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Consider an airport where taxis and customers arrive (exponential interarrival times) with respective rates of 1...

Consider an airport where taxis and customers arrive (exponential interarrival times) with respective rates of 1 and 2 per hour. No matter how many other taxis are present, a taxi will wait. If an arriving customer does not find a taxi, the customer immediately leaves. (a) Model this system as a birth-death process (Hint: determine what the state of the system is at any given time and draw a rate diagram.) (b) Find the average number of taxis that are waiting for a customer. (c) Suppose all customers who use a taxi pay a $2 fare. During a typical hour, how much revenue will the taxis receive in total?

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Answert Given information, Arvival rate 1 = 1 customers/minute sovice rate u = a customers minute. The traffic intensity of tTho=&P = Thus, . The steady state probability that Haxi will be Present is, Ti - Me - ixteen - Thus, 1. The steady state probThus, The steady state probability that staris will be present The resort Thus, in general, the steady state probability thatCY ® find average number * The average number oy tanís that are waiting for a customer, L ine- .. where, pat Now, substitute

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