Consider an infinite-horizon discounted version of the discrete-time queueing admission control model with a deterministic service rate that was presented in Example 3.7.1. Assume that the per period holding cost h(x) is linear in the system content and that there is an infinite waiting room.
a. Provide the optimality equations for this model and choose a bounding function w so that they have a unique solution in V,.
b. Show that N-state approximations converge to u:.
c. Find a priori bounds on the precision of the approximation under the assumption that the arrivaf distribution g(n) is geometric with parameter (Y.
d. Show that a control limit policy is optimal.
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