Ali Baba's Car Wash Service Centre is open 6 days a week, but its busi

scottyqegi

scottyqegi

Answered question

2021-11-30

Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes, One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: 

Calculate the value of probability that there are no car in the system.

Answer & Explanation

Howell

Howell

Beginner2021-12-01Added 11 answers

Step 1
It is said to assume Poisson arrivals and exponential service times. The mean number of cars per hour will be 30 So let the Poisson probability of arrival be λ=(30)re30r! and the service time be μ=er.
Probability that there are no cars in the system
The average utilization of the system is given by p=λμ. So it is given by:
p=(30)re30r!er=(30)re30err!
Probability that n customers are served in the system is given by Pn=(1p)pn
P0=(1p)p0=1p
P0=1(30)0e30e00!
=1e301

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