Related papers: Proportional fairness and its relationship with mu…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…
Fair division is typically framed from a centralized perspective. However, in practice resource allocation often occurs via decentralized networks. We study a decentralized variant of fair division inspired by altruistic dynamics observed…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
While queueing network models are powerful tools for analyzing service systems, they traditionally require substantial human effort and domain expertise to construct. To make this modeling approach more scalable and accessible, we propose a…
In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel--Legendre transform of the network capacity region. We use this characterization to prove…
In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another.…
In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural…
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
In previous papers we developed a deterministic fluid approximation for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…
A heterogeneous closed network with one-server queues with finite capacity and one infinite-server queue is studied. A target application is bike-sharing systems. Heterogeneity is taken into account through clusters whose queues have the…
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an…
Robustness of distributed routing policies is studied for dynamical flow networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical flow network is modeled as a system of ordinary differential…
The mathematical approaches for modeling dynamic traffic can roughly be divided into two categories: discrete packet routing models and continuous flow over time models. Despite very vital research activities on models in both categories,…
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…
We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…
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…
A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity $K$, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal.…
We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…