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We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…
We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for…
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism…
A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…
A current trend in networking and cloud computing is to provide compute resources over widely dispersed places exemplified by initiatives like Network Function Virtualisation. This paves the way for a widespread service deployment and can…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…
This paper considers a wireless link with randomly arriving data that is queued and served over a time-varying channel. It is known that any algorithm that comes within $\epsilon$ of the minimum average power required for queue stability…
In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…
This paper studies the problem of congestion control and scheduling in ad hoc wireless networks that have to support a mixture of best-effort and real-time traffic. Optimization and stochastic network theory have been successful in…
We analyze the problem of scheduling in wireless networks to meet end-to-end service guarantees, defined by instantaneous throughput and hard packet deadlines. Using a network slicing model to decouple the queueing dynamics between flows,…
We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…
We describe a competetive equillibrium in a railway cargo transportation model. We reduce the problem of finding this equillibrium to the solution of to mutually dual convex optimization problems. According to L.V. Kantorvich we interpret…
In this study, we formulate the VSL control problem for the traffic system in a zone upstream to a lane-drop bottleneck based on two traffic flow models: the Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional partial…
We introduce a macroscopic model for a network of conveyor belts with various speeds and capacities. In a different way from traffic flow models, the product densities are forced to move with a constant velocity unless they reach a maximal…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and…
Vehicle bypassing is known to negatively affect delays at traffic diverges. However, due to the complexities of this phenomenon, accurate and yet simple models of such lane change maneuvers are hard to develop. In this work, we present a…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
We study the power of (competitive) algorithms with predictions in a multiagent setting. To this goal, we introduce a multiagent version of the ski-rental problem. In this problem agents can collaborate by pooling resources to get a group…
This paper aims at coordinating interconnected agents where the control input of each agent is limited by the control input of others. In that sense, the systems have to share a limited resource over a network. Such problems can arise in…