components of a system.

4.  Differentiate between numerical and analytical methods in system simulation.

4. Explain about system, its environment and its components.

5.  Describe different phases of simulation study with the help of flow chart.

5.  Describe the importance of differential/Partial differential equations in simulation.

5.  Describe different phases of simulation study with the help of flow chart.

5.  Describe the importance of differential/Partial differential equations in simulation.

4. Discuss the  merits and demerits of system simulation.

6.  What do you understand by interactive system? Explain

7.  What do you understand by distributed lag model? explain with example.

7.  Define activity, event and state variables. List out the activities and events for the following systems;

a.       Super market

b.      Inventory control

c.       Hospital

8.  What are the different phases that are employed in system simulation study? Explain in brief.

11.  Describe the distributed lag model with the help of any practical example.

11.  “To simulate is to experiment”. Justify it.

12.  “There is no unified theory in simulation”. Verify it.

12.  Name the entities, attributes, activities, events, and state variables for the following system:

a.       Cafeteria

b.      Inventory

c.        Banking

d.      A hospital emergency room

e.       Communication 

12.  Explain the distributed lag model.

12.  Identify, with reasons, four different problems from your own experience that you think should be solved using digital simulation rather than analytically.

13.  Write short note on:

a.       System, boundary and system environment

b.      Real time simulation

13.  List out the entities, attributes, activities and events for Banking, Communication, Production, Inventory and Supermarket systems.

13.  Describe the basic nature of simulation in brief.

12. Write short notes on (any two).( 2 x 2.5 = 5)

a) System and its environment.

b) Simulation run statistics.

1.  What do you understand by analog method of system simulation? Explain it with suitable example. [3+7]

1.  Differentiate between analog and digital methods of simulation. Explain the analog method of simulation with the help of suitable example.

4.  Differentiate between discrete and continuous system.

6.  What do you understand by interactive and feedback system in simulation? Explain.

5. What is analog computer? Design a basic analog computer that represents a simple dynamic system.

7.  Explain, how do you update the clock time in system simulation.

6. What is non-stationary Poisson process? How can we convert it into a stationary Poisson process?

6. Define arrival pattern. Explain non-stationary Poisson process.

7. Explain Monte Carlo simulation method with an example.

10.  Differentiate between clock time and simulation time used in system simulation.

10.  What do you mean by Hybrid simulation?

10.  What do you understand by feedback systems? Explain

10.  Differentiate between fixed time step and event to event model with the help of suitable examples.

10.  Explain Hybrid simulation with example.

10.  Differentiate between fixed time step and event to event model with the help of suitable examples.

11.  How do you update the clock time in simulation? Explain.

13.  Write short note on:

a.       Discrete system modeling

b.      Feedback systems

1. What are the characteristics of Queuing System? What are the various performance measures in single server (M/M/1) queuing system simulation? (5 +5)

2.  Define the queuing system. Explain the elements of queuing system with example.

2.  What do you mean by Queuing system? Explain the characteristics of Queuing system with example.

1. Define queuing system. Explain different queuing disciplines. Also explain different performance measures for evaluation of queuing system.

3.  Define congestion. Describe different types of components, characteristics and queueing disciplines of a queueing system.

3.  Define congestion in a queuing system. Describe different types of components and characteristics of a queueing system.

5.  What do you mean by server utilization?

5.  What do you mean by Multi Server Queues?

5.  Define congestion in a queuing system, and describe its major characteristics.

5.  What are the elements of queuing system?

8.  Define queuing discipline. Describe different types of queuing disciplines with example.

9.  Define traffic intensity and server utilization. Write down the kendall’s notation for queuing system.

9.  Define traffic intensity and server utilization. Write down the Kendall’s notation for queuing system with example.

9.  What are the Kendall notation of Queuing System?

10.  What do you understand by queueing and queueing discipline? An office works for 5 days, 8 hours per day, and receives 1200 telephone call in the week. Calculate the mean arrival rate and mean inter-arrival time of the calls.

13.  Write short note on:

a.       Queuing discipline                                            

b.   CSMP

1.  Define and describe Markov chain in detail with the help of suitable examples. Also describe at least three areas of application of Markov chain.

