Unit 1: Introduction to Simulation
1. Difference between static physical and dynamic physical models.
Solutoin
2. Describe different phases of simulation study with help of flowchart.
Solution
Phases of Simulation Study
A simulation study is carried out in four main phases consisting of several steps.
1. Phase I: Problem Formulation (Discovery Phase)
Define the problem clearly
Set objectives and project plan
Decide whether simulation is appropriate
2. Phase II: Model Building and Data Collection
Model conceptualization (abstract system)
Data collection
Model translation (coding)
Verification (check correctness of program)
Validation (check model with real system)
3. Phase III: Running the Model
Experimental design
Production runs
Output analysis
More runs if required
4. Phase IV: Implementation
Documentation and reporting
Implementation of results
3. What are the application areas of simulation?
Solution
Simulation is the process of designing a model of a real system and conducting experiments with it for the purpose of analysis, design, optimization, and training.
Application Areas of Simulation
Industrial and Business: Used for manufacturing system design, inventory control, supply chain management, and business decision-making.
Healthcare: Used for hospital management, patient flow analysis, medical facility planning, and disease/epidemic modeling.
Transportation: Used for traffic control, road network design, railway/airline scheduling, and airport logistics planning.
Engineering: Used in civil engineering for bridge, building, and earthquake simulation, as well as system design and performance testing.
Computer and Communication Systems: Used for network design, performance evaluation, operating system testing, and internet communication systems.
Military and Defense: Used for war strategy simulation, mission planning, operator training, and weapon system testing.
Environmental: Used for pollution control analysis, waste management systems, and environmental impact studies.
Training and Education: Used in flight simulators, operator training systems, and virtual learning environments to train personnel safely.
Scientific Research: Used for biological system modeling, population studies, physics simulations, and queuing system analysis.
4. What is a system modeling? What are the steps involved in system modeling.
Solution
System Modeling
System modeling is the process of creating a simplified representation of a real-world system to understand its behavior and predict its performance under different conditions.
Steps Involved in System Modeling
1. Phase I: Problem Formulation (Discovery Phase)
Define the problem clearly
Set objectives and project plan
Decide whether simulation is appropriate
2. Phase II: Model Building and Data Collection
Model conceptualization (abstract system)
Data collection
Model translation (coding)
Verification (check correctness of program)
Validation (check model with real system)
3. Phase III: Running the Model
Experimental design
Production runs
Output analysis
More runs if required
4. Phase IV: Implementation
Documentation and reporting
Implementation of results
5. Why model of a system is built? What is static model? Differentiate between static and dynamic mathematical models in simulation.
solution
A model of a system is built to study and analyze a system without using the real system.
Reasons:
To analyze systems before implementation and reduce design errors
To save cost and time compared to real experimentation
To study systems that are complex or not directly observable
To predict the effect of changes without disturbing the real system
To provide training environments (e.g., simulators)
To understand relationships between system components
Static Model
A static model is a model that represents a system at a particular point in time and does not consider changes over time.
Features:
Time-independent
Shows system in equilibrium/state
Simple and less flexible
Does not show system behavior over time
Example:
Architectural model of a building
Snapshot of a market at a fixed price
6. Differentiate between discrete and continuous system.
Solution
7. Discuss the merits and demerits of system simulation.
Solution
Merits (Advantages)
Allows safe experimentation without affecting real system
Saves cost and time in system design and testing
Helps in understanding complex systems
Useful for “what-if” analysis
Can identify bottlenecks and inefficiencies
Time can be compressed or expanded
Suitable for dangerous or real-time systems
Helps in decision making and planning
Demerits (Disadvantages)
Requires skilled personnel and training
Model building is time-consuming and costly
Results may be difficult to interpret
Output may be affected by randomness
Models may not be accurate representations
Not suitable when analytical solution is easier
Requires large amount of data
8. What do you understand by static mathematical model? Explain with example. Differentiate between stochastic and deterministic activities.
Solution
A static mathematical model is a model that represents a system using mathematical equations at a specific point in time, without considering any changes over time.
