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Probability and Math Finance Seminar
Arka Ghosh, Iowa State University"Optimal buffer size and dynamic rate control for a queueing network with reneging in heavy traffic" AbstractWe address a rate control problem associated with a single server finitebuffer Markovian queueing system with customer abandonment in heavy traffic. The controller can choose and fix a buffer size of the queue and can dynamically control the arrival and/or the service rates depending on the current state of the network. We consider the infinite horizon discounted cost criterion, where the cost function includes a penalty for each rejected customers, a control cost related to the adjustment of the arrival and service rates as well as a penalty for each abandoned customer. Here we obtain an explicit solution of the approximating diffusion control problem (Brownian control problem or BCP) and using this solution, construct controls for the queueing network control problem. We also prove asymptotic optimality of this policy, using generalized regulator maps(Skorohod maps) and weak convergence techniques. In addition, we identify the parameter regimes where infinite buffer size is optimal. (Joint work with Ananda Weerasinghe, Iowa State University, U.S.A, ananda@iastate.edu)
