on average 2 customers per hour use the public telephone in the sheriff\'s deten

Question

on average 2 customers per hour use the public telephone in the sheriff's detention area, and this use has a Poisson distribution. The length of the phone call follows exponential distribution with a mean of 6 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone. What is the arrival rate that justifies a second telephone booth?

Question 3 options:

a)

none of the answers

b)

4 per hour

c)

2.5 per hour

d)

3.33 per hour

e)

8 per hour

a)

none of the answers

b)

4 per hour

c)

2.5 per hour

d)

3.33 per hour

e)

8 per hour

Explanation / Answer

Arrival rate (A) = 2 per hour

Service rate (S) = 6 min or 60/6 = 10 per hour

Lq = A/(S*(S-A))

For Lq = 3/60 hour and S = 10,

3/60 = A/(10*(10-A))

0.5*(10-A) = A

3A = 10

A = 3.33 per hour

Ans D

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