It has been recently advocated that in large communication systems it is beneficial both for the users and for the network as a whole to store content closer to users. One particular implementation of such an approach is to co-locate caches with wireless base stations. In this paper we study geographically distributed caching of a fixed collection of files. We model cache placement with the help of stochastic geometry and optimize the allocation of storage capacity among files in order to minimize the cache miss probability. We consider both per cache capacity constraints as well as an average capacity constraint over all caches. The case of per cache capacity constraints can be efficiently solved using dynamic programming, whereas the case of the average constraint leads to a convex optimization problem. We demonstrate that the average constraint leads to significantly smaller cache miss probability. Finally, we suggest a simple LRU-based policy for geographically distributed caching and show that its performance is close to the optimal.
An important step in the Markov reward approach to error bounds on stationary performance measures of Markov chains is to bound the bias terms. Affine functions have been successfully used for these bounds for various models, but there are also models for which it has not been possible to establish such bounds. So far, no theoretical results have been available that guarantee bounds on the bias terms.We consider random walks in the positive orthant and provide sufficient conditions under which quadratic and/or geometric functions can be used to bound the bias terms. In addition, we provide a linear programming framework that establishes the quadratic bounds as well as the resulting bound on the stationary performance.
We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. We also apply our approximation scheme to a coupled-queue in which only one of the buffers has finite capacity.The two-node queue is one of the most extensively studied topics in queueing theory. It can be often modeled as a two-dimensional random walk on the quarter-plane. Hence, it is sufficient to find performance measures of the corresponding two-dimensional random walk if we are interested in the performance of the two-node queue. In this work we analyze the steadystate performance of a two node queue for the particular case that one or
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