Consider a service facility with s (where s ≥ 1) parallel servers. Assume that inter-arrival times of customers are IID exponential random variables with mean E(A) and that service times of customers (regardless of the server) are IID exponential random variables with mean E(S). If a customer arrives and finds an idle server, the customer begins service immediately, choosing the leftmost (lowest-numbered) idle server if there are several available. Otherwise, the customer joins the tail of a single FIFO queue that supplies customers to all the servers. (This is called an M/M/s queue; see App. 1B.) Write a general program to simulate this system that will estimate the expected average delay in queue, the expected time-average number in queue, and the expected utilization of each of the servers, based on a stopping rule of n delays having been completed. The quantities s, E(A), E(S), and n should be input parameters. Run the model for s = 5, E(A) = 1, E(S) = 4, and n = 1000.
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