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Abstract: Robots are deployed by a Web search engine for collecting information from different Web servers in order to maintain the currency of its data base of Web pages. In this paper, we investigate the number of robots to be used by a search engine so as to maximize the currency of the data base without putting an unnecessary load on the network. We adopt a finite-buffer queueing model to represent the system. The arrivals to the queueing system are Web pages brought by the robots; service corresponds to the indexing of these pages. Good performance requires that the number of robots, and thus the arrival rate of the queueing system, be chosen so that the indexing queue is rarely starved or saturated. Thus, we formulate a multi-criteria stochastic optimization problem with the loss rate and empty-buffer probability being the criteria. We take the common approach of reducing the problem to one with a single objective that is a linear function of the given criteria. Both static and dynamic policies can be considered. In the static setting the number of robots is held fixed; in the dynamic setting robots may be re-activated/de-activated as a function of the state. Under the assumption that arrivals form a Poisson process and that service times are independent and exponentially distributed random variables, we determine an optimal decision rule for the dynamic setting, i.e., a rule that varies the number of robots in such a way as to minimize a given linear function of the loss rate and empty-buffer probability. Our results are compared with known results for the static case. A numerical study indicates that substantial gains can be achieved by dynamically controlling the activity of the robots. |

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