Trucks arrive at a retail store that has two docks at the rate of $16$ per hour. Arriving trucks join a line and then proceed to the first available empty dock. The loading and unloading 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?

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

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

d$)$ What is the average number of trucks waiting?

e$)$ What is the average number of trucks in waiting and service?

Question Answer Formula used and calculations

a$)$

$3\mathrm{.}75$ mins

$1/16=\mathrm{.}0625$

$60*\mathrm{.}0625=3\mathrm{.}75$ mins

b$)$

$67\%$

Service rate $=2/5=\mathrm{.}4$

Arrival rate $=16/60=\mathrm{.}2666$

$\mathrm{.}2666/\mathrm{.}4=\mathrm{.}6666$

c$)$

d$)$

e$)$