Business at the Kwik-E-Mart is brisk,with customers 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?

Question

Quizplus · Accepted Answer

The system can be modeled as a M/M/1 queue, where:

- λ = 6 customers per hour (arrival rate)
- μ = 30 customers per hour (= 1/2 minutes per customer, service rate)

The utilization factor (ρ) can be calculated as:

ρ = λ/μ = 6/30 = 0.2

The average number of customers in the system (L) can be calculated as:

L = ρ/(1-ρ) = 0.2/(1-0.2) = 0.25

Therefore, the answer is C) 0.25.

Business at the Kwik-E-Mart Is Brisk,with Customers Arriving at a Rate