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In this paper, we look at content placement in the high-dimensional regime: there are $$n$$ servers, and $${\mathrm {O}}(n)$$ distinct types of content. Each server can store and serve $${\mathrm {O}}(1)$$ types at any given time. Demands for these content types arrive and have to be served in an online fashion; over time, there are a total of $${\mathrm {O}}(n)$$ of these demands. We consider the algorithmic task of content placement: determining which types of content should be on which server at any given time, in the setting where the demand statistics (i.e., the relative popularity of each type of content) are not known a-priori, but have to be inferred from the very demands we are trying to satisfy. This is the high-dimensional regime because this scaling (everything being $${\mathrm {O}}(n)$$ ) prevents consistent estimation of demand statistics; it models many modern settings where large numbers of users, servers, and videos/webpages interact in this way. We characterize the performance of any scheme that separates learning and placement (i.e., which uses a portion of the demands to gain some estimate of the demand statistics, and then uses the same for the remaining demands), showing it is order-wise strictly suboptimal. We then study a simple adaptive scheme-which myopically attempts to store the most recently requested content on idle servers-and show it outperforms schemes that separate learning and placement. Our results also generalize to the setting where the demand statistics change with time. Overall, our results demonstrate that separating the estimation of demand, and the subsequent use of the same, is strictly suboptimal. [ABSTRACT FROM AUTHOR]

It has been recently shown that queue-based carrier sense multiple access (CSMA) algorithms are throughput-optimal. In these algorithms, each link of the wireless network has two parameters: a transmission probability and an access probability. The transmission probability of each link is chosen as an appropriate function of its queue length, however the access probabilities are simply regarded as some random numbers since they do not play any role in establishing the network stability. In this paper, we show that the access probabilities control the mixing time of the CSMA Markov chain and, as a result, affect the delay performance of the CSMA. In particular, we derive formulas that relate the mixing time to access probabilities and use these to develop the following guideline for choosing access probabilities: Each link i should choose its access probability equal to 1/(d_i+1), where d_i is the number of links that interfere with link i. Simulation results show that this choice of access probabilities results in good delay performance. [ABSTRACT FROM AUTHOR]