Economical Caching with Stochastic Prices

In the economical caching problem, an online algorithm is given a sequence of prices for a certain commodity. The algorithm has to manage a buffer of fixed capacity over time. We assume that time proceeds in discrete steps. In step i, the commodity is available at price ci ∈ [α, β], where β > α ≥ 0 and ci ∈ N. One unit of the commodity is consumed per step. The algorithm can buy this unit at the current price ci, can take a previously bought unit from the storage, or can buy more than one unit at price ci and put the remaining units into the storage. In this paper, we study the economical caching problem in a probabilistic analysis, that is, we assume that the prices are generated by a random walk with reflecting boundaries α and β. We are able to identify the optimal online algorithm in this probabilistic model and analyze its expected cost and its expected savings, i.e., the cost that it saves in comparison to the cost that would arise without having a buffer. In p...

• Type: Conference
• Year: 2009
• Where: SAGA
• Authors: Matthias Englert, Berthold Vöcking, Melanie Winkler
• Keywords: Algorithm, Control Systems, Economical Caching Problem, Price Ci, SAGA 2009