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In this paper, the authors propose a stochastic model to describe how search service providers charge client companies based on users' queries for the keywords related to these companies' ads by using certain advertisement assignment strategies. They formulate an optimization problem to maximize the long-term average revenue for the service provider under each client's long-term average budget constraint, and design an online algorithm which captures the stochastic properties of users' queries and click-through behaviors. They solve the optimization problem by making connections to scheduling problems in wireless networks, queueing theory and stochastic networks.
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