A manufacturing system consists of two machines in parallel and a single queue. Jobs arriv...

A manufacturing system consists of two machines in parallel and a single queue. Jobs arrive with exponential interarrival times at a rate of 10 per hour, and each machine has exponential processing times at a rate of 8 per hour. During the first 16 hours of each day both machines are operational, but only one machine is used during the final 8 hours.

(a) Determine whether the system is well defined by computing the utilization factor ρ and comparing it with 1.

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(b) Let N_i be the throughput for the ith hour. Does N₁, N₂, … have a steady-state distribution?

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(c) Make 10 replications of the simulation of length 480 hours (20 days) each. Plot the averaged process

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(d) Let M_i be the throughput for the ith 24-hour day. Use the data from part (c) and the replication/deletion approach to construct a point estimate and 90 percent confidence interval for the steady-state mean daily throughput v = E(M) = 240.