Related papers: Spatial homogenization in a stochastic network wit…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
A critical aspect in strategic modeling of transportation systems is user heterogeneity. In many real-world scenarios, e.g., when tolls are charged and drivers have different trade-offs between time and money, or when they get informed…
Multi-class queueing networks (McQNs) extend the classical concept of Jackson network by allowing jobs of different classes to visit the same server. While such a generalization seems rather natural, from a structural perspective there is a…
Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. We discuss several applications which have…
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em finite} networks we establish stability and some steady-state moment bounds under natural…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms…
Distributed processing across a networked environment suffers from unpredictable behavior of speedup due to heterogeneous nature of the hardware and software in the remote machines. It is challenging to get a better performance from a…
Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…
Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative…