1. Customers arrive randomly at the “Snips, Snails, & Puppy Dog Tails” pet care shop, which operates in a manner consistent with the Model A queuing formulas. The average customer arrival rate is 10 per hour (? = 10). When the shop is busy, it can serve an average of 12 customers per hour (? = 12). For each of the following, state the name of the proper formula (Ls, Wq, etc.), and find the answer to 3 decimal placesshowing work:
a. Average length of time in minutes that a customer waits until it is his or her turn.
b. Average length of time in minutes that a customer spends in the shop (waiting and being served).
c. Average number of customers waiting for service, not counting the customer currently being served if any.
d. Average number of customers in the shop, counting the customer currently being served if any.
e. Average percentage of the day that the shop has no customers.
f. (Bonus: +1) The shop has just three parking places for customers. When they are filled, customers have to park at parking meters on the street. If each customer comes in a separate vehicle, what percentage of the day does at least one customer have to park on the street?
Use the Model A formulas, and be careful about identifying which formula to use for each part.
Answer questions that require minutes by first calculating the answer in hours, then converting.
2. A bank with one teller has customers arrive randomly an average of 15 minutes apart. The teller can serve a customer in an average of 12 minutes, exponentially distributed. Find the exact values for the following per hour showing work:
a. ? (Lambda: arrival rate)
b. ? (Mu: service rate)
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