J.S.H. van Leeuwaarden

Achieving target throughputs in random-access networks

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector of back-off rates that achieves this throughput vector. This result entails proving global invertibility of the non-linear function that describes the throughputs of all nodes in the network. We present several numerical procedures for calculating this inverse, based on fixed-point iteration and Newtons method. Finally, we provide closed-form results for several special conflict graphs using the theory of Markov random fields.

Universality of load balancing schemes on the diffusion scale

We consider a system of

Equalizing throughputs in random-access networks

N

Throughput of CSMA networks with buffer dynamics

parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among d randomly selected servers otherwise

Delay performance of backlog based random access

(1 \leq d \leq N)

CSMA networks in a many-sources regime: A mean-field approach

. This load balancing scheme subsumes the so-called Join-the-Idle Queue (JIQ) policy

Queues with random back-offs

(d = 1)

Efficient load balancing in large-scale systems

and the celebrated Join-the-Shortest Queue (JSQ) policy

Slow Transitions and Starvation in Dense Random-Access Networks

(d = N)

Spatial mean-field limits for ultra-dense random-access networks

as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin-Whitt heavy-traffic regime, and establish that it does not depend on the value of