Johan S. H. van Leeuwaarden
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Johan S. H. van Leeuwaarden has a total of 52 co-authors. Here are the top co-authors by number of shared publications:
- Augustus J. E. M. Janssen
Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands
11 shared publications - Charles Knessl
University of Illinois at Chicago
10 shared publications - Sem C. Borst
Eindhoven University of Technology, Eindhoven, Netherlands
9 shared publications - Remco van der Hofstad
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
7 shared publications - Augustus. J. E. M. Janssen
Philips Research
5 shared publications - Fabrice Guillemin
Orange Labs, Lannion, France
4 shared publications
Latest Publications
- 1 August 2019
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 44 (3) , 821-864
Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations
We consider a single-server queue that serves a finite population of n customers that will enter the queue (require service) only once, also known as the Δ(i)/G/1 queue. This paper presents a metho...
- 1 August 2019
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 44 (3) , 821-864
Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations
We consider a single-server queue that serves a finite population of n customers that will enter the queue (require service) only once, also known as the Δ(i)/G/1 queue. This paper presents a metho...
- Open Access
Asymptotically Optimal Load Balancing Topologies
We consider a system of $N$ servers inter-connected by some underlying graph topology $G_N$. Tasks arrive at the various servers as independent Poisson processes of rate $\lambda$. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in $G_N$. Tasks have unit-mean exponential service times and leave the system upon service completion. The above model has been extensively investigated in the case $G_N$ is a clique. Since the servers are exchangeable in that case, the queue length process is quite tractable, and it has been proved that for any $\lambda < 1$, the fraction of servers with two or more tasks vanishes in the limit as $N \to \infty$. For an arbitrary graph $G_N$, the lack of exchangeability severely complicates the analysis, and the queue length process tends to be worse than for a clique. Accordingly, a graph $G_N$ is said to be $N$-optimal or $\sqrt{N}$-optimal when the occupancy process on $G_N$ is equivalent to that on a clique on an $N$-scale or $\sqrt{N}$-scale, respectively. We prove that if $G_N$ is an Erd\H{o}s-R\'enyi random graph with average degree $d(N)$, then it is with high probability $N$-optimal and $\sqrt{N}$-optimal if $d(N) \to \infty$ and $d(N) / (\sqrt{N} \log(N)) \to \infty$ as $N \to \infty$, respectively. This demonstrates that optimality can be maintained at $N$-scale and $\sqrt{N}$-scale while reducing the number of connections by nearly a factor $N$ and $\sqrt{N} / \log(N)$ compared to a clique, provided the topology is suitably random. It is further shown that if $G_N$ contains $\Theta(N)$ bounded-degree nodes, then it cannot be $N$-optimal. In addition, we establish that an arbitrary graph $G_N$ is $N$-optimal when its minimum degree is $N - o(N)$, and may not be $N$-optimal even when its minimum degree is $c N + o(N)$ for any $0 < c < 1/2$.Open AccessAsymptotically Optimal Load Balancing Topologies
We consider a system of $N$ servers inter-connected by some underlying graph topology $G_N$. Tasks arrive at the various servers as independent Poisson processes of rate $\lambda$. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in $G_N$. Tasks have unit-mean exponential service times and leave the system upon service completion. The above model has been extensively investigated in the case $G_N$ is a clique. Since the servers are exchangeable in that case, the queue length process is quite tractable, and it has been proved that for any $\lambda < 1$, the fraction of servers with two or more tasks vanishes in the limit as $N \to \infty$. For an arbitrary graph $G_N$, the lack of exchangeability severely complicates the analysis, and the queue length process tends to be worse than for a clique. Accordingly, a graph $G_N$ is said to be $N$-optimal or $\sqrt{N}$-optimal when the occupancy process on $G_N$ is equivalent to that on a clique on an $N$-scale or $\sqrt{N}$-scale, respectively. We prove that if $G_N$ is an Erd\H{o}s-R\'enyi random graph with average degree $d(N)$, then it is with high probability $N$-optimal and $\sqrt{N}$-optimal if $d(N) \to \infty$ and $d(N) / (\sqrt{N} \log(N)) \to \infty$ as $N \to \infty$, respectively. This demonstrates that optimality can be maintained at $N$-scale and $\sqrt{N}$-scale while reducing the number of connections by nearly a factor $N$ and $\sqrt{N} / \log(N)$ compared to a clique, provided the topology is suitably random. It is further shown that if $G_N$ contains $\Theta(N)$ bounded-degree nodes, then it cannot be $N$-optimal. In addition, we establish that an arbitrary graph $G_N$ is $N$-optimal when its minimum degree is $N - o(N)$, and may not be $N$-optimal even when its minimum degree is $c N + o(N)$ for any $0 < c < 1/2$. - Open Access
