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The minimumbacklog problem
 IN PROC. 5TH CANAD. CONF. COMPUT. GEOM
, 1993
"... We introduce and study the minimumbacklog problem (MBP). The MBP arises in sensor networks and is related to the classic kserver problem. It can be understood as a 2person game played on a graph G = (V, E). The “player ” moves along the edges of the graph; the opponent is the “adversary. ” The ..."
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Cited by 20 (7 self)
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We introduce and study the minimumbacklog problem (MBP). The MBP arises in sensor networks and is related to the classic kserver problem. It can be understood as a 2person game played on a graph G = (V, E). The “player ” moves along the edges of the graph; the opponent is the “adversary. ” The game proceeds in timesteps. In each timestep the adversary pours a total of one unit of water into “cups ” that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player’s objective is to minimize the maximum amount of water (the backlog) in any cup at any time. We show that the competitive ratio of any algorithm for the MBP has a lower bound of Ω(∆), where ∆ is the diameter of the graph. Thus, we focus on determining a strategy for the player that guarantees a uniform upper bound on the backlog. In general graphs, the deamortization analysis of Dietz and Sleator gives a bound of O( ∆ ln V ). Our main result is that in geometric settings (e.g., sensor fields), one can obtain substantially better bounds on the maximum backlog. In particular, for a 2dimensional nbyn grid, we achieve a backlog of O(n √ ln ln n), improving the O(n ln n) upper bound for general graphs, and coming close to the naive Ω(n) lower bound. Then, in a model of continuous motion of the player and continuous pouring by the adversary, for cups placed at m points in the plane we show that the backlog can be bounded by O(D √ ln ln m), where D is the diameter of the point set. Our methods apply also to higher (fixed) dimensions. We study also the variant of the MBP in which the adversary has a location within the graph and must act locally (filling cups) with respect to his position, just as the player acts locally (emptying cups) with respect to her position. We prove that deciding the value of this game is PSPACEhard.
On Decentralized Policies for the Stochastic kServer Problem
, 2006
"... In this paper we study a dynamic resource allocation problem which we call the stochastic kserver problem. In this problem, requests for some service to be performed appear at various locations over time, and we have a collection of k mobile servers which are capable of servicing these requests. Wh ..."
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In this paper we study a dynamic resource allocation problem which we call the stochastic kserver problem. In this problem, requests for some service to be performed appear at various locations over time, and we have a collection of k mobile servers which are capable of servicing these requests. When servicing a request, we incur a cost equal to the distance traveled by the dispatched server. The goal is to find a strategy for choosing which server to dispatch to each incoming request which keeps the average service cost as small as possible. In the model considered in this paper, the locations of service requests are drawn according to an IID random process. We show that, given a statistical description of this process, we can compute a simple decentralized statefeedback policy which achieves an average cost within a factor of two of the cost achieved by an optimal statefeedback policy. In addition, we demonstrate similar results for several extensions of the basic stochastic kserver problem. 1