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Showing 2016 · math.PRShow all

19 papers · 2 filters

math.PR2016★ 7 cited

Mesoscopic scales in hierarchical configuration models

Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis

To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. The connections between the commun…

math.PR2016★ 1 cited

Slightly subcritical hypercube percolation

Tim Hulshof, Asaf Nachmias

We study bond percolation on the hypercube in the slightly subcritical regime where and but $\varepsilon_m \gg 2^{-m/…

math.PR2016★ 16 cited

Asymptotic Optimality of Power-of- Load Balancing in Large-Scale Systems

Debankur Mukherjee, Sem C. Borst, Johan S. H. van Leeuwaarden +1

We consider a system of identical server pools and a single dispatcher where tasks arrive as a Poisson process of rate . Arriving tasks cannot be queued, and must immedia…

math.PR2016★ 71 cited

Universality of Power-of- Load Balancing in Many-Server Systems

Debankur Mukherjee, Sem C. Borst, Johan S. H. van Leeuwaarden +1

We consider a system of parallel single-server queues with unit exponential service rates and a single dispatcher where tasks arrive as a Poisson process of rate . When a…

math.PR2016★ 36 cited

Heavy-tailed configuration models at criticality

Souvik Dhara, Remco van der Hofstad, Johan S. H. van Leeuwaarden +1

We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying functi…

math.PR2016★ 31 cited

Local clustering in scale-free networks with hidden variables

Remco van der Hofstad, A. J. E. M. Janssen, Johan S. H. van Leeuwaarden +1

We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out s…

math.PR2016

Scaling Laws for Maximum Coloring of Random Geometric Graphs

Sem Borst, Milan Bradonjić

We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant…

math.PR2016

Networks of fixed-cycle intersections

Marko Boon, Johan van Leeuwaarden

We present an algorithmic method for analyzing networks of intersections with static signaling, with as primary example a line network that allows traffic flow over several interse…

math.PR2016★ 3 cited

Heavy traffic analysis of roving server networks

Marko Boon, Rob van der Mei, Erik Winands

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal proce…

math.PR2016★ 3 cited

Corrected mean-field model for random sequential adsorption on random geometric graphs

Souvik Dhara, Johan S. H. van Leeuwaarden, Debankur Mukherjee

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the -dimensional Euclidean…

math.PR2016★ 8 cited

When is a scale-free graph ultra-small?

Remco van der Hofstad, Julia Komjathy

In this paper we study typical distances in the configuration model, when the degrees have asymptotically infinite variance. We assume that the empirical degree distribution follow…

math.PR2016★ 26 cited

Networks of Server Queues with Shot-Noise-Driven Arrival Intensities

David Koops, Michel Mandjes, Onno Boxma

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise…

math.PR2016

Time-dependent analysis of an preemptive priority system with two priority classes

Jori Selen, Brian Fralix

We analyze the time-dependent behavior of an priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More partic…

math.PR2016★ 48 cited

Critical window for the configuration model: finite third moment degrees

Souvik Dhara, Remco van der Hofstad, Johan S. H. van Leeuwaarden +1

We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that,…

math.PR2016

Transient error approximation in a Lévy queue

Britt Mathijsen, Bert Zwart

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization persp…

math.PR2016★ 26 cited

Structures in supercritical scale-free percolation

Markus Heydenreich, Tim Hulshof, Joost Jorritsma

Scale-free percolation is a percolation model on which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices…

math.PR2016★ 146 cited

A consensus-based model for global optimization and its mean-field limit

René Pinnau, Claudia Totzeck, Oliver Tse +1

We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, namely a consensus-based optimization (CBO) algorithm, which…

math.PR2016★ 7 cited

Generalized random sequential adsorption on Erdős-Rényi random graphs

Souvik Dhara, Johan S. H. van Leeuwaarden, Debankur Mukherjee

We investigate Random Sequential Adsorption (RSA) on a random graph via the following greedy algorithm: Order the vertices at random, and sequentially declare each vertex eithe…

math.PR2016

Scaling limits for infinite-server systems in a random environment

Mariska Heemskerk, Johan van Leeuwaarden, Michel Mandjes

This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arriv…