Virginia\'s Ron McPherson Electronics Corporation retains a service crew to repa

Question

Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average =3 per 8-hour workday (appoximately Poisson in nature). The crew can service an average of u=8 machines per workday, with a repair time distribution that resembles the exponential distribution.

a) What is the utilization rate of this service system?

b) what is the average downtime for a broken machine?

c) How many machines are waiting to be srviced at any given time?

d) What is the probability that more than 1 machine is in the system? The probability that more than 2 are broken and waiting to be repaired or being serviced? More than 3? More than 4?

Please list the step by step process, thank you.

Explanation / Answer

a)

lambda = 3

mu = 8

Utilization rate = 3/8

=37.5%

b) average down time = 1/(8-3)

= 0.2 hours or 12 minutes

c) Machines waiting to be serviced at any given time = 3/(8-3)

= 1 (approx.)

d) probability that more than 1 machine in the system = probability that server is busy and all are in line - probability of exactly 1 customers in queue

= .375-.234

= 0.14

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