Q$-2$: $[52]$

Answer the following question:

a$.$ Customers arrive at a shop with one counter at a rate of $30$ per hour. It takes about $3$ minutes to serve a customer. What is the inter$-$arrivai time for customer? Do you expect the queue to grow? Explain.

b$.$ If customers arrive at the rate of one every $15$ seconds, how many customer do you expect in two hours? Explain.

c$.$ If a server can serve $50$ clients per hour, what inter$-$arrival time is needed to ensure a queue dose not form? Explain.

$50$ clients $\frac{?}{?}$ hour $(1$ hour $60$min clients $\frac{?}{\text{m}\text{i}\text{n}}$ Inter$-$arrival time $=\frac{1}{0\mathrm{.}83333}=1\mathrm{.}2$min

d$.$ Describe the $\frac{M}{G}\frac{?}{?}\frac{4}{?}$ co queueing model.

e$.$ A shoebox company knows that the average arrival rate of boxes into the warehouse is $1,000$ shoeboxes$/$year$,$ and that the average time they spend in the warehouse is about $3$ months. What is the average number of shoeboxes in the warehouse? Explain.