It is time-independent (no past or future behavior).
Describes the system in a state of equilibrium.
Does not show how variables change, only their final relationship.
Focuses on structure rather than behavior.
9. Describe the phases in simulation.
Solution
Phases in Simulation
The simulation process is divided into four main phases:
1. Phase I: Problem Formulation (Discovery Phase)
Define the problem clearly
Set objectives and project plan
Decide whether simulation is appropriate
2. Phase II: Model Building and Data Collection
Model conceptualization (abstract system)
Data collection
Model translation (coding)
Verification (check correctness of program)
Validation (check model with real system)
3. Phase III: Running the Model
Experimental design
Production runs
Output analysis
More runs if required
4. Phase IV: Implementation
Documentation and reporting
Implementation of results
Conclusion
Simulation is an iterative process, meaning steps may be repeated until satisfactory results are obtained.
10. Write short notes on:
a. System and its environment
System:
A system is a collection of interrelated components that work together to achieve a common objective.
Components of a System:
Entities: Objects of interest in the system
Attributes: Properties of entities
Activities: Processes that cause changes in the system
State of System:
The state is the condition of the system at a specific time, described by its variables.
b. System Environment
The system environment consists of all external factors that affect the system but are not part of it.
A boundary separates the system from its environment
The environment influences system behavior
Types of Activities:
Endogenous: Occur inside the system
Exogenous: Occur outside but affect the system
Types of Systems:
Open System: Interacts with environment
Closed System: No interaction (rare in real life)
Unit 2: Simulation of Continuous and Discrete System
1. What is analog computer? Explain with suitable example.
Solution
Analog Computer
An analog computer is a computing device that uses continuous physical quantities (such as voltage, current, or mechanical motion) to represent and solve mathematical problems.
-Works with continuous data
-Used to solve differential equations
-Provides approximate results
-Faster for real-time simulation of physical systems
Example: Electrical Circuit Analogy
An electrical circuit can be used to simulate a mechanical system.
Components like:
Resistance (R) → represents damping
Inductance (L) → represents mass
Capacitance (C) → represents elasticity
By adjusting these components, the behavior of a real system can be studied.
2. Differentiate between analog and digital computer.
Solution
3. Why accuracy of analog computer is low? Explain analog computer with suitable example.
Solution
Analog Computer:-
An analog computer is a computing device that uses continuous physical quantities (such as voltage, current, or mechanical motion) to represent and solve mathematical problems.
Accuracy of Analog Computer is Low:
Limited Precision in Measurement:
Physical quantities like voltage cannot be measured exactly, leading to errors.
Noise and Disturbances:
Electrical noise affects signals and reduces accuracy.
Component Imperfections:
Devices like resistors and capacitors have tolerances and are not ideal.
Approximate Nature:
Analog computers give approximate results, not exact values.
Example: Electrical Circuit Analogy
An electrical circuit can be used to simulate a mechanical system.
Components like:
Resistance (R) → represents damping
Inductance (L) → represents mass
Capacitance (C) → represents elasticity
By adjusting these components, the behavior of a real system can be studied.
4. Explain Monte Carlo simulation.
Solution
Monte Carlo Simulation:
Monte Carlo simulation is a technique that uses random numbers and repeated sampling to simulate and analyze the behavior of a system with uncertainty.
It is based on probability and randomness
Used when systems are too complex for analytical solutions
Produces approximate results through multiple trials
Steps in Monte Carlo Simulation:
Define the problem and model
Identify probability distributions of input variables
Generate random numbers
Perform simulation trials
Analyze the results
Example:
Suppose we want to estimate the probability of getting heads in coin tosses.
We simulate many random coin tosses using random numbers.
By repeating this many times, we estimate the probability.
5. Explain the concept of discrete event simulation. Explain poisson’s arrival pattern.
Solution
Discrete Event Simulation:
Discrete Event Simulation (DES) is a simulation technique in which the state of a system changes only at specific discrete points in time due to the occurrence of events.
