QUESTION $2$: $(25$ MARKS$)$

KFC Drive$-$through services allows customers to purchase their products without

leaving their cars. KFC outtet at Jumbo$-$Phoenix has only one Drive$-$through counter.

Customers arrive at the counter in their cars at random from $1$ to $6$ minutes apar

Each possible value of inter$-$arrival time has probability of occurrence as shown in

Table $1.$

Table $1$: Distribution of time between arrivals

The service time vary from $1$ to $5$ minutes with the probabilities shown in Table $2.$

Table $3$: Time$-$Between$-$Arrivals Determination

$(5$ marks$)$

$($ii$)$

Copy and complete the simulation Table $4$ to analyze the system.

Table $4$: Service$-$Times Generated

$(5$ marks$)$

$($iii$)$ Copy and complete the simulation Table $5$ for the single$-$channel

A: customer number

B: time since last arriva

C: arrival time

$D$ : service time $($minutes$)$

E: time service begins

F: time customer waits in queve

$G$ : time service ends

H: time customer spends in system $($minutes$)$

l: idle time of counter

$(10$ marks$)$

$($b$)$

Hence, compute the following statistics:

$($i$)$ The average waiting time for a customer.

$($ii$)$ The probability that a customer has to wait in the queue.

$($iii$)$ The fraction of idle time of the counter.

$($iv$)$ The average service time.

$($v$)$ The average time a customer spends in the system.

$(1+1+1+1+1=5$ marks $)$