Section A$.($Each question is $10$ points$)$

Q$1.$ Deserthe the following terms used in simulation:

a$)$ Event Driven Simulation

b$)$ Replication Technique

c$)$ Imminent Event

d$)$ Steady State

c$)$ Random Number streams

Q$2.$ Describe when you would use Finite Horizon and Infinite Horizon simulation approaches as

applied to dynamic systems.

Q$3.$ Describe when simulation is the appropriate tool in analysing systems or their performance

Q$4.$ State the Central Limir Theorem and indicate why it is important in simulation output analyais.

Q$5.$ What are the main desimble properties of random numbers. Discuss with reference to a

uniformly distributed random variable. State the pdf and edf of a random variable $x$ uniformly

disuributed on she interval $a,b.$

Q$6.$ Deseribe the types of simulation software used in developing simulation models. Give

examples of each.

Q$7.$ Prove that mean waiting time in an $\frac{M}{M}\frac{?}{?}$ queue for customers is:

$W=T_{4q}=\frac{}{(-)}$

$$ : utilization factor. $$ : mean service rate $($curomers $/$ second$).$

$$ : mean arrival rate $($cusomers $/$ second$)$

Section B$.($Each question is $20$ points$)$

Q$8.$ A smali post$-$office has carried out statistical measurements of its customer inter$-$arrival and

service times on a particular day and has recorded them in a table. Below is a list from that table

for the first $8$ customers that have entered and exited the system. $($a$)$ Fill up the table. $($b$)$ draw

the step diagram for the number of customers in the system vs time, and $($c$)$ calculate the

following values assuming that the system can be modelled as an $\frac{M}{M}\frac{?}{1}$ queuing system

$($Hint $1^{In}$ customer iat is from $t=0$ when measurement was started$)$:

Mean service time $($T$,)$

Mean number in the system

Mean service rate

Mean time in the system $($mean response

Utilization factor

time$)$

Probability of finding the server idle

Mean time spent by a customer in the queue.

Mean number in the queue

thatem