State changes occur only at event times
Between events, the system state remains constant
Events include arrival, departure, service completion, etc.
Widely used in systems like banks, queues, networks
Example:
In a bank system, the number of customers changes only when:
A customer arrives
A customer leaves after service
Poisson Arrival Pattern:
A Poisson arrival pattern describes a process where arrivals occur randomly and independently over time.
Key Characteristics:
Arrivals occur one at a time
Arrivals are independent
Average arrival rate (λ) is constant
Used to model random events like customer arrivals
6. Write short notes on:
a. Feedback system
b. Non-Stationary Poisson process
c. Digital analog simulator
a. Feedback System
A feedback system is a system in which the output is fed back into the input to control or regulate the system.
Types:
Positive Feedback: Enhances or increases output
Negative Feedback: Reduces or stabilizes output
Example:
Thermostat in AC: maintains room temperature by using feedback
b. Non-Stationary Poisson Process
A Non-Stationary Poisson Process is a process in which the arrival rate (λ) changes over time.
Key Points:
Arrival rate is not constant
Depends on time (rush hours, peak periods, etc.)
Violates stationary increment property
Used in systems with varying traffic like networks or customer flow
c. Digital Analog Simulator
A digital-analog simulator is a digital system or software that simulates the behavior of an analog computer to solve continuous mathematical problems.
Key Features:
Uses digital computers to simulate continuous systems
Performs operations like integration, addition, and differentiation
More accurate and flexible than physical analog computers
Example:
Simulation of a mechanical or electrical system using software like simulation tools (e.g., MATLAB/Simulink)
Unit 3: Queuing System
1.Write short notes:
Queuing discipline
Random variate
Queuing Discipline:
Queuing discipline is the rule used to decide the order of serving customers/jobs in a queue.
It determines which task is processed first in a waiting line.
It is important for system performance and fairness.
FCFS (First Come First Served): Jobs are served in the order of arrival.
LCFS (Last Come First Served): The most recent job is served first.
Priority Scheduling: Jobs are served based on priority level.
Round Robin: Each job gets a fixed time slice in rotation.
Shortest Job First (SJF): Job with the smallest execution time is served first.
Example: In a bank, customers are usually served using FCFS discipline.
Conclusion: Queuing discipline ensures efficient and fair processing of tasks in a system.
Random Variate
A random variate is a numerical value generated from a probability distribution.
It represents the outcome of a random process.
It is widely used in simulation and modeling.
It can be discrete (e.g., number of customers).
It can be continuous (e.g., time between arrivals).
Generated using random number generators and transformation methods.
Common distributions: Uniform, Normal, Exponential, Poisson.
Example: Generating inter-arrival time of customers using an exponential distribution.
Conclusion: Random variates help in simulating real-world randomness in systems.
2.Define traffic intensity and server utilization. Write down the Kendall’s notation for a queuing system with an example.
Solution
Traffic Intensity:
Traffic intensity is the measure of load on a queuing system.
It is the ratio of arrival rate to service capacity.
It indicates how busy the system is.
Represented as ρ (rho).
Formula: ρ = λ / (μ × s)
, where λ = arrival rate, μ = service rate, s = number of servers.
If ρ < 1, system is stable.
If ρ ≥ 1, system becomes overloaded and queues grow.
Example: If λ = 4 customers/min, μ = 5 customers/min, s = 1 → ρ = 0.8.
Conclusion: Traffic intensity shows system load and stability condition.
Server Utilization:
Server utilization is the fraction of time a server is busy serving customers.
It reflects the efficiency of server usage.
It is closely related to traffic intensity.
Represented as ρ (rho) in single-server systems.
Value ranges from 0 to 1.
High utilization means server is busy most of the time.
Low utilization means server is idle often.
Example: If server is busy 80% of the time, utilization = 0.8.
Conclusion: Server utilization indicates how effectively resources are used.
Kendall’s Notation:
Kendall’s notation is a standard format to describe a queuing system.
It represents arrival, service, and system characteristics.
