arXiv subjects

Milad Mahdian

Publications and source records attributed to Milad Mahdian.

4 recordsLinked to original sources

arXiv2019

Kelly Cache Networks

We study networks of M/M/1 queues in which nodes act as caches that store objects. Exogenous requests for objects are routed towards nodes that store them; as a result, object traffic in the network is determined not only by demand but, crucially, by where objects are cached. We determine how to place objects in caches to attain a certain design objective, such as, e.g., minimizing network congestion or retrieval delays. We show that for a broad class of objectives, including minimizing both the expected network delay and the sum of network queue lengths, this optimization problem can be cast as an NP- hard submodular maximization problem. We show that so-called continuous greedy algorithm attains a ratio arbitrarily close to $1 - 1/e \approx 0.63$ using a deterministic estimation via a power series; this drastically reduces execution time over prior art, which resorts to sampling. Finally, we show that our results generalize, beyond M/M/1 queues, to networks of M/M/k and symmetric M/D/1 queues.

cs.NI↗

arXiv2018

Updating Content in Cache-Aided Coded Multicast

Motivated by applications to delivery of dynamically updated, but correlated data in settings such as content distribution networks, and distributed file sharing systems, we study a single source multiple destination network coded multicast problem in a cache-aided network. We focus on models where the caches are primarily located near the destinations, and where the source has no cache. The source observes a sequence of correlated frames, and is expected to do frame-by-frame encoding with no access to prior frames. We present a novel scheme that shows how the caches can be advantageously used to decrease the overall cost of multicast, even though the source encodes without access to past data. Our cache design and update scheme works with any choice of network code designed for a corresponding cache-less network, is largely decentralized, and works for an arbitrary network. We study a convex relation of the optimization problem that results form the overall cost function. The results of the optimization problem determines the rate allocation and caching strategies. Numerous simulation results are presented to substantiate the theory developed.

cs.IT↗

arXiv2017

MinDelay: Low-latency Forwarding and Caching Algorithms for Information-Centric Networks

We present a new unified framework for minimizing congestion-dependent network cost in information-centric networks by jointly optimizing forwarding and caching strategies. As caching variables are integer-constrained, the resulting optimization problem is NP-hard. To make progress, we focus on a relaxed version of the optimization problem, where caching variables are allowed to be real-valued. We develop necessary optimality conditions for the relaxed problem, and leverage this result to design MinDelay, an adaptive and distributed joint forwarding and caching algorithm, based on the conditional gradient algorithm. The MinDelay algorithm elegantly yields feasible routing variables and integer caching variables at each iteration, and can be implemented in a distributed manner with low complexity and overhead. Over a wide range of network topologies, simulation results show that MinDelay typically has significantly better delay performance in the low to moderate request rate regions. Furthermore, the MinDelay and VIP algorithms complement each other in delivering superior delay performance across the entire range of request arrival rates.

cs.NI↗

arXiv2017

Throughput and Delay Scaling of Content-Centric Ad Hoc and Heterogeneous Wireless Networks

We study the throughput and delay characteristics of wireless caching networks, where users are mainly interested in retrieving content stored in the network, rather than in maintaining source-destination communication. Nodes are assumed to be uniformly distributed in the network area. Each node has a limited-capacity content store, which it uses to cache contents. We propose an achievable caching and transmission scheme whereby requesters retrieve content from the caching point which is closest in Euclidean distance. We establish the throughput and delay scaling of the achievable scheme, and show that the throughput and delay performance are order-optimal within a class of schemes. We then solve the caching optimization problem, and evaluate the network performance for a Zipf content popularity distribution, letting the number of content types and the network size both go to infinity. Finally, we extend our analysis to heterogeneous wireless networks where, in addition to wireless nodes, there are a number of base stations uniformly distributed at random in the network area. We show that in order to achieve a better performance in a heterogeneous network in the order sense, the number of base stations needs to be greater than the ratio of the number of nodes to the number of content types. Furthermore, we show that the heterogeneous network does not yield performance advantages in the order sense if the Zipf content popularity distribution exponent exceeds 3/2.

cs.NI↗