Probability, Stochastic Processes, and Queueing Theory

Nelson, Randolph

doi:10.1007/978-1-4757-2426-4

Cited by 344 publications

(152 citation statements)

References 21 publications

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“…We show that an accurate analytical estimate S* for the slow-down S observed in empirical temporal networks can be calculated based on the eigenvalue spectrum of higher-order, time-aggregated representations of temporal networks. Our approach uses a state space expansion to obtain a higher-order Markovian representation of non-Markovian temporal networks 40 . This means that a non-Markovian sequence of interactions in which the next interaction only depends on the previous one (that is, one-step memory) can be modelled by a Markovian stochastic process that generates a sequence of two-paths.…”

Section: Resultsmentioning

confidence: 99%

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

et al. 2014

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Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.

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Section: Resultsmentioning

confidence: 99%

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

et al. 2014

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“…Loss probability and its minimization [15] [16] [17] [18] As there is a waiting room with just one place is available in the system, the probability that the two servers are busy and the waiting room has a customer is E. A. Kamel equivalent to the probability of loss of customers in the system. That is, Formula (48) is equal to the loss probability.…”

Section: E a Kamelmentioning

confidence: 99%

Minimizing the Loss Probability in M/M/2/1 Queueing System with Ordered Entry

Kamel¹

2018

AJOR

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This study analyzed the M/M/2/1 queueing model with queue of length one (waiting room of capacity just one), heterogeneous servers and ordered entry using the method of semi-Markov process. The customers who arrive in the system enter the free server; if the two servers are free, the customers enter the first server. If the two servers are busy, just one customer can wait at the waiting room. If the two servers are busy and the waiting room has a customer, the following customers will leave the system without receiving any service. Such a customer is called LOST COSTOMER. The probability of lost customers in the queueing system under examination was computed. Furthermore, by using inequality shown that the loss probability was minimum when inter-arrival times fit deterministic distribution [1] [2].

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“…The probabilistic prediction involves computing the convolution of the score distributions of different index lists. To this end, we explore a variety of techniques including histograms, efficiently evaluable Poisson estimations, and convolutions based on moment-generating functions with generalized ChernoffHoeffding bounds [32,35] for the resulting tail probabilities. As the overhead of these techniques is crucial, the details of our bookkeeping and candidate testing strategies are all but straightforward; we explore a range of strategies based on different setups of priority queues.…”

Section: Contributionmentioning

confidence: 99%

“…With uniform distributions f i (x) plugged in, this yields a function from which we cannot easily infer the density of the convolution. Instead, we apply ChernoffHoeffding bounds to the tail probability of the convolution [32,35]:…”

Section: Guarantees With Uniform Distributionsmentioning

confidence: 99%

Top-k Query Evaluation with Probabilistic Guarantees

Theobald

Weikum

Schenkel

et al. 2004

Proceedings 2004 VLDB Conference

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Top-k queries based on ranking elements of multidimensional datasets are a fundamental building block for many kinds of information discovery. The best known general-purpose algorithm for evaluating top-k queries is Fagin's threshold algorithm (TA). Since the user's goal behind top-k queries is to identify one or a few relevant and novel data items, it is intriguing to use approximate variants of TA to reduce run-time costs. This paper introduces a family of approximate top-k algorithms based on probabilistic arguments. When scanning index lists of the underlying multidimensional data space in descending order of local scores, various forms of convolution and derived bounds are employed to predict when it is safe, with high probability, to drop candidate items and to prune the index scans. The precision and the efficiency of the developed methods are experimentally evaluated based on a large Web corpus and a structured data collection.

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Probability, Stochastic Processes, and Queueing Theory

Cited by 344 publications

References 21 publications

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Minimizing the Loss Probability in M/M/2/1 Queueing System with Ordered Entry

Top-k Query Evaluation with Probabilistic Guarantees

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