- 18 February 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 175 (1) , 161-184
Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs
- 18 February 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 175 (1) , 161-184
Open AccessCounting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs
- Open Access
- 11 December 2018
- Published by Springer Nature in Queueing Systems
- Vol. 91 (1-2) , 89-111
Pollaczek contour integrals for the fixed-cycle traffic-light queue
- 11 December 2018
- Published by Springer Nature in Queueing Systems
- Vol. 91 (1-2) , 89-111
Open AccessPollaczek contour integrals for the fixed-cycle traffic-light queue
- Open Access
- 3 March 2018
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 171 (1) , 38-95
Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent \(\tau \in (3,4)\), the sequence of clusters ordered in decreasing size and multiplied through by \(n^{-(\tau -2)/(\tau -1)}\) converges as \(n\rightarrow \infty \) to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237–269, 2001) for the Erdős–Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.- 3 March 2018
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 171 (1) , 38-95
Open AccessCluster Tails for Critical Power-Law Inhomogeneous Random Graphs
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent \(\tau \in (3,4)\), the sequence of clusters ordered in decreasing size and multiplied through by \(n^{-(\tau -2)/(\tau -1)}\) converges as \(n\rightarrow \infty \) to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237–269, 2001) for the Erdős–Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments. - Open Access
Spitzer's identity for discrete random walks
Spitzer's identity describes the position of a reflected random walk over time in terms of a bivariate transform. Among its many applications in probability theory are congestion levels in queues and random walkers in physics. We present a new derivation of Spitzer's identity under the assumption that the increments of the random walk have bounded jumps to the left. This mild assumption facilitates a proof of Spitzer's identity that only uses basic properties of analytic functions and contour integration. The main novelty, believed to be of broader interest, is a reversed approach that recognizes a factored polynomial expression as the outcome of Cauchy's formula.
Open AccessSpitzer's identity for discrete random walks
Spitzer's identity describes the position of a reflected random walk over time in terms of a bivariate transform. Among its many applications in probability theory are congestion levels in queues and random walkers in physics. We present a new derivation of Spitzer's identity under the assumption that the increments of the random walk have bounded jumps to the left. This mild assumption facilitates a proof of Spitzer's identity that only uses basic properties of analytic functions and contour integration. The main novelty, believed to be of broader interest, is a reversed approach that recognizes a factored polynomial expression as the outcome of Cauchy's formula.
- Open Access
Optimal Service Elasticity in Large-Scale Distributed Systems
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 user-perceived performance in the presence of uncertain and time-varying demand patterns. Auto-scaling provides a popular paradigm for automatically adjusting service capacity in response to demand while meeting performance targets, and queue-driven auto-scaling techniques have been widely investigated in the literature. In typical data center architectures and cloud environments however, no centralized queue is maintained, and load balancing algorithms immediately distribute incoming tasks among parallel queues. In these distributed settings with vast numbers of servers, centralized queue-driven auto-scaling techniques involve a substantial communication overhead and major implementation burden, or may not even be viable at all. Motivated by the above issues, we propose a joint auto-scaling and load balancing scheme which does not require any global queue length information or explicit knowledge of system parameters, and yet provides provably near-optimal service elasticity. We establish the fluid-level dynamics for the proposed scheme in a regime where the total traffic volume and nominal service capacity grow large in proportion. The fluid-limit results show that the proposed scheme achieves asymptotic optimality in terms of user-perceived delay performance as well as energy consumption. Specifically, we prove that both the waiting time of tasks and the relative energy portion consumed by idle servers vanish in the limit. At the same time, the proposed scheme operates in a distributed fashion and involves only constant communication overhead per task, thus ensuring scalability in massive data center operations.
