A service facility consists of two type A servers and one type B server (not necessarily in the psychological sense). Assume that customers arrive at the facility with inter-arrival times that are IID exponential random variables with a mean of 1 minute. Upon arrival, a customer is determined to be either a type 1 customer or a type 2 customer, with respective probabilities of 0.75 and 0.25. A type 1 customer can be served by any server but will choose a type A server if one is available. Service times for type 1 customers are IID exponential random variables with a mean of 0.8 minute, regardless of the type of server. Type 1 customers who find all servers busy join a single FIFO queue for type 1 customers. A type 2 customer requires service from both a type A server and the type B server simultaneously. Service times for type 2 customers are uniformly distributed between 0.5 and 0.7 minute. Type 2 customers who arrive to find both type A servers busy or the type B server busy join a single FIFO queue for type 2 customers. Upon completion of service of any customer, preference is given to a type 2 customer if one is present and if both a type A and the type B server are then idle. Otherwise, preference is given to a type 1 customer. Simulate the facility for exactly 1000 minutes and estimate the expected average delay in queue and the expected time-average number in queue for each type of customer. Also estimate the expected pro-portion of time that each server spends on each type of customer.
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