2.  Explain Markov Chains with example.

2.  Explain the Markov chains with examples and its applications.

6.  What are the key features of Markov chains?

7.  Define a Markov chains and its application.

5. Explain markov's chain with a suitable example.

13.  Write short notes on:

a.       Markov Chain

b.      Feedback system

13.  Define and describe Markov Chain with example.

12. Write short notes on: (2 × 2.5 = 5)

    a. Differential equation

    b. Markov Chain 

2.  Differentiate between true and pseudo random numbers. What are the basic properties of random numbers? The sequence of numbers 0.37, 0.29, 0.19, 0.88 0.44, 0.63, 0.77, 0.70 0.21, and 0.58 has been generated. Use K-S test to determine if the numbers are uniformly distributed (Dα = 0.41 for α = 0.05  (2 + 2 + 6)

2. Define and develop a Poker test for four-digit random numbers. A sequence of 10,000 random numbers, each of four digits has been generated. The analysis of the numbers reveals that in 5120 numbers all four digits are different, 4230 contain exactly one pair of like digits, 560 contain two pairs, 75 have three digits of a kind and 15 contain all like digits. Use Poker test to determine whether these numbers are independent. (Critical value of chi-square test for α=0.05 and N=4 is 9.49)

2.  Use multiplicative congruential method to generate a sequence of three digits random numbers between (0, 1) with X₀=27, a=3 and m=1000. Use any one of the uniformity test to find out whether the generated numbers are uniformly distributed or not? (Critical value for α=0.05 and N=5 is 0.565).

2.  Use multiplicative congruential method to generate a sequence of three digits random numbers between (0, 1) with X₀=27, a=3 and m=1000. Use any one of the uniformity test to find out whether the generated numbers are uniformly distributed or not? (Critical value for α=0.05 and N=5 is 0.565).

2.  Define and develop a Poker test for four-digit random numbers. A sequence of 10,000 random numbers, each of four digits has been generated. The analysis of the numbers reveals that in 5120 numbers all four digits are different, 4230 contain exactly one pair of like digits, 560 contain two pairs, 75 have three digits of a kind and 15 contain all like digits. Use Poker test to determine whether these numbers are independent. (Critical value of chi-square test for α=0.05 and N=4 is 9.49)

2.  Describe the linear congruential method for random number generation. Use the Multiplicative congruential method to generate a sequence of four-three digit random integers, with seed = 117, constant multiplier = 43 and modulus = 1000.  [4+6]

3.  Define frequency test for random numbers. Develop the Poker test for four digit numbers, and use it to test whether a sequence of following 1000-four digit numbers are independent. [2+4+4]

(Use Use α=0.05 and N=4 is 9.49)

3.  What is the main objective of gap test? Explain gap test algorithm with example.

3.  Explain the independence test. A sequence of 1000 four digit numbers has been generated and an analysis indicates the following combinations and frequencies.

Based on poker test, test whether these numbers are independent. Use α=0.05 and N=4 is 9.49.

3.  What do you mean by uniformity test? Explain the poker test with example.

2. Differentiate between chi-square test and KS test for uniformity. Use KS test to check for the uniformity for the input set of random numbers given below.0.54, 0.73, 0.98, 0.11,0.68,0.45. Assume level of significance to be D_{α = 0.05}=> 0.565.

3.  What are the properties of random number? The sequence of numbers 0.54, 0.73, 0.98, 0.11 and 0.68 has been generated. Use the Kolmogorov-Smirnov test α=0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval 0 to 1 can be rejected. (Note that the critical value of D for α=0.05 and N=5 is 0.565).

5.  What do you mean by Pseudo random numbers?

6.  Define random numbers and describe why the random numbers generated by computer called pseudo random numbers?

6.  Why the random numbers generated by computer called pseudo random number? List out different types of errors that may occur while generating pseudo-random numbers.

6.  Explain non-uniform random number generation.

6.  What do you mean by non-uniform random number?

6.  What do you mean by pseudo random numbers?

7.  Why an auto-correlation test is needed in random number?

7.  Explain the process of testing for auto-correlation test.

7.  Describe the rejection method of generating the random numbers.

7.  Explain the congruence method of generating random numbers.

8.  Use the linear congruential method to generate a sequence of three two-digit random integers. Let X₀=29, α=9, c=49 and m=100.

9.  The sequence of numbers 0.54, 0.73, 0.97, 0.10 and 0.67 has been generated. Use the Kolmogorov-Smirnov test α=0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval [0, 1] can be rejected. (Note that the critical value of D for α=0.05 and μ=5 is 0.565).

8. Use mixed congruential method to generate a sequence of random numbers with X0 = 27, a = 17, m = 100 and c = 43. 

10.  Use the multiplicative congruential method to generate five three digit random integers. X₀=118, α=45 and m=1000.

9. Use Multiplicative congruential method to generate a sequence of 10 three-digit random integers and corresponding random variables. Let X₀ = 5, a = 3 and c=2. 

11.  Use the mixed congruential method to generate a sequence of three two-digit random numbers with X₀=37, α=7, c=29 and m=100.

