A saloon has three barbers to handle customers. At the present time, customers arrive at an average rate of eight customers per hour. Each barber can cut hair at a rate of four customers per hour. Arrivals appear to follow the Poisson distribution, and service times follow the exponential distribution. i. How long will the waiting line be on average? ii. How long does the average customer wait until service begins? iii. Suppose customers arrive at a rate of 10 per hour. What effects will this have?

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Chapter1: Combinatorial Analysis
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A saloon has three barbers to handle customers. At the present time, customers
arrive at an average rate of eight customers per hour. Each barber can cut
hair at a rate of four customers per hour. Arrivals appear to follow the Poisson
distribution, and service times follow the exponential distribution.
i. How long will the waiting line be on average?
ii. How long does the average customer wait until service begins?
iii. Suppose customers arrive at a rate of 10 per hour. What effects will this
have?
Transcribed Image Text:A saloon has three barbers to handle customers. At the present time, customers arrive at an average rate of eight customers per hour. Each barber can cut hair at a rate of four customers per hour. Arrivals appear to follow the Poisson distribution, and service times follow the exponential distribution. i. How long will the waiting line be on average? ii. How long does the average customer wait until service begins? iii. Suppose customers arrive at a rate of 10 per hour. What effects will this have?
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