Open AccessOptimal Service Elasticity in Large-Scale Distributed Systems
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 user-perceived performance in the presence of uncertain and time-varying demand patterns. Auto-scaling provides a popular paradigm for automatically adjusting service capacity in response to demand while meeting performance targets, and queue-driven auto-scaling techniques have been widely investigated in the literature. In typical data center architectures and cloud environments however, no centralized queue is maintained, and load balancing algorithms immediately distribute incoming tasks among parallel queues. In these distributed settings with vast numbers of servers, centralized queue-driven auto-scaling techniques involve a substantial communication overhead and major implementation burden, or may not even be viable at all. Motivated by the above issues, we propose a joint auto-scaling and load balancing scheme which does not require any global queue length information or explicit knowledge of system parameters, and yet provides provably near-optimal service elasticity. We establish the fluid-level dynamics for the proposed scheme in a regime where the total traffic volume and nominal service capacity grow large in proportion. The fluid-limit results show that the proposed scheme achieves asymptotic optimality in terms of user-perceived delay performance as well as energy consumption. Specifically, we prove that both the waiting time of tasks and the relative energy portion consumed by idle servers vanish in the limit. At the same time, the proposed scheme operates in a distributed fashion and involves only constant communication overhead per task, thus ensuring scalability in massive data center operations.
- Open Access
Critical window for the configuration model: finite third moment degrees
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, at criticality, the finite third moment assumption on the asymptotic degree distribution is enough to guarantee that the sizes of the largest connected components are of the order $n^{2/3}$ and the re-scaled component sizes (ordered in a decreasing manner) converge to the ordered excursion lengths of an inhomogeneous Brownian Motion with a parabolic drift. We use percolation to study the evolution of these component sizes while passing through the critical window and show that the vector of percolation cluster-sizes, considered as a process in the critical window, converge to the multiplicative coalescent process in the sense of finite dimensional distributions. This behavior was first observed for Erd\H{o}s-R\'enyi random graphs by Aldous (1997) and our results provide support for the empirical evidences that the nature of the phase transition for a wide array of random-graph models are universal in nature. Further, we show that the re-scaled component sizes and surplus edges converge jointly under a strong topology, at each fixed location of the scaling window.Open AccessCritical window for the configuration model: finite third moment degrees
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, at criticality, the finite third moment assumption on the asymptotic degree distribution is enough to guarantee that the sizes of the largest connected components are of the order $n^{2/3}$ and the re-scaled component sizes (ordered in a decreasing manner) converge to the ordered excursion lengths of an inhomogeneous Brownian Motion with a parabolic drift. We use percolation to study the evolution of these component sizes while passing through the critical window and show that the vector of percolation cluster-sizes, considered as a process in the critical window, converge to the multiplicative coalescent process in the sense of finite dimensional distributions. This behavior was first observed for Erd\H{o}s-R\'enyi random graphs by Aldous (1997) and our results provide support for the empirical evidences that the nature of the phase transition for a wide array of random-graph models are universal in nature. Further, we show that the re-scaled component sizes and surplus edges converge jointly under a strong topology, at each fixed location of the scaling window. - Open Access
Robust heavy-traffic approximations for service systems facing overdispersed demand
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.
Open AccessRobust heavy-traffic approximations for service systems facing overdispersed demand
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.
- Open Access
Networks of fixed-cycle intersections
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 intersections in one main direction. The method decomposes the network into separate intersections and treats each intersection in isolation using an extension of the fixed-cycle traffic-light (FCTL) queue. The network effects are modeled by matching the output process of one intersection with the input process of the next (downstream) intersection. This network analysis provides insight into wave phenomena due to vehicles experiencing progressive cascades of green lights and sheds light on platoon forming in case of imperfections. Our algorithm is shown to match results from extensive discrete-event simulations and can also be applied to more complex network structures.
Open AccessNetworks of fixed-cycle intersections
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 intersections in one main direction. The method decomposes the network into separate intersections and treats each intersection in isolation using an extension of the fixed-cycle traffic-light (FCTL) queue. The network effects are modeled by matching the output process of one intersection with the input process of the next (downstream) intersection. This network analysis provides insight into wave phenomena due to vehicles experiencing progressive cascades of green lights and sheds light on platoon forming in case of imperfections. Our algorithm is shown to match results from extensive discrete-event simulations and can also be applied to more complex network structures.