BE Computer Engineering (Pokhara University) Simulation and Modeling (PU, CMP 338) Question Paper 2078

(a) Define a system and explain the difference between the state of a system, an entity, an attribute, an activity and an event with suitable examples drawn from a bank teller service. (7)

(b) Classify models on the basis of (i) static vs. dynamic, (ii) deterministic vs. stochastic and (iii) continuous vs. discrete. Where does a Monte Carlo model and where does a discrete-event simulation model fall in this classification? (5)

(c) List any three situations where simulation is the appropriate tool and two situations where simulation should not be used. (3)

A single-channel queuing system (single server, FIFO) receives customers whose inter-arrival times and service times (in minutes) are to be hand-simulated.

Inter-arrival times: 0, 2, 4, 1, 2, 6, 1, 3, 2, 1

Service times: 2, 1, 3, 2, 1, 4, 2, 5, 1, 3

(a) Construct the simulation table showing clock time of arrival, service-begin time, service-end time, waiting time in queue and time the server is idle for all 10 customers. (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. (5)

(c) Explain how the event-scheduling / time-advance algorithm advances the simulation clock in a discrete-event simulation, and contrast it with the fixed-increment time-advance approach. (3)

(a) Using the linear congruential method with multiplier a = 17, increment c = 43, modulus m = 100 and seed X₀ = 27, generate the first five random numbers and the corresponding U(0,1) values. Comment on the achievable period of this generator. (6)

(b) State the conditions (Hull–Dobell theorem) under which a linear congruential generator achieves the maximum period m. (4)

(c) Derive the inverse-transform algorithm for generating a random variate from an exponential distribution with mean 1/λ, and use U = 0.25 to generate one exponential variate for λ = 0.5. (5)

(a) Distinguish clearly between verification and validation of a simulation model. Describe any four techniques used to verify a simulation program. (7)

(b) What is meant by the transient (warm-up) period in a steady-state simulation, and why must it be handled before output analysis? Briefly describe Welch's method for determining the warm-up length. (4)

(c) Explain the difference between terminating and non-terminating (steady-state) simulations with one example of each. (3)

For an M/M/1 queue with arrival rate λ = 8 customers/hour and service rate μ = 10 customers/hour, compute (i) the server utilization ρ, (ii) the average number of customers in the system L, (iii) the average time a customer spends in the system W, and (iv) the average number waiting in the queue Lq.

Explain any two statistical tests used to test random numbers for uniformity and independence. Briefly describe how the chi-square frequency test and the runs (runs up and down) test are carried out, stating the null hypothesis in each case.

(a) Describe the acceptance-rejection technique for generating random variates and state when it is preferred over the inverse-transform method. (4)

(b) Outline how the convolution method can be used to generate an Erlang variate. (2)

Differentiate between continuous simulation and discrete-event simulation, and explain with a labelled diagram the components of a discrete-event simulation model (system state, clock, event list, statistical counters).

(a) What is a confidence interval for the mean response of a simulation, and how is it constructed from the replications of a terminating simulation? (4)

(b) Explain the method of replication for estimating the variance of the sample mean. (2)

Describe the steps in a sound simulation study (from problem formulation to documentation and implementation) using a flowchart. Indicate where verification and validation fit in the cycle.

State Little's law and explain the physical meaning of each term. Use it to find the average time in system for a stable queue in which L = 4 customers and the mean arrival rate is λ = 2 customers per minute. List the assumptions under which Little's law holds.

Write short notes on any two of the following:

(a) Generating a discrete empirical (table-lookup) random variate.

(b) Poisson process and its relation to the exponential distribution.

(c) Pseudo-random numbers and the desirable properties of a good random number generator.