Question

Problem 11-17 (Algorithmic)

The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of 6 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 8 boats per hour. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously.

Note: Use P₀ values from Table 11.4 to answer the questions below.

1. What is the probability that the boat dock will be idle? Round your answer to four decimal places.
   
   P₀ = ________
   
2. What is the average number of boats that will be waiting for service? Round your answer to four decimal places.
   
   L_q = ________
   
3. What is the average time a boat will spend waiting for service? Round your answer to four decimal places.
   
   W_q = _______ hours
   
4. What is the average time a boat will spend at the dock? Round your answer to four decimal places.
   
   W = _______ hours
   
5. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing?
   
   Yes
   
   Why or why not? Round your answers to whole numbers.
   
   Because the average wait time is _____ seconds. Each channel is idle _____ % of the time.

Answer 1

Answers are in BOLD

	Lamda = arrival rate =		6.0	per hour
	Mu = mean service rate = 60/serving time		8.0	per hour
	Serving time= 1/Mu=		0.125	hours
	Utilization = rho = lamda / mu =		0.7500
Answer b:	Average no. in queue:
	Average no queue =Lq = (rho)2 / (1-rho)
	Average no of customers waiting in line =Lq =		2.2500	customers
Answer c:	Average time spent in queue:
	Wq = waiting time in the line for service = Lq / lambda =		0.3750	hours
Answer d:	Average time spent in the system:
	W = average time in the system = Wq + serving time =		0.5000	hours
Answer a:	Probability of zero customers in system:
	P (0)= 1-rho		0.2500

Note: Chegg's guidelines mandate to solve one question or 1^st four subparts of a question at a time. Please post again for remaining questions.