Introduction to linear and nonlinear programming

https://www-sop.inria.fr/members/Eitan.Altman/PAPERS/srvUpdate.pdf

A survey on networking games in telecommunications

/pdf/the-powermatcher-smart-coordination-for-the-smart-21kvidaf2r.pdf

The PowerMatcher: Smart Coordination for the Smart Electricity Grid

In this paper, a time-varying pricing model of a road bottleneck with elastic traffic demand is formulated using the optimal control theory. It is assumed that the optimal use of the bottleneck is achieved when social benefit over the whole time horizon of study is maximized. The necessary conditions for optimal solution are derived and their economic interpretations are given. Different from conventional analyses, queuing is not pre-assumed to be zero when obtaining the optimal time-varying toll, and the exit capacity of the bottleneck is assumed either to be constant or to vary with queue length. An approximate iterative algorithm is proposed for solving the model in a discrete time version. Three numerical examples are presented to demonstrate the applications of the proposed model and algorithm.

Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory

In classical traffic flow theory, there are two velocities associated with a given level of traffic flow. Following Vickrey, economists have termed travel at the higher speed congested travel and at the lower speed hypercongested travel. Since the publication of Walters. classic paper, there has been an on-going debate concerning whether a steady-state hypercongested equilibrium can be stable. For a particular structural model of downtown traffic flow and parking, this paper demonstrates that a steady-state hypercongested equilibrium can be stable. Some other sensible models of traffic congestion conclude that steady-state hypercongested travel cannot be stable, and that queues develop to ration the demand in steady states. Thus, we interpret our result to imply that, when steady-state demand is so high that it cannot be rationed through congested travel, the trip price increase necessary to ration the demand may be generated either through the formation of steady-state queues or through hypercongested travel, and that which mechanism occurs depends on details of the traffic system.

The Stability of Downtown Parking and Traffic Congestion

The theory of congestion tolls

Two analytic models of a store-and-forward communications network are constructed, one to find the optimal message routing and the other to illustrate the equilibrium (stationary state) maintained by an adaptive routing algorithm. These models show that adaptive routing does not satisfy the necessary conditions for an optimal routing. Adaptive routing tends to overuse the direct path and underuse alternate routes because it does not consider the impact of its current routing decision on the future state of the network. The form of the optimality conditions suggests that a modification of the adaptive algorithm will result in optimality. The modification requires the substitution of a quadratic bias term instead of a linear one in the routing table maintained at each network node. Simulation results are presented which confirm the theoretical analysis for a simple network.

Carson E. Agnew

Papers

The theory of congestion tolls

On quadratic adaptive routing algorithms