Question: Suppose that a single-server queueing system fits all the assumptions of the birth-and-death process except that customers always arrive in pairs (but are still served

Suppose that a single-server queueing system fits all the assumptions of the birth-and-death process except that customers always arrive in pairs (but are still served individually). The mean arrival rate is 2 pairs per hour (4 customers per hour) and the mean service rate (when the server is busy) is 5 customers per hour.

a. Construct the mathematical model for this queueing system, i.e., specify states, arrival rates, departure rates, and transition probabilities.

b. Formulate the balance equations for nodes 0 through node 3

c. Solve these equations and determine P0, P1, and P2.

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