11.  Use the multiplicative congruential method to generate a sequence of four three-digit random numbers. Let X₀=118, α=4 and m=1000.

12.  Write a computer program in C that will generate four digit random numbers using the multiplicative congruential method. Allow the user to input values of X₀, a, c and m. 

12.  Write a computer program that will generate three digit random numbers using the linear congruential method. Allow the user to input values of X₀, a, c and m.

12.  Write a computer program in C that will generate four digit random numbers using the multiplicative congruential method. Allow the user to input values of X₀, a, c and m. 

10. Explain generation of non uniform random number generation using inverse method.

4.  Verification is concerned with building the “model right” and validation is concerned with building the “right model”. Justify it with suitable reasons.

6.  Describe the process of model building, verification, and validation in brief.

8.  What do you mean by calibration and validation of models?

8.  Describe the process of model building, verification and validation in detail.

8.  What do you mean by calibration and validation?

8.  Explain with example of calibration and validation of model.

8.  Describe the process of calibration and validation in detail.

8.  Describe the process of calibration and validation in detail with example.

8.  Describe the process of model building, verification and validation in detail with example.

7. Differentiate between validation and calibration. How can we perform validation of model?

9.  Why do we use verification and validation in simulation?

8. Explain the three step approach of validation of models in simulation

11.  Explain the iterative process of calibrating a model.

12.  Explain with example verification of simulation models.

1.  Why do we perform the analysis of simulation output? Explain how do you use simulation run statistics in the output analysis.                       [4+6]

5.  How do you use estimation method in the analysis of simulation output? Explain in brief.

7.  Define confidence interval. How do you use estimation method in simulation output analysis? Explain.

7.  Define confidence interval and I.I.D in output analysis. How do you use simulation run statistics in simulation output analysis? Explain.

9.  How do you eliminate the effect of transient and initial bias in simulation output?

9.  When is estimation method appropriate? Explain.

9.  Explain the replication of runs.

11.  Why do we need the analysis of simulation output? How do you use simulation run statistics in output analysis? Explain.

11.  Why do we need the analysis of simulation output? How do you use estimation method in output analysis? Explain.

10. Why Confidence interval is needed in the analysis of simulation output. How can we can we establish a confidence interval?

9. What do you understand by replication of runs. Why is it necessary?

13.  Write short note on:

a.       Replication of Runs

b.      Simulation tools

3.  Consider that a machine tool in a manufacturing shop is turning out parts at the rate of one every 5 minutes. As they are finished, the parts go to an inspector, who takes 4±3 minutes to examine each one and rejects 10% of the parts. Now, develop a block diagram and write the code for simulating the above problem using GPSS, and also explain the function of each block used in the block diagram in detail.      [3+3+4]

3.  Why is GPSS called transaction flow oriented language? A machine tool in a manufacturing shop is turning out parts at the rate of every 5 minutes. When they are finished, the parts are sent to an inspector, who takes 4±3 minutes to examine each one and rejects 15% of the parts. Draw and explain a block diagram and write a GPSS program to simulate using the concept of facility.

3.  Why is GPSS called transaction flow oriented language? A machine tool in a manufacturing shop is turning out parts at the rate of every 5 minutes. When they are finished, the parts are sent to an inspector, who takes 4±3 minutes to examine each one and rejects 20% of the parts. Draw and explain a block diagram for it and write a GPSS program to simulate using the concept of FACILITY.

6.  Explain any four program control statements that are used in GPSS.

9.  Draw and describe the different types of GPSS blocks that are used to gather statistics?

9.  Draw and describe different types of GPSS blocks that are used to deal with queues?

10.  Describe different types of statements, used in CSMP, with suitable examples.

10.  Explain the data and control statement in CSMP.

11.  What is absolute clock and relative clock time in GPSS? How do you update the clock time in simulation? Explain.

11.  What do you mean by simulation tool?

11. Create a GPSS model and program to simulate a barber shop for a day (9am to 4pm), where a costumer enters the Shop every 10 ± 2 minutes and a barber takes 13 ± 2 for a haircut.

12.  Explain GPSS with example.

12.  Write short note on:

a)      GPSS

b)      Server Utilization

13.  Define CSMP. Describe different types of statements in CSMP with example.

11. Parts are being made at the rate of one every 10 minutes. They are of two types, A and B. And are mixed randomly with about 10% being type B. A separate inspector is assigned to examine each part. Inspection of part A takes 6±2 minutes while B takes 10±2 minutes. Both inspector rejects 10% of parts they inspect. Draw GPSS block diagram to simulate the the above problem for 100 parts.