2017/02/21 by Asaf Cohen, Cohen, Asaf · 1 citation
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #Supply Chain and Inventory Management #Auction Theory and Applications
paper · pdf · doi:10.48550/arxiv.1702.06479
We consider a multidimentional Brownian control problem (BCP) with model\nuncertainty that formally emerges from a multiclass M/M/1 queueing control\nproblem under heavy-traffic with model uncertainty. The BCP is formulated as a\nmultidimensional stochastic differential game with two players: a minimizer\nthat has an equivalent role to the decision maker in the queueing control\nproblem and a maximizer whose role is to set up the uncertainty of the model.\nThe dynamics are driven by a Brownian motion. We show that a state-space\ncollapse propery holds. That is, the multidimensional BCP can be reduced to a\none-dimensional BCP with model uncertainty that also takes the form of a\ntwo-player stochastic differential game. Then, the value function of both of\nthe games is characterized as the unique solution to a free-boundary problem\nfrom which we extract equilibria for both games. Finally, we analyze the\ndependence of the value function and the equilibria on the ambiguity\nparameters.\n