Speedy Oil provides a single-server automobile oil change and lubrication service. Customers arrive at a rate of 2.5 cars per hour (assume Poisson arrival rate). On average the shop can process a car in 12 minutes (assume exponential service rates). a.) What is the average number of cars in the system? b.) What is the average time a car spends waiting for service to begin? c.) What is the average time a car spends in the system? d.) What is the probability an arriving car has to wait for service? e.) What percentage of time are there 2 or fewer cars in the system?
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers arrive at a rate of 2.5 cars per hour (assume Poisson arrival rate). On average the shop can process a car in 12 minutes (assume exponential service rates). a.) What is the average number of cars in the system? b.) What is the average time a car spends waiting for service to begin? c.) What is the average time a car spends in the system? d.) What is the probability an arriving car has to wait for service? e.) What percentage of time are there 2 or fewer cars in the system?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Step 1: A)Average Number of Cars in Waiting Line = (Arrival Rate)^2/Service Rate* (Service Rate- Arrival Rat
VIEWStep 2: b)Average Time a car spend waiting for service to begin = Average No of Cars in Waiting Line/Arrive
VIEWStep 3: C)Average Time a Car Spend in System = Average Time a car spend waitingfor service to begin +(1/S.r)
VIEWStep 4: D)Probability that a car has to wait = Arrival Rate/Service Rate
VIEWStep 5: E)system = Probability of O car in system +Probability of 1 car in system + Probability of 2 car in
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