In recent times, exponential type cost structure has become popular in control theory. In this talk we formulate and discuss a risk- sensitive type control problem for a multi-class queuing system under the moderate deviation scaling. It is known that the rate function corresponding to the moderate deviation scaling is of Gaussian type. This property of the rate function is often useful for mathematical analysis. We show that the limiting game corresponding to our control problem is solvable. Also the limiting game has a similarity to the well-studied Brownian control problems. This problem is also related to a conjecture of Damon Wischik (2001). The main difficulty in working with G/G/1 queuing network is that the underlying state dynamics is not Markov. Markov property has proven useful for these type of problems (see e.g., Atar-Goswami-Shwartz(2012)). The standard way to solve these problems is to look at the pde associated with the state dynamics and sandwich the limiting value between the upper and lower value of the game. This technique does not work when the state dynamics is not Markov. We will see that the special structure of the rate function and moderate deviation settings will be helpful to overcome such difficulties. Extension to many-server models will also be discussed.

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Last updated: 29 Feb 2024