Question: Queueing problem. DN is a canoe & kayak rental service in L.A. Families can rent a family size canoe for $30 per hour for a

Queueing problem.

DN is a canoe & kayak rental service in L.A. Families can rent a family size canoe for $30 per hour for a timespan of two hours. This time is assumed to be constant and families must return within this time of two hours to avoid late penalties.

The rental service owns (and rents out) 16 family size canoes.

Based on historical data, the rental service has indicated that families arrive with an average inter-arrival time of 10 minutes with a standard deviation of 20 minutes. Currently, the rental service has one single line for families.

Q1.What is the coefficient of variation (CV) of the inter-arrival times?

Q2.Can we model the family size canoe queueing system of the canoe & kayak rental service as an M/D/20 queue?

Q3.What is the average number of families waiting in the queue (queue length)?

Q4.On average, how long does each family spend in the queue waiting for a family size canoe (in minutes)? Please keep two decimal places.

Q5.Next, assume the trip durations follow an exponential distribution with an average trip duration of 2 hours. What is the average time a family spends in the queue waiting for a family size canoe in this case (in minutes)? Please keep two decimal places.

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