Dynamic Erdős-Rényi Graphs

Mandjes, Michel; Starreveld, N.J.; Bekker, René; Spreij, Peter

doi:10.1007/978-3-319-91908-9_8

Cited by 8 publications

(6 citation statements)

References 15 publications

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“…In a recent contributions, results on dynamic random graphs have been reported; see e.g. [9,10,14,23]. Our paper can be regarded as being among the first to facilitate describing queueing processes on a randomly evolving graph (but it is noticed that the model we propose is substantially more general, as the multiplicative transitions are not restricted to node failures and repairs).…”

Section: Introductionmentioning

confidence: 96%

Networks of infinite-server queues with multiplicative transitions

Fiems

Mandjes

Patch

2018

Performance Evaluation

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This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a 'multiplicative transition'). For this model we characterize the joint probability generating function in terms of a system of partial differential equations; this system enables the evaluation of (transient as well as stationary) moments. We show that several relevant systems fit in the framework developed, such as networks of retrial queues, networks in which jobs can be rerouted when links fail, and storage systems. Numerical examples illustrate how our results can be used to support design problems.

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Section: Introductionmentioning

confidence: 96%

Networks of infinite-server queues with multiplicative transitions

Fiems

Mandjes

Patch

2018

Performance Evaluation

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“…Many real networks are dynamical, i.e., the pattern of interactions between their nodes vary over time, e.g., network of exchanged emails in a company. The abundance of such datasets and the development of optimal numerical methods have led to a growing number of studies in this field [1][2][3][4]. In addition, interactions between nodes can be reciprocated, e.g., the people whom one retweets and the number of times she retweets them vary over time; so do the papers that researchers cite in their manuscripts and papers that cite one's scientific output.…”

Section: Introductionmentioning

confidence: 99%

Reciprocity, community detection, and link prediction in dynamic networks

Safdari¹,

Contisciani²,

Bacco³

2021

Preprint

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Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to model dynamic interactions. Particular interest has been devoted to extend the stochastic block model and its variant, to capture community structure as the network changes in time. While these models assume that edge formation depends only on the community memberships, recent work for static networks show the importance to include additional parameters capturing structural properties, as reciprocity for instance. Remarkably, these models are capable of generating more realistic network representations than those that only consider community membership. To this aim, we present a probabilistic generative model with hidden variables that integrates reciprocity and communities as structural information of networks that evolve in time. The model assumes a fundamental order in observing reciprocal data, that is an edge is observed, conditional on its reciprocated edge in the past. We deploy a Markovian approach to construct the network's transition matrix between time steps and parameters' inference is performed with an Expectation-Maximization algorithm that leads to high computational efficiency because it exploits the sparsity of the dataset. We test the performance of the model on synthetic dynamical networks, as well as on real networks of citations and email datasets. We show that our model captures the reciprocity of real networks better than standard models with only community structure, while performing well at link prediction tasks.

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“…Where static random graphs form a classical topic in probability theory, dating back to the pioneering work of Erdős and Rényi [12] and Gilbert [15], only recently the behavior of randomly evolving graphs has received substantial attention; see e.g. [16,17,23,28] for a few examples. Examples of papers on random processes on (dynamic) random graphs are [3,9,10].…”

Section: Introductionmentioning

confidence: 99%

Queues on a Dynamically Evolving Graph

2018

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This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between 'up' and 'down'. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues' time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links' outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

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Dynamic Erdős-Rényi Graphs

Cited by 8 publications

References 15 publications

Networks of infinite-server queues with multiplicative transitions

Networks of infinite-server queues with multiplicative transitions

Reciprocity, community detection, and link prediction in dynamic networks

Queues on a Dynamically Evolving Graph

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