We study the problem of optimal content placement over a network of caches, a problem naturally arising in several networking applications, including ICNs, CDNs, and P2P systems. Given a demand of content request rates and paths followed, we wish to determine the content placement that maximizes the expected caching gain, i.e., the reduction of routing costs due to intermediate caching. The offline version of this problem is NP-hard and, in general, the demand and topology may be a priori unknown. Hence, a distributed, adaptive, constant approximation content placement algorithm is desired. We show that path replication, a simple algorithm frequently encountered in literature, can be arbitrarily suboptimal when combined with traditional eviction policies, like LRU, LFU, or FIFO. We propose a distributed, adaptive algorithm that performs stochastic gradient ascent on a concave relaxation of the expected caching gain, and constructs a probabilistic content placement within 1-1 e factor from the optimal, in expectation. Motivated by our analysis, we also propose a novel greedy eviction policy to be used with path replication, and show through numerical evaluations that both algorithms significantly outperform path replication with traditional eviction policies over a broad array of network topologies.
The path replication eviction policy we propose also relates to greedy maximization techniques used in throughput-optimal backpressure algorithms---see, e.g., Stolyar @cite_21 and, more recently, @cite_26 , for an application to throughput-optimal caching in ICN networks. We minimize routing costs and ignore throughput issues, as we do not model congestion. Investigating how to combine these two research directions, capitalizing on commonalities between these greedy algorithms, is an interesting open problem.
@cite_21 @cite_26
2059060883 2262385276 2963602389 2136954685
.We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89–148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5–25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks. 1. Introduction. This paper is a continuation of Dai and Lin (2005), in which maximum pressure policies are shown to be throughput optimal for a class of stochastic processing networks. Throughput optimality is an important, first-order objective for many networks, but it ignores some key secondary performance measures like queueing delays experienced by jobs in these networks. In this paper we show that maximum pressure policies enjoy additional optimality properties; they are asymptotically optimal in minimizing a certain workload or holding cost of a stochastic processing network. Stochastic processing networks have been introduced in a series of three papers by Harrison (2000, 2002, 2003). In Dai and Lin (2005) and this paper we consider a special class of Harrison’s model. This class of stochastic processing networks is much more general than multiclass queueing networks that have been a subject of intensive study in the last 20 years; see, for example, Harrison (1988), Williams In any caching system, the admission and eviction policies determine which contents are added and removed from a cache when a miss occurs. Usually, these policies are devised so as to mitigate staleness and increase the hit probability. Nonetheless, the utility of having a high hit probability can vary across contents. This occurs, for instance, when service level agreements must be met, or if certain contents are more difficult to obtain than others. In this paper, we propose utility-driven caching, where we associate with each content a utility, which is a function of the corresponding content hit probability. We formulate optimization problems where the objectives are to maximize the sum of utilities over all contents. These problems differ according to the stringency of the cache capacity constraint. Our framework enables us to reverse engineer classical replacement policies such as LRU and FIFO, by computing the utility functions that they maximize. We also develop online algorithms that can be used by service providers to implement various caching policies based on arbitrary utility functions. We consider the canonical shared link caching network formed by a source node, hosting a library of @math information messages (files), connected via a noiseless multicast link to @math user nodes, each equipped with a cache of size @math files. Users request files independently at random according to an a-priori known demand distribution q. A coding scheme for this network consists of two phases: cache placement and delivery. The cache placement is a mapping of the library files onto the user caches that can be optimized as a function of the demand statistics, but is agnostic of the actual demand realization. After the user demands are revealed, during the delivery phase the source sends a codeword (function of the library files, cache placement, and demands) to the users, such that each user retrieves its requested file with arbitrarily high probability. The goal is to minimize the average transmission length of the delivery phase, referred to as rate (expressed in channel symbols per file). In the case of deterministic demands, the optimal min-max rate has been characterized within a constant multiplicative factor, independent of the network parameters. The case of random demands was previously addressed by applying the order-optimal min-max scheme separately within groups of files requested with similar probability. However, no complete characterization of order-optimality was previously provided for random demands under the average rate performance criterion. In this paper, we consider the random demand setting and, for the special yet relevant case of a Zipf demand distribution, we provide a comprehensive characterization of the order-optimal rate for all regimes of the system parameters, as well as an explicit placement and delivery scheme achieving order-optimal rates. We present also numerical results that confirm the superiority of our scheme with respect to previously proposed schemes for the same setting. This paper considers the problem of throughput optimal routing scheduling in a multi-hop constrained queueing network with random connectivity whose special cases include opportunistic multi-hop wireless networks and input-queued switch fabrics. The main challenge in the design of throughput optimal routing policies is closely related to identifying appropriate and universal Lyapunov functions with negative expected drift. The few well-known throughput optimal policies in the literature are constructed using simple quadratic or exponential Lyapunov functions of the queue backlogs and as such they seek to balance the queue backlogs across network independent of the topology. By considering a class of continuous, differentiable, and piece-wise quadratic Lyapunov functions, this paper provides a large class of throughput optimal routing policies. The proposed class of Lyapunov functions allow for the routing policy to control the traffic along short paths for a large portion of state-space while ensuring a negative expected drift. This structure enables the design of a large class of routing policies. In particular, and in addition to recovering the throughput optimality of the well-known backpressure routing policy, an opportunistic routing policy with congestion diversity is proved to be throughput optimal.