We study the content placement problem for cache delivery video-on-demand systems under static random network topologies with fixed heavy-tailed video demand. The performance measure is the amount of server load; we wish to minimize the total download rate for all users from the server and maximize the rate from caches. Our approach reduces the analysis for multiple videos to consideration of decoupled systems with a single video each. For each placement policy, insights gained from the single video analysis carry back to the original multiple video content placement problem. Finally, we propose a hybrid placement technique that achieves near optimal performance with low complexity.
Wu and Li @cite_3 studied the optimal cache replacement algorithm and suggested that the simplest heuristics perform as well as the optimal algorithms, with very insignificant differences. While our formulation assumes random but static video requests, we also look for a simple suboptimal alternative to the optimal content placement algorithm. In this direction, we decompose the analysis of the content placement problem from the scale of the entire system with multiple videos into decoupled systems, each with only a single video of given popularity. @cite_2 formulated the adaptive whole storage placement problem as a mixed integer program (MIP) subject to a storage constraint and link bandwidth constraint. The adaptive whole storage placement problem is solved approximately by MIP. In our work, we derive an upper and a lower bound on the performance of the single video adaptive whole storage placement policy using analytical and heuristic approaches. Zhang @cite_6 used MDS codes to relax the integer constraint and converted the integer program into a convex, adaptive fractional storage placement problem that can be solved exactly. This result provides an upper bound on the performance of any content placement policy, including all single video placement policies.
@cite_6 @cite_3 @cite_2
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We investigate the problem of coded caching for nonuniform demands when the structured clique cover algorithm proposed by Maddah-Ali and Niesen for decentralized caching is used for delivery. We apply this algorithm to all user demands regardless of their request probabilities. This allows for coding among the files that have different request probabilities but makes the allocation of memory to different files challenging during the content placement phase. As our main contribution, we analytically characterize the optimal placement strategy that minimizes the expected delivery rate under a storage capacity constraint. It is shown that the optimal placement follows either a two or a three group strategy, where a set of less popular files are not cached at all and the files within each of the other sets are allocated identical amounts of storage as if they had the same request probabilities. We show that for a finite set of storage capacities, that we call the base-cases of the problem, the two group strategy is always optimal. For other storage capacities, optimal placement is achieved by memory sharing between certain base-cases and the resulting placement either follows a two or a three group strategy depending on the corresponding base-cases used. We derive a polynomial time algorithm that determines the base-cases of the problem given the number of caches and popularity distribution of files. Given the base-cases of the problem, the optimal memory allocation parameters for any storage capacity are derived analytically. In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show how the hit probability evolves as the deployment density of the SBSs varies. We show that the heuristic of placing the most popular content in the MBSs is almost optimal after deploying the SBSs with optimal placement policies. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we show that solving the individual problems to find the optimal placement policies for different types of BSs iteratively, namely repeatedly updating the placement policies, does not improve the performance. IPTV service providers offering Video-on-Demand currently use servers at each metropolitan office to store all the videos in their library. With the rapid increase in library sizes, it will soon become infeasible to replicate the entire library at each office. We present an approach for intelligent content placement that scales to large library sizes (e.g., 100Ks of videos). We formulate the problem as a mixed integer program (MIP) that takes into account constraints such as disk space, link bandwidth, and content popularity. To overcome the challenges of scale, we employ a Lagrangian relaxation-based decomposition technique combined with integer rounding. Our technique finds a near-optimal solution (e.g., within 1-2 ) with orders of magnitude speedup relative to solving even the LP relaxation via standard software. We also present simple strategies to address practical issues such as popularity estimation, content updates, short-term popularity fluctuation, and frequency of placement updates. Using traces from an operational system, we show that our approach significantly outperforms simpler placement strategies. For instance, our MIP-based solution can serve all requests using only half the link bandwidth used by LRU or LFU cache replacement policies. We also investigate the trade-off between disk space and network bandwidth. Optimal cache content placement in a wireless small cell base station (sBS) with limited backhaul capacity is studied. The sBS has a large cache memory and provides content-level selective offloading by delivering high data rate contents to users in its coverage area. The goal of the sBS content controller (CC) is to store the most popular contents in the sBS cache memory such that the maximum amount of data can be fetched directly form the sBS, not relying on the limited backhaul resources during peak traffic periods. If the popularity profile is known in advance, the problem reduces to a knapsack problem. However, it is assumed in this work that, the popularity profile of the files is not known by the CC, and it can only observe the instantaneous demand for the cached content. Hence, the cache content placement is optimised based on the demand history. By refreshing the cache content at regular time intervals, the CC tries to learn the popularity profile, while exploiting the limited cache capacity in the best way possible. Three algorithms are studied for this cache content placement problem, leading to different exploitation-exploration trade-offs. We provide extensive numerical simulations in order to study the time-evolution of these algorithms, and the impact of the system parameters, such as the number of files, the number of users, the cache size, and the skewness of the popularity profile, on the performance. It is shown that the proposed algorithms quickly learn the popularity profile for a wide range of system parameters.