Question. Consider a single-server system where there can be at most two customers in the system(including the one being served). In each hour, a new customer enters to the system with probability% unless there are already 2 customers in the system. Assume that new arrival occurs at the end ofeach hour.At the beginning of each hour, the server can decide a configuration if there is a customer in thesystem. If the configuration is fast, with probability 0.7, one customer is served and it leaves the systemin a given hour. On the other hand, if the configuration is slow, this probability decreases to 0.4. 80 TLrevenue is obtained for each customer whose service is completed. The costs of slow and fastconfigurations are 10 and 15 TL per hour, respectively. The hourly discount rate is B=0.8.We would like to maximize the total expected discounted profit over an infinite horizon.Formulate the problem as MDP model by defining states, decision sets, transitionprobabilities and expected rewards clearly.Find the optimal policy using Policy Iteration where the initial policy is to use fastconfiguration whenever there is at least one customer in the system.a.b.C.Develop an LP model for the MDP. Assume that you have solved the LP optimally.What is the optimal solution, which constraints in your model are binding and why? (Do notsolve the LP model; you can determine the binding constraints by observing the optimalsolution found in part b).

we need to define the states, decision sets, transition probabilities, and expected rewards. Let's…

Question. Consider a single-server system where there can be at most two customers in the system (including the one being served). In each hour, a new customer enters to the system with probability % unless there are already 2 customers in the system. Assume that new arrival occurs at the end of each hour.

Question. Consider a single-server system where there can be at most two customers in the system (including the one being served). In each hour, a new customer enters to the system with probability % unless there are already 2 customers in the system. Assume that new arrival occurs at the end of each hour.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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