Upon arrival of a job, a controller routes it to one of two parallel queueing systems. Assume that interarrival times follow an exp(y) distribution, and that the service times are exp(pi) at queue i, i = 1,2. Further assume that holding cost rates are linear with rate ci at queue i.
a. Formulate this as a continuous-time Markov decision process.
b. Give the optimality equation for the discounted version of this problem, and show that it has a solution.
c. Determine the form of an optimal policy for the discounted problem, and investigate its sensitivity to c,, c2, F,, and pz.
d. Give the average reward optimality equation, and provide conditions under which it has a solution.
e. Repeat (c) for the average reward model.
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