Let the taxi stand at which customers arrive rate of lambda1 and taxis arrive at rate lambda2. Taxis wait for customers and form queue. Customers, though, do not wait for taxi; if they find no taxi waiting on their arrival, they simply leave.

a) model this system as Markov process. Indentify state space and draw transition rate diagram.
b) Assume that lambda1 > lambda2. Describe why this Markov process has the unique steady state distribution, and commpute it.
c) Now assume that half of the customers who arrive are patient and decide to wait in the queue if there is no taxi available immediately. Other half, impatient customers, take the taxi only if one is available immediately and otherwise leave stand without service.
c) Model this system as the Markov process. Recognize state space and draw transition rate diagram.
d) Under what situations on lambda1 and lambda2 will this system have the steady state distribution? Describe your answer.