A coffee shop operates between 7 am and 7 pm every day. The customers who are on their way to work in the morning arrive at the coffee shop at a steadily increasing rate that starts with an initial rate of 3 customers per hour at 7 am and reaches a maximum of 15 customers per hour at 9 am. Then, the arrival rate remains constant at 15 customers per hour from 9 am to 1 pm. From 1 pm to 3 pm, after lunch, the rate steadily increases and reaches a rate of 21 customers per hour at 3 pm. For the rest of the operation hours, from 3 pm to 7 pm, the arrival rate drops steadily and the arrival rate is 5 customers per hour at 7 pm. Assume that the numbers of customers arriving at the coffee shop during disjoint time periods are independent.

a. What is a good probability model for the coffee shop arrival process? Define the arrival rate for this process as a function of time.