2. A shopping center parking lot has ten spaces. Cars arrive at the...

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2. A shopping center parking lot has ten spaces. Cars arrive at the lot according to a Poisson process with rate λ > 0. If a car arrives at the lot and there is an empty space, it takes the space. If a car arrives and there are no empty spaces, the car moves on to another lot and never returns. Any parked car remains in its space for an exponentially distributed amount of time with mean 1/μ where M is a positive finite number. Assume that the times that different cars remain parked are independent and that these times are independent of the Poisson arrival process. Take as given that the number of cars in the lot at time t is a continuous time Markov chain.
(a) Determine the infinitesimal transition probabilities (that is the Q matrix) for this Markov chain. (It may be helpful to draw a diagram of the states with the infinitesimal rates marked on it).

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