Consider a queue to which customers arrive according to a Poisson process with rate λ per hour. Suppose that the queue has two servers. Each customer who arrives at the queue counts the length r of the queue (including any customers being served) and decides to leave with probability pr, for r = 2, 3, . . . . A customer who leaves does not enter the queue. Each customer who enters the queue waits in the order of arrival until at least one of the two servers is available, and then begins being served by the available server. If both servers are available, the customer chooses randomly between the two servers with probability ½ for each, independent of all other random variables. For server i (i = 1, 2), the time (in hours) to serve a customer, after beginning service, is an exponential random variable with parameter μi. Assume that all service times are independent of each other and of all arrival times. Describe how to simulate the number of customers in the queue (including any being served) at a specific time t.
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