The Infinite Help Desk (M/M/∞) Imagine that you could call up a company for customer service and never get the message, "We're sorry; all of our service representatives are busy with other customers..." This can be modeled by a queueing system with an infinite number of servers. Concretely, consider the M/M/00 queueing system, where interarrival times are Exponential with rate A and the service times are Exponential with rate μ, but where there are an infinite number of servers (k = 0). (a) Draw a state diagram for the continuous-time Markov chain of this system. (b) Derive the limiting probabilities. You need to get a closed-form expression here that is simple and easy to recognize. (c) From the limiting probabilities, derive a closed-form expression for the expected number of jobs in the system, E[N]. (d) Applying Little's Law gives you E [T]. Does E [T] make sense? Explain.