3. A small one-way road crosses a border from country A towards country B. Vehicles have to cross successively two checkpoints, one to get out of A, one to get in B. There is only one officer at each checkpoint. In average, there are a vehicles arriving per hour. The officer at the first checkpoint let pass in expectation u vehicles per hour, the second one H2. (a) Specify a queuing model that can model the queue at the first checkpoint. (b) State when the latter model is positive recurrent. Give the invariant measure and explain why the process is reversible. (c) Explain what it means for the reversed process to increase or decrease by 1 in terms of the initial queuing process. (d) Model the lengths of the two queues by a continuous-time Markov chain. Specify its Q-matrix. (e) Write the equations of an invariant measure. (f) Show that for 1