General form: A / B / s : (N / D)
A: Arrival distribution (e.g., M = Markovian/Poisson).
B: Service time distribution (e.g., M = Markovian,exponential).
s: Number of servers.
N: Population size .
D: Queue discipline.
Common symbols:
M: Markovian (Poisson/exponential)
D: Deterministic
G: General distribution
Example: M/M/1
Poisson arrivals, exponential service time, 1 server.
Conclusion: Kendall’s notation provides a compact way to describe queuing models.
3.What is a queuing system? Explain the elements of queuing system with example.
Solution
Queuing System
A queuing system is a model used to represent waiting lines in real-life systems.
It consists of customers, queue, and service mechanism.
It helps to analyze delays and system performance.
Used in banks, hospitals, networks, call centers.
Example: Customers waiting in a bank queue for service.
Conclusion: A queuing system models waiting situations to improve efficiency.
Elements of Queuing System are
Calling Population (Source):
Set of customers that arrive in the system.
Can be finite or infinite.
Example: People visiting a bank.
Arrival Process:
Describes how customers arrive over time.
Can follow Poisson distribution or other patterns.
Example: Customers arriving randomly at a counter.
Queue (Waiting Line):
Place where customers wait before service.
Can be single queue or multiple queues.
Example: Line in front of a ticket counter.
Service Mechanism:
Describes how service is provided.
Includes number of servers and service rate.
Example: One or more clerks serving customers.
Queuing Discipline:
Rule for serving customers.
Types: FCFS, Priority, SJF, Round Robin.
Example: Bank follows First Come First Served.
System Capacity:
Maximum number of customers the system can hold.
Can be limited or unlimited.
Example: Limited seats in a waiting room.
Conclusion: Elements of a queuing system define how customers arrive, wait, and get served, affecting overall performance.
3. What is the calling population? Explain the arrival and service process in a queue.
Solution
Calling Population:
Calling population is the source of customers that enter a queuing system.
It represents the total number of potential customers.
It affects the arrival pattern and system behavior.
Can be finite (limited customers).
Can be infinite (very large, practically unlimited).
Finite population affects arrival rate over time.
Infinite population assumes constant arrival rate.
Example:
Finite: Machines in a repair system.
Infinite: Customers arriving at a bank.
Conclusion: Calling population defines the source and size of incoming customers.
Arrival Process:
Arrival process describes how customers enter the queue.
It defines the arrival rate and pattern over time.
It is important for queue formation and waiting time.
Represented by arrival rate (λ).
Can follow Poisson distribution (random arrivals).
Inter-arrival time may be exponential.
Arrivals can be single or in batches.
Example: Customers arriving randomly at a service counter.
Service Process:
Service process describes how customers are served.
It defines the service rate and service time.
It impacts the speed of queue clearance.
Represented by service rate (μ).
Service time may follow exponential or deterministic distribution.
Can have single or multiple servers.
Service can be uniform or variable.
Example: A cashier serving customers at a fixed or variable rate.
Conclusion: Arrival and service processes determine queue length, waiting time, and system efficiency.
4. Explain basic characteristics of a Queueing System
Solution
A queuing system is defined by features that describe how customers arrive, wait, and are served.
These characteristics determine system behavior and performance.
They are essential for analyzing waiting time and efficiency.
The basic characteristics of a Queueing System:
Calling Population — The source of customers entering the system, which can be finite or infinite.
Arrival Process — The pattern of arrivals is defined by the arrival rate (λ) and a distribution such as Poisson.
Service Process — The manner in which service is provided, defined by service rate (μ) and service time distribution.
Number of Servers (Channels) — The number of service points available, either single-server or multi-server.
Queue Capacity — The maximum number of customers allowed in the system, either limited or unlimited.
Queuing Discipline — The rule used for serving customers, such as FCFS, Priority, SJF, or Round Robin.
System Structure — The arrangement of queues and servers, such as single queue-single server or single queue-multiple server.
5. Explain the Kendall’s notation for a queuing system? What are the various performance measures in a single-server queuing System? Explain which of them determines system stability and how?
