It's a beautiful sunny day after a week of rainy weather and both of the local car washes are busy. One car wash is fully automated, touchless, and can wash a vehicle of any size to a dazzling luster in 5 minutes flat
The other car wash is a fund raiser staffed by eager amateurs that work on one car at a time and can finish it in about 4 minutes (their time is governed by the Poisson distribution). Customer arrivals at both car washes are Poisson distributed with a mean of 10 per hour. How long does it take the average customer to work his way through either system? How many customers are in the systems on average?
What will be an ideal response?
Answer: The automatic car wash has an arrival rate of 10 customers per hour and a constant service rate of 12 customers per hour.
TS = TW + = +
TS = + = .2917 hours
CS = CW + = +
CS = + = 2.9167 customers
The fundraiser system (Poisson distributed service times) has an arrival rate of 10 customers per hour and a service rate with a mean of 15.
TS = TW + = +
TS = + = .2 hours
CS = CW + = +
CS = + = 2 customers
At first glance you might think it's a wash, but the fund-raiser system is faster than the automatic.
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