The Disk Layout Problem

Imagine that we keep a daily log of the files that our computer reads from its hard disk. For most computer users the logs of one day compared to the next may be very similar. For example, opening up a commonly used program may require access to the same files in the same order every time that event occurs. We shall call such a sequence of files a trace. The essence of the problem therefore is: given a set of traces that are expected to be representative of common use, we must rearrange the files on the disk so that the performance is optimized. Programs called disk defragmenters use these simple principles to rearrange data records on a disk so that each file is contiguous, with no holes or few holes between data records. Some more sophisticated disk defragmenters also try to place related files near each other, usually based on simple static structure rather than a dynamic analysis of the accesses. We are interested in more dynamic defragmentation procedures. We first consider a 1D model of the disk. We then look at the results from an investigation of the 2D disk model followed by a discussion of caching strategies. Finally we list some of the complications that may need to be addressed in order to make the models more realistic

Edge-Caching Wireless Networks: Performance Analysis and Optimization

Edge-caching has received much attention as an efficient technique to reduce delivery latency and network congestion during peak-traffic times by bringing data closer to end users. Existing works usually design caching algorithms separately from physical layer design. In this paper, we analyse edge-caching wireless networks by taking into account the caching capability when designing the signal transmission. Particularly, we investigate multi-layer caching where both base station (BS) and users are capable of storing content data in their local cache and analyse the performance of edge-caching wireless networks under two notable uncoded and coded caching strategies. Firstly, we propose a coded caching strategy that is applied to arbitrary values of cache size. The required backhaul and access rates are derived as a function of the BS and user cache size. Secondly, closed-form expressions for the system energy efficiency (EE) corresponding to the two caching methods are derived. Based on the derived formulas, the system EE is maximized via precoding vectors design and optimization while satisfying a predefined user request rate. Thirdly, two optimization problems are proposed to minimize the content delivery time for the two caching strategies. Finally, numerical results are presented to verify the effectiveness of the two caching methods.Comment: to appear in IEEE Trans. Wireless Commu

Fundamental Limits of Coded Caching: Improved Delivery Rate-Cache Capacity Trade-off

A centralized coded caching system, consisting of a server delivering N popular files, each of size F bits, to K users through an error-free shared link, is considered. It is assumed that each user is equipped with a local cache memory with capacity MF bits, and contents can be proactively cached into these caches over a low traffic period; however, without the knowledge of the user demands. During the peak traffic period each user requests a single file from the server. The goal is to minimize the number of bits delivered by the server over the shared link, known as the delivery rate, over all user demand combinations. A novel coded caching scheme for the cache capacity of M= (N-1)/K is proposed. It is shown that the proposed scheme achieves a smaller delivery rate than the existing coded caching schemes in the literature when K > N >= 3. Furthermore, we argue that the delivery rate of the proposed scheme is within a constant multiplicative factor of 2 of the optimal delivery rate for cache capacities 1/K N >= 3.Comment: To appear in IEEE Transactions on Communication