Soluiton
Kendall’s Notation:
Kendall’s notation is a standard format to describe a queuing system.
It represents arrival, service, and system characteristics.
General form: A / B / s : (N / D)
A: Arrival distribution (e.g., M = Markovian/Poisson).
B: Service time distribution (e.g., M = Markovian,exponential).
s: Number of servers.
N: Population size .
D: Queue discipline.
Common symbols:
M: Markovian (Poisson/exponential)
D: Deterministic
G: General distribution
Example: M/M/1
Poisson arrivals, exponential service time, 1 server.
Conclusion: Kendall’s notation provides a compact way to describe queuing models.
Performance Measures in a Single-Server Queuing System:
Performance measures evaluate the efficiency and behavior of a queue.
They help in analyzing waiting time, queue length, and utilization.
Average Number of Customers in the System (L) — Total customers present in the system, including both those waiting and the one being served.
Average Number of Customers in the Queue (Lq) — Number of customers waiting in line, excluding the one currently being served.
Average Time Spent in the System (W) — Total time a customer spends from arrival to departure, including both waiting and service time.
Average Waiting Time in the Queue (Wq) — Time a customer spends only in the queue before service begins.
Server Utilization (ρ) — Proportion of time the server remains busy, calculated as ρ = λ/μ.
Throughput — Rate at which customers are successfully served and discharged from the system.
Stability Measure — System Utilization (ρ):
System Utilization (ρ) is the primary measure that determines whether a single-server queuing system is stable or not.
How it Determines Stability:
Stable System (ρ < 1) — When service rate (μ) exceeds arrival rate (λ), the server clears tasks faster than they arrive, the system reaches a steady state, and all measures like L and Lq remain finite.
Unstable System (ρ ≥ 1) — When arrival rate equals or exceeds service rate, the server cannot keep up, causing queue length (Lq) and waiting time (Wq) to grow infinitely.
Critical Point (ρ → 1) — As utilization approaches 100%, even minor fluctuations in arrivals create a permanent backlog that the server cannot eliminate, causing wait times to rise exponentially.
IN simple term
Stable System (ρ < 1) : Imagine a cashier at a shop who serves customers faster than they arrive. The line never gets too long because the cashier always has time to clear it. Everything runs smoothly.
Unstable System (ρ ≥ 1) : Now imagine more customers are arriving than the cashier can handle. The line keeps growing longer and longer with no end. The cashier can never catch up, so the queue becomes endless.
Critical Point (ρ → 1) : This is like the cashier being just barely keeping up. Even one extra customer arriving at the wrong moment creates a small pile-up, and since the cashier has zero free time, that pile-up never gets cleared — it just keeps building slowly
6. List down the applications of the queuing system?
Solution
Applications of Queuing System:
Banking Systems:- Used to manage customer waiting lines at counters and ATMs.
Hospital Management:- Applied to handle patient flow in OPD, emergency wards, and appointments.
Telecommunication Systems:- Used to manage call traffic and reduce network congestion.
Computer Systems:- Applied in CPU scheduling, process queues, and job management.
Transportation Systems:- Used for traffic control at toll booths, airports, and railway stations.
Customer Service Centers:- Applied to manage incoming calls and reduce waiting time in help desks.
Manufacturing Systems:- Used to handle production lines and schedule machine servicing.
Retail and Supermarkets:- Applied to manage billing counters and checkout queues efficiently.
7. Explain traffic intensity and server utilization.
Solution
Traffic Intensity:
Traffic intensity (ρ) is the measure of load on a queuing system.
It is the ratio of arrival rate to service rate.
It shows how busy the system is.
Formula: ρ = λ / μ (for single server)
If ρ < 1, system is stable.
If ρ ≥ 1, system is unstable.
Higher ρ means longer queues and delays.
Example: λ = 3, μ = 5 → ρ = 0.6 (stable system)
Conclusion: Traffic intensity determines system load and stability.
Server Utilization:
Server utilization is the fraction of time a server is busy.
