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Register a new userOn the Minimum Achievable Age of Information for General Service-Time Distributions
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Added by
Jaya Prakash Champati Dr
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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There is a growing interest in analysing the freshness of data in networked systems. Age of Information (AoI) has emerged as a popular metric to quantify this freshness at a given destination. There has been a significant research effort in optimizing this metric in communication and networking systems under different settings. In contrast to previous works, we are interested in a fundamental question, what is the minimum achievable AoI in any single-server-single-source queuing system for a given service-time distribution? To address this question, we study a problem of optimizing AoI under service preemptions. Our main result is on the characterization of the minimum achievable average peak AoI (PAoI). We obtain this result by showing that a fixed-threshold policy is optimal in the set of all randomized-threshold causal policies. We use the characterization to provide necessary and sufficient conditions for the service-time distributions under which preemptions are beneficial.
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In cloud storage systems with a large number of servers, files are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze the mean latency of such a split-and-replicate cloud storage system under general sub-exponential service time. We present a novel scheduling scheme that utilizes the load-balancing policy of the textit{power of $d$ $(geq 2)$} choices. An alternative to split-and-replicate is to use erasure-codes, and recently, it has been observed that they can reduce latency in data access (see cite{longbo_delay} for details). We argue that under high redundancy (integer redundancy factor strictly greater than or equal to 2) regime, the mean latency of a coded system is upper bounded by that of a split-and-replicate system (with same replication factor) and the gap between these two is small. We validate this claim numerically under different service distributions such as exponential, shift plus exponential and the heavy-tailed Weibull distribution and compare the mean latency to that of an unsplit-replicated system. We observe that the coded system outperforms the unsplit-replication system by at least $20%$. Furthermore, we consider the mean latency for an erasure coded system with low redundancy (fractional redundancy factor between 1 and 2), a scenario which is more pragmatic, given the storage constraints (cite{rashmi_thesis}). However under this regime, we restrict ourselves to the special case of exponential service time distribution and use the randomized load balancing policy namely textit{batch-sampling}. We obtain an upper bound on mean delay that depends on the order statistics of the queue lengths, which, we further smooth out via a discrete to continuous approximation.
We consider a transmission scheduling problem in which multiple systems receive update information through a shared Time Division Multiple Access (TDMA) channel. To provide timely delivery of update information, the problem asks for a schedule that minimizes the overall age of information. We call this problem the Min-Age problem. This problem is first studied by He textit{et al.} [IEEE Trans. Inform. Theory, 2018], who identified several special cases where the problem can be solved optimally in polynomial time. Our contribution is threefold. First, we introduce a new job scheduling problem called the Min-WCS problem, and we prove that, for any constant $r geq 1$, every $r$-approximation algorithm for the Min-WCS problem can be transformed into an $r$-approximation algorithm for the Min-Age problem. Second, we give a randomized 2.733-approximation algorithm and a dynamic-programming-based exact algorithm for the Min-WCS problem. Finally, we prove that the Min-Age problem is NP-hard.
In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the destination. We obtain a general formula of the stationary distribution of the AoI, under the assumption of ergodicity. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI) metric. Furthermore, we consider three different single-server system models and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. The first model is a first-come-first-served (FCFS) queue, the second model is a preemptive last-come-first-served (LCFS) queue, and the last model is a bufferless system with packet dropping. We build upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems, using representations of functions as power series.
The main contribution of this paper is to design an Information Retrieval (IR) technique based on Algorithmic Information Theory (using the Normalized Compression Distance- NCD), statistical techniques (outliers), and novel organization of data base structure. The paper shows how they can be integrated to retrieve information from generic databases using long (text-based) queries. Two important problems are analyzed in the paper. On the one hand, how to detect false positives when the distance among the documents is very low and there is actual similarity. On the other hand, we propose a way to structure a document database which similarities distance estimation depends on the length of the selected text. Finally, the experimental evaluations that have been carried out to study previous problems are shown.
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($Phi$) in the brain is related to the level of consciousness. IIT proposes that to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that if a measure of $Phi$ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of $Phi$ is submodular, the lat
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