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:&nbsp;1) Compute the average number of cars in line.&nbsp;2) Calculate the value of probability that there are no car in the system.&nbsp;3) Compute the average time that a car spends in the system.

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Ali Baba&#039;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:&amp;nbsp;1) Compute the average number of cars in line.&amp;nbsp;2) Calculate the value of probability that there are no car in the system.&amp;nbsp;3) Compute the average time that a car spends in the system.

George Woody · Accepted Answer

Introduction  The Poisson distribution can be established using the formula P(x)=mre−mr!  where r is the number of arrivals per unit time  P(x) is the probability of x arrivals  m is the average arrival rate.  Part 1  Let m be the mean car arrivals per hour and s be the mean number of cars serviced per hour.  It is given that new car arrives every 2 minutes so m=30 cars per hour  so the average number of cars in the line is given by:  Ls=ms−m=30s−30  Part 2   The probability that there are no cars in the system is given by:  P0=1−ms=1−30s  Part 3   Average time that a unit spends in the system is given by  Ws=1s−m=1s−30

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

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