It indicates efficiency of server usage.
In single-server systems, it is equal to traffic intensity (ρ).
Value ranges from 0 to 1.
High utilization → server is mostly busy.
Low utilization → server is often idle.
Helps in capacity planning.
Example: If server is busy 70% of the time → utilization = 0.7.
Conclusion: Server utilization shows how effectively the server is used.
8. Explain the arrival pattern and the service process.
Solution
Arrival Pattern:
Arrival pattern describes how customers arrive in the system.
It defines the timing and distribution of arrivals.
It affects queue formation.
Represented by arrival rate (λ).
Often follows Poisson distribution.
Inter-arrival time may be exponential.
Can be single or batch arrivals.
Example: Customers arriving randomly at a bank.
Service Process:
The service process describes how customers are served.
It defines the service time and service rate.
It affects waiting time and system performance.
Represented by service rate (μ).
Service time may follow an exponential or deterministic distribution.
Can have single or multiple servers.
Service may be uniform or variable.
Example: A cashier serving customers at a certain rate.
Conclusion: Arrival pattern and service process together determine queue behavior and efficiency.
Unit 4: Markov Chains
1. Explain a Markov chain with a suitable example. What are the different application areas of Markov chains?
Solution
Markov Chain:
A Markov Chain is a mathematical model describing a sequence of events where the probability of the next event depends only on the current state, not on how it got there.
This is called the "memoryless property."
Example — Weather Prediction:
Assume the weather has three states: Sunny, Cloudy, Rainy.
If Sunny today → 70% chance Sunny, 20% Cloudy, 10% Rainy tomorrow.
If Rainy today → 50% chance Rainy, 50% Cloudy tomorrow.
These probabilities are stored in a Transition Matrix, which allows us to predict weather several days ahead based only on today's condition — not last week's.
Application Areas of Markov Chain:
Search Engines (Google PageRank):— Models a random surfer clicking links; the probability of landing on a page determines its rank and importance.
Text Prediction & NLP:— Autocomplete on phones predicts the next word based only on the current word typed using frequency patterns.
Finance & Economics:— Models stock market trends (Bull/Bear/Stagnant) and estimates loan default risk based on a customer's current credit status.
Genetics & Biology:— Models DNA sequences where the next base pair depends on the current one, helping identify genes and predict protein structures.
Queueing Theory:— Calculates waiting times and service efficiency by modeling how customers arrive and move through a service system.
Example Numerical
Unit 5: Random Numbers
Unit 6: Verification and Validation
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Explain iterative process of calibrating a simulation model.
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Describe the process of model building, verification and validation in detail with example.
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What is three step approach for validation of simulation models?
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Define verification and validation. Explain the process of model verification in brief.
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Differentiate between validation and calibration. How can we perform validation of a model?
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Define the terms verification, calibration, validation and accreditation of models.
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“Building a model right” and “Building a right model”. Discuss the importance of V & V.
Unit 7: Analysis of Simulation Output
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Why is it necessary to analyze the simulation output? Explain different estimation methods used in simulation output analysis.
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Why confidence interval is needed in the analysis of simulation output? How can we establish a confidence interval?
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Explain different estimation methods used in simulation output analysis.
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What do you mean by replication of runs? Why it is necessary?
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Explain the importance of elimination of initial bias during simulation.
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Write short notes on:
a. Hypothesis testing
b. Simulation run statistics
Unit 8: Simulation of Computer Systems
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Develop GPSS block diagram and code for a manufacturing shop problem and explain blocks used.
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Why is GPSS called transaction flow oriented language?
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What is storage in GPSS? Describe the blocks associated to storage in GPSS.
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What is transaction in GPSS? Explain about facility in GPSS.
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Draw GPSS block diagram for barbershop system and run simulation.
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Represent the system in GPSS using facility and run simulation for given parts.
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Draw GPSS block diagram to simulate the inspection system for 100 parts.
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Draw GPSS block diagram to simulate supply store problem for 100 requisitions.
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Write short notes on:
a. Simulation tools