A ship yard with 1 Dry Dock to repair ferry ships, one phase repair, any ferry s

Question

A ship yard with 1 Dry Dock to repair ferry ships, one phase repair, any ferry ship can come in. One Queue Arrival rate of ferries: Poisson distribution, mean= 9 and STD = 1 Service rate: Constant, 10 First come first serve rule. Find the following:

a- Average number of ferries in the system (waiting and being served).

b- Average time a ferry spends in the system (waiting time plus service time).

c- Average number of the ferries waiting in the queue.

d- Average time a ferry spends waiting in the queue.

Explanation / Answer

The appropriate model choice for the Queue: M/D/1

L = arrival rate = 9 per hour
M = service rate = 10 hour

(a)

Average length of the queue = Lq = L2 / {2M*(M - L)} = 81 / (20*(10 - 9)) = 4.05

Average number of ferries in the system = Ls = Lq + (L / M) = 4.05 + 0.9 = 4.95

(b)

Average time a ferry spends in the system = Ws = Ls / L = 4.95 / 9 = 0.55 hours = 33 minutes

(c)

Average number of the ferries waiting in the queue = Lq = 4.05 (found in step-a already)

(d)

Average time a ferry spends waiting in the queue = Wq = Lq / L = 4.05 / 9 = 0.45 hours = 27 minutes

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