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.

Answer 1

Here, we are given the mean arrival rate and mean service rate as:

$\lambda = 9, \mu =10$

a) The average number of ferries in the system is computed as:

$L = \frac{\lambda}{\mu - \lambda} = \frac{9}{10-9} =9$

b) The average time spent in the system is computed as:

$W = \frac{1}{\mu -\lambda} = \frac{1}{10-9} = 1$

c) The average number of ferries in the queue waiting for turn is computed as:

$L_q = \frac{\lambda^2}{\mu (\mu - \lambda)} = \frac{9^2}{10(10-9)} = 8.1$

d) The average waiting time in the queue is computed as:

$W_q = \frac{\lambda}{\mu (\mu - \lambda) } = \frac{9}{10(10-9)} = 0.9$