In a single channel manual soft cloth wash, cars arrive following Poisson distribution at the rate of 8 per hour. It takes an average of 6 minutes to wash a car and the service time follows exponential distribution. The probability of exactly 2 customers in the system will be
A) 0.8
B) 0.2
C) 0.16
D) 0.128

Question

Quizplus · Accepted Answer

The system can be modeled as an M/M/1 queue, where the arrival rate (λ) is 8 cars per hour and the service rate (μ) is 10 cars per hour (since it takes 6 minutes to wash a car, and there are 60 minutes in an hour, 60/6 = 10). The probability of having exactly n customers in the system in an M/M/1 queue is given by P(n) = (1 - ρ) * ρ^n, where ρ = λ/μ. Here, ρ = 8/10 = 0.8. Thus, the probability of exactly 2 customers in the system is P(2) = (1 - 0.8) * 0.8^2 = 0.128.

In a Single Channel Manual Soft Cloth Wash, Cars Arrive