Question1 Empty taxis pass by a street corner at a Poisson rate of 2 per minutes and pick up a passenger if one is waiting there. Passengers arrive at the street corner at a Poisson rate of 1 per minute and wait for a taxi only if there are fewer than four persons waiting; otherwise, they leave and never return. a. b. c. d. Draw a state-diagram for this system and define what is a state. Show that the state-diagram corresponds to a Markov chain. Find the arrival rate of passengers who join the queue. Show that the average waiting time of a passenger who joins the queue is 13/15 min. Question1 Empty taxis pass by a street corner at a Poisson rate of 2 per minutes and pick up a passenger if one is waiting there. Passengers arrive at the street corner at a Poisson rate of 1 per minute and wait for a taxi only if there are fewer than four persons waiting; otherwise, they leave and never return. a. b. c. d. Draw a state-diagram for this system and define what is a state. Show that the state-diagram corresponds to a Markov chain. Find the arrival rate of passengers who join the queue. Show that the average waiting time of a passenger who joins the queue is 13/15 min