Business at the Kwik-E-Mart is brisk, with one customer arriving at a rate of six per hour on average. Ringing up purchases is an easy matter for owner/operator Apu; he can usually do so in 2 minutes. If both arrival and service rates are Poisson distributed, how many customers are in the store on average?
A)0.05
B)0.16
C)0.25
D)0.50

Question

Quizplus · Accepted Answer

First, we need to calculate the arrival rate (λ) and service rate (µ):
λ = 6 customers per hour
µ = 30 customers per hour (since 2 minutes = 1/30 hour)
Next, we need to calculate the utilization factor (ρ = λ/µ):
ρ = 6/30 = 0.2
If ρ is less than 1, we can use Little's Law to calculate the average number of customers in the store (L):
L = λ/(µ-λ) = 6/(30-6) = 0.25
Therefore, on average, there are 0.25 customers in the store at any given time. The best choice is C.

Business at the Kwik-E-Mart Is Brisk, with One Customer Arriving