Q$1$: Single Server System

A small coffee shop has a single server to take orders and serve customers. On average, customers arrive at the shop at a rate of $10$ customers per hour, following a Poisson distribution. The service time for each customer, including ordering and receiving their coffee, is distributed exponentially with an average service rate of $12$ customers per hour.

a$)$ Calculate the utilization $()$ of the server.

b$)$ Find the average number of customers in the system $($Ls$).$

c$)$ Determine the average time a customer spends in the system $($Ws$).$