BE Computer Engineering (Pokhara University) Simulation and Modeling (PU, CMP 338) Question Paper 2079

(a) Define a system and explain the difference between the system environment and the system entities, illustrating your answer with a suitable example such as a bank or a manufacturing shop. (6)

(b) Models used in a simulation study can be classified as physical vs. mathematical, static vs. dynamic, deterministic vs. stochastic and discrete vs. continuous. With one concrete example for each pair, explain these classifications and state which class of model a discrete-event simulation belongs to. (8)

A single-server queuing system (M/M/1) is to be analysed by hand simulation. The following inter-arrival times and service times (in minutes) are given for the first 8 customers:

(a) Construct a simulation table showing arrival time, service-begin time, waiting time, service-end time and time the customer spends in the system for each customer. (8)

(b) From your table, compute the average waiting time per customer, the probability that a customer has to wait, the average service time, and the server utilization. (6)

(a) Describe the linear congruential method for generating pseudo-random numbers and state the conditions (Hull–Dobell theorem) under which a mixed congruential generator achieves the maximum (full) period. (6)

(b) Using the multiplicative congruential generator $X_{i+1} = (5 X_i)\bmod 16$ with seed $X_0 = 3$, generate the first six random integers and the corresponding uniform $(0,1)$ random numbers. Comment on the period obtained and why it is not full. (6)

(a) State and prove the inverse-transform technique for generating a random variate from a continuous distribution with cumulative distribution function $F(x)$. (5)

(b) Using the inverse-transform method, derive the formula for generating an exponential random variate with rate $\lambda$. Given $\lambda = 0.5$ and a random number $R = 0.35$, compute the corresponding variate. (5)

Explain the steps in a sound simulation study, from problem formulation to documentation and implementation, using a flow diagram. At which step are verification and validation carried out?

Describe the Monte Carlo method. Using it, set up the procedure to estimate the value of $\pi$ by simulating random points in a unit square, and state how the accuracy of the estimate depends on the number of samples.

For an M/M/1 queue with arrival rate $\lambda = 8$ customers/hour and service rate $\mu = 10$ customers/hour, compute: (a) the server utilization $\rho$, (b) the expected number of customers in the system $L$, and (c) the expected waiting time in the queue $W_q$.

Distinguish between verification and validation of a simulation model. List any four techniques that can be used to increase the validity and credibility of a model.

Explain why generated random numbers must be tested. Describe the Kolmogorov–Smirnov test for uniformity and state how the test statistic is compared with the critical value to accept or reject the hypothesis.

Differentiate between terminating (transient) and steady-state (non-terminating) simulations with an example of each. Explain why the replication–deletion approach and a warm-up period are needed when analysing steady-state output.

Define the following terms used in discrete-event simulation: (a) event, (b) event notice, (c) future event list (FEL), (d) system state, and (e) activity. Briefly explain how the simulation clock advances in the event-scheduling approach.

The average customer delay obtained from 5 independent replications of a queuing simulation is 4.2, 5.1, 3.8, 4.6 and 4.9 minutes. Construct a 95% confidence interval for the mean delay (use $t_{0.025,4} = 2.776$).