Reference no: EM131812168

Question: Taxis arrive at the pick up area of a hotel at a Poisson rate of µ. Independently, passengers arrive at the same location at a Poisson rate of λ. If there are no passengers waiting to be put in service, the taxis wait in a queue until needed. Similarly, if there are no taxis available, passengers wait in a queue until their turn for a taxi service. For n ≥ 0, let X(t) = (n, 0) if there are n passengers waiting in the queue for a taxi. For m ≥ 0, let X(t) = (0, m) if there are m taxis waiting in the queue for passengers. Show that $ X(t): t ≥ 0 % is a continuous-time Markov chain, and write down the balance equations for the states of this Markov chain. You do not need to find the limiting probabilities.