# Two people who prepare tax forms are working in a store at a local mall. Each has a chair next

## Question:

Two people who prepare tax forms are working in a store at a local mall. Each has a chair next to his desk where customers can sit and be served. In addition, there is one chair where customers can sit and wait. Customers arrive at rate λ = 2 but will go away if there is already someone sitting in the chair waiting. Suppose that server i requires an exponential amount of time with rate μi = i + 2 ( i = 1,2) and that when both servers are free an arriving customer is equally likely to choose either one.

a) Formulate a Markov chain model (i.e., identify transition rates νi's and transition probabilities p_{ij}'s) for this system with state space {0,1,2,12,3} where the first four states indicate the servers that are busy while the last indicates that there is a total of three customers in the system: one at each server and one waiting.

b) Set-up the balance equations (exit rates = entry rates) needed to solve for the proportion of time the Markov chain is in the different states.

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