Question $1$: Trucks arrive at a retail store that has one dock at the rate of $8$ per hour. The loading and unloading at the dock takes on an average $5$ minutes with a standard deviation of $6$ minutes. Assume that the coefficient of variation of inter$-$arrival time is $1.$

a$)$ What is the average interarrival time $($in minutes$)$ of trucks $($a$)?$

b$)$ What is the utilization of the dock $($u$)?$

c$)$ What is the average wait time of the trucks $($Tq$)?$

d$)$ What is the total wait time of trucks $($Tq $+$ p$)?$ Question $2$: This question builds on Question $1$ to investigate the effect of reduced variability in the service time.

Trucks arrive at a retail store that has one dock at the rate of $8$ per hour. Assume that coefficient of variation of inter$-$arrival time is $1.$ If the standard deviation of loading and unloading time is reduced from $6$ minutes $($in Question $1)$ to $3$ minutes, what is the impact of this on the

a$)$ average wait time of trucks and

b$)$ the average number of trucks in waiting?

Question Answer

Impact on the average wait time. Please choose one and explain. Answer: Up$,$ Down, or No Change $($Choose one$)$

Show your work:

b$)$ Impact on the number of trucks waiting. Please choose one and explain. Answer: Up$,$ Down, or No Change $($Choose one$)$

Show your work: