Related papers: Fluid limits for networks with bandwidth sharing a…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
Spreading (diffusion) of innovations is a stochastic process on social networks. When the key driving mechanism is peer effects (word of mouth), the rate at which the aggregate adoption level increases with time depends strongly on the…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
We consider a single-hop switched queueing network. Amongst a plethora of applications, these networks have been used to model wireless networks and input queued switches. The MaxWeight scheduling policies have proved popular, chiefly,…
We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We…
Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of the multidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and…
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…
In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…
We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow…
Consider a network of $n$ single-server queues where tasks arrive independently at each server at rate $\lambda_n$. The servers are connected by a graph that is resampled at rate $\mu_n$ in a way that is symmetric with respect to the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
Network traffic analysis increasingly uses complex machine learning models as the internet consolidates and traffic gets more encrypted. However, over high-bandwidth networks, flows can easily arrive faster than model inference rates. The…
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian…
This work addresses the problem of evaluating optimal link capacities of a packet-flow network for the objective of congestion minimization. We present a simple model of packet flow in networks and present a numerical approach to evaluate…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…