Customers arriving to a fully occupied shop leave

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Unformatted text preview: 4.7. 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 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 and that when both servers are free an arriving customer is equally likely to choose either one. (a) Formulate a Markov chain model 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) Consider the special case in which = 2, µ1 = 3 and µ2 = 3. Find the stationary distribution. 4.8. Two queues in series. Consider a two station queueing network in which arrivals only occur at the first server and do so at rate 2. If a customer finds server 1 free he enters the system; otherwise he goes away. When a customer is done at the first...
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