About this previous year paper
MODELING AND SIMULATION (NIT062)
SECTION – A
(Attempt All | 10 × 2 = 20 Marks)
(a) Actual system vs Simulation
An actual system is a real-world system that exists physically, whereas simulation is an abstract or mathematical representation of that system used to study its behavior without disturbing the real system.
(b) Purpose of Dynamic Modeling
Dynamic modeling is used to represent time-dependent behavior of systems where system variables change with time, such as population growth or inventory systems.
(c) Simulating gender of children using random numbers
Assume:
Random number 0–49 → Male
Random number 50–99 → Female
By generating random numbers, the gender of children can be simulated assuming equal probability.
(d) Why simulation is required?
Simulation is required when: Real system experimentation is costly or risky
Analytical solutions are not possible System is complex and stochastic
Time compression or expansion is needed
(e) Outcomes of Cobweb Model
Cobweb model outcomes include: Convergent oscillations
Divergent oscillations Continuous oscillations
Stable equilibrium
(f) Flow chart for next-event simulation
Main steps: Initialize system state
Advance simulation clock to next event Execute event
Update system state Schedule future events
Check termination condition (Drawn neatly in exam.)
(g) Stochastic simulation
Stochastic simulation involves random variables and probabilistic behavior.
Example: Queuing system with random arrivals and service times.
(h) Builder selling houses problem
As unsold houses decrease, selling rate decreases → negative feedback system.
This represents a dynamic simulation problem solved using differential equations or system dynamics.
(i) Advantages & disadvantages of simulation languages
Advantages: Faster model development
Built-in random generators Easy statistical analysis
Disadvantages: Limited flexibility
Requires learning specific syntax Higher execution time
(j) Important feature in project planning & control
Critical Path is the most important feature.
It is resolved using CPM (Critical Path Method) to identify minimum project duration.
SECTION – B
(Attempt Any Five | 5 × 10 = 50 Marks)
(a) Components of Discrete Event System Model Main components:
Entities: Customers, jobs Attributes: Properties of entities
Activities: Time-consuming operations Events: Instantaneous occurrences
State variables: Describe system state Queues: Waiting lines
Example: Bank queuing system.
(b) Classification of Models & Limitations
Classification: Physical vs Mathematical
Static vs Dynamic Deterministic vs Stochastic
Continuous vs Discrete
Limitations: Approximation of reality
Requires assumptions May ignore human behavior
(c) Fixed time-step vs Next-event model
| Fixed Time-Step | Next-Event |
|---|---|
| Time advances uniformly | Time jumps to next event |
| Simple but inefficient | Efficient & accurate |
| Suitable for continuous systems | Suitable for discrete systems |
(d) Monte Carlo Simulation & Area under sine curve
Steps: Define problem
Identify probability distribution Generate random numbers
Perform experiment Analyze results
Area under sin(x) from 0 to π: Exact value = 2
Monte Carlo estimates area by random sampling.
(e) Exponential growth & decay models
Growth:
dXdt=kX⇒X=X0ekt\frac{dX}{dt} = kX \Rightarrow X = X_0 e^{kt}dtdX=kX⇒X=X0ekt
Decay:
dXdt=−kX⇒X=X0e−kt\frac{dX}{dt} = -kX \Rightarrow X = X_0 e^{-kt}dtdX=−kX⇒X=X0e−kt
Examples: Population growth, radioactive decay.
(f) ATM machine simulation (Single-server queue) Arrivals → Poisson distribution
Service → Exponential distribution One server (ATM)
Performance measures: Average waiting time
Queue length Server utilization
(g) CPM for given activities
Steps: Draw network diagram
Forward pass → earliest times Backward pass → latest times
Identify critical path (zero slack) Critical path determines minimum project duration.
(h) Simulation languages & selection Examples: GPSS, SIMSCRIPT, SIMULA
Selection depends on: Type of system
Model complexity User expertise
Output & visualization needs
SECTION – C
(Attempt Any Two | 2 × 15 = 30 Marks)
(a) Casino dice fairness test
Observed data for 100 trials:
| Sixes | Observed | Expected (Binomial) |
|---|---|---|
| 0 | 48 | 57.9 |
| 1 | 35 | 34.7 |
| 2 | 15 | 6.9 |
| 3 | 3 | 0.5 |
Using Chi-square test, calculated χ² > critical value →
Conclusion: Dice are not fair.
(b) Pseudo random number generation
Methods: Linear Congruential Method
Xn+1=(aXn+c)mod mX_{n+1} = (aX_n + c) \mod mXn+1=(aXn+c)modm
Middle square method Properties:
Uniformity Independence
Long period
Simulation of Water Reservoir System
Steps: Identify inflow & outflow
Define storage capacity Use mass balance equation
Storaget+1=Storaget+Inflow−OutflowStorage_{t+1} = Storage_t + Inflow - OutflowStoraget+1=Storaget+Inflow−Outflow
Simulate over time Analyze overflow and shortage
Applications: dams, irrigation planning.
Bakery shop demand simulation
Demand distribution:
| Demand | Probability | RN Interval |
|---|---|---|
| 0 | 0.01 | 00 |
| 15 | 0.15 | 01–15 |
| 25 | 0.20 | 16–35 |
| 35 | 0.50 | 36–85 |
| 40 | 0.12 | 86–97 |
| 50 | 0.02 | 98–99 |
Random numbers:
21, 27, 47, 54, 60, 39, 43, 91, 25, 20
Simulated demand (10 days):
25, 25, 35, 35, 35, 35, 35, 40, 25, 25