Question: D E 7 8 9 #VALUE! #DIVIO #DIV/0! #DIVIO #DIV/0! #DIV/0! 1 Multiple Channel Waiting Line Model 2 Assumptions 4 Poisson Arrivals 5 Exponential Service

D E 7 8 9 #VALUE! #DIVIO #DIV/0! #DIVIO #DIV/0! #DIV/0! 1 Multiple Channel Waiting Line Model 2 Assumptions 4 Poisson Arrivals 5 Exponential Service Times 6 Number of Channels Arrival Rate Service Rate For Each Channel 10 11 12 Operating Characteristics 13 14 Probability that no customers are in the system, Po 15 Average number of customers in the waiting line, La 16 Average number of customers in the system, L 17 Average time a customer spends in the waiting line, Wa 18 Average time a customer spends in the system, W 13 Probability an arriving customer has to wait, Pw 20 21 Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of icar every 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 cars per hour. 22 23 1. What is the probability that the station 24 will be idle? 25 2. What is the average number of cars that 26 will be waiting for service? 3. What is the average time a car will be 28 waiting for service? 4. What is the average time a car will be at the gas and wash station? 27 29 30 31 32 Solution

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