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Showing 2017 · math.PRShow all

19 papers · 2 filters

math.PR2017★ 15 cited

Triadic closure in configuration models with unbounded degree fluctuations

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

The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded deg…

math.PR2017★ 9 cited

Weighted distances in scale-free configuration models

Erwin Adriaans, Julia Komjathy

In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent . We assign indepe…

math.PR2017★ 29 cited

Asymptotically Optimal Load Balancing Topologies

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

We consider a system of servers inter-connected by some underlying graph topology . Tasks arrive at the various servers as independent Poisson processes of rate . Each…

math.PR2017★ 1 cited

Infinite-server queues with Hawkes input

David Koops, Mayank Saxena, Onno Boxma +1

In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentia…

math.PR2017★ 5 cited

Load Balancing in Large-Scale Systems with Multiple Dispatchers

Mark van der Boor, Sem Borst, Johan van Leeuwaarden

Load balancing algorithms play a crucial role in delivering robust application performance in data centers and cloud networks. Recently, strong interest has emerged in Join-the-Idl…

math.PR2017★ 10 cited

Explosion and distances in scale-free percolation

Remco van der Hofstad, Julia Komjathy

We investigate the weighted scale-free percolation (SFPW) model on . In the SFPW model, the vertices of are assigned i.i.d. weights $(W_x)_{x\in \mathbb…

math.PR2017

Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation

Onno Boxma, Ewan Cahen, David Koops +1

We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point i…

math.PR2017

Queue-length balance equations in multiclass multiserver queues and their generalizations

Marko Boon, Onno Boxma, Offer Kella +1

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epo…

math.PR2017★ 3 cited

Average nearest neighbor degrees in scale-free networks

Dong Yao, Pim van der Hoorn, Nelly Litvak

The average nearest neighbor degree (ANND) of a node of degree is widely used to measure dependencies between degrees of neighbor nodes in a network. We formally analyze ANND i…

math.PR2017★ 25 cited

Optimal Service Elasticity in Large-Scale Distributed Systems

Debankur Mukherjee, Souvik Dhara, Sem Borst +1

A fundamental challenge in large-scale cloud networks and data centers is to achieve highly efficient server utilization and limit energy consumption, while providing excellent use…

math.PR2017

Rare-event analysis of mixed Poisson random variables, and applications in staffing

Mariska Heemskerk, Julia Kuhn, Michel Mandjes

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to…

math.PR2017★ 27 cited

Universality for critical heavy-tailed network models: Metric structure of maximal components

Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad +1

We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed…

math.PR2017★ 18 cited

The dynamics of power laws: Fitness and aging in preferential attachment trees

Alessandro Garavaglia, Remco van der Hofstad, Gerhard Woeginger

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching proce…

math.PR2017★ 2 cited

Occupation times for the finite buffer fluid queue with phase-type ON-times

N. J. Starreveld, R. Bekker, M. Mandjes

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fr…

math.PR2017

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

Mahmoud Talebi, Jan Friso Groote, Jean-Paul Linnartz

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded numb…

math.PR2017

Heavy-traffic approximations for a layered network with limited resources

Angelos Aveklouris, Maria Vlasiou, Jiheng Zhang +1

Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nod…

math.PR2017★ 7 cited

Expansion of percolation critical points for Hamming graphs

Lorenzo Federico, Remco van der Hofstad, Frank den Hollander +1

The Hamming graph is the Cartesian product of complete graphs on vertices. Let be the degree and be the number of vertices of . Let $p…

math.PR2017

Two queues with random time-limited polling

Mayank Saxena, Onno Boxma, Stella Kapodistria +1

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server…

math.PR2017★ 2 cited

Pollaczek contour integrals for the fixed-cycle traffic-light queue

Marko Boon, A. J. E. M. Janssen, Johan S. H. van Leeuwaarden +1

The fixed-cycle traffic-light (FCTL) queue is the standard model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by…