Arrivals at a Jiffy Lube follow a Poisson process with rate 10/hour. Service tim

Question

Arrivals at a Jiffy Lube follow a Poisson process with rate 10/hour. Service time is exponentially distributed with mean 15 minutes per customer. There are 2 servers available. Since there is a competitor across the street, only 80% of arriving customers stay for service if they find one car WAITING in queue for service; only 60% stay if they find two can> waiting in queue fur service; only 40% stay if they find three cars waiting in queue for service; none stay for service if they find four cars waiting in queue for service. Let X(f) represent the number of cars in the system at time t. Convert all rates to hourly rates. What is the probability that an arriving customer will be served immediately? What is the long run expected number of cars in the system? What is the average amount of time a customer spends at the system? What is the arrival rate of customers INTO Jiffy Lube?

Explanation / Answer

Part C) The average amount of time cars is calculated sum up every time that each custumer have to wait if they find a car wainting in queue. Time = (45 + 60 + 75) minutes = 60 minutes.

45 minutes if a custumer found a car waiting in queue

60 if a custumer found 2 cars waiting in queue.

75 if a custumer found 3 cars waiting in queue.

Part d) The arrival rate of custumers is 10 custumer per hr.

Part b) The long run expected is 75 minutes

if a custumer found a 3 waiting in queue.

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