Question

The photo booth at the Apple County fair takes snapshots in exactly 90 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 25 per hour. Using this information, determine the following:

a.	the average number of customers waiting to use the photo machine
b.	the average time a customer spends in the system
c.	the probability an arriving customer must wait for service.

Answer 1

Answer:

Given,

Arrival rate = 25 per hour

Service rate = 3600/90 = 40 per hour

a)

Average number of customers waiting to use the photo machine Lq = ^2/(-)

substitute values

= 25^2 / (40(40 - 25))

= 1.042

b)

average time a customer spends in the system W = 1/(-)

= 1 /(40-25)

= 1/15

= 0.0667 *60

= 4 min

c)

probability an arriving customer must wait for service = /

= 25/40

= 0.625

= 62.5%