Question

Classic car care has one worker who washes cars in a four-step method ---- soap, rinse, dry, vacuum. The time to complete each step is exponentially distributed, with mean 9 minutes. Every car goes through every step before another car begins the process. On the average, one car every 45 minutes arrives for a wash job, according to a Poisson process (the interarrival is exponentially distributed). What is the average time a car waits to begin the wash job? What is the average number of cars in the car wash system? What is the average time required to wash a car

Answer 1

Solution:

Given: Mean,=9 minutes for 4 services=9*4=36 mins

So, 60/36=1.67 cars/hrs

On an average one car arrives every 45 minutes, so =60/45=1.33 cars/hrs.

1) Average time a car waits to begin the wash job,Lq=1.33/(1.67(1.67-1.33))=2.34 hrs

2) Average number of cars in the car wash system=1.33/(1.67-1.33)=3.91=4 cars

3)Average time required to wash a car=Lq/=2.34/1.33=1.76 hrs