Braess's Paradox and Power-Law Nonlinearities in Five-Arc and Six-Arc Two-Terminal Networks

Penchina, Claude M.

doi:10.2174/1874447800903010008

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…It could happen, even with positive travel times, if there are exactly compensating other negative costs (such as popular scenery, carefully adjusted monetary subsidies, etc). It may be a more realistic approximation for various other analogous physical networks (electrical, mechanical, and thermal [9][10][11] or water [12]), but then the analog of tolls is not obvious. A more clearly applicable analog might be a data network.…”

Section: Summary For Inelastic Demand and Power Law Congestion Costsmentioning

confidence: 99%

Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function

Penchina¹

2009

TOTJ

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Marginal-Cost (MC) tolls are known to produce economic efficiency of network flows. Yet, MC pricing has not been widely adopted, because of various perceived unpopular aspects, such as complexity, collection costs, and inequities. Minimal Revenue (MinRev) pricing has been suggested as a means to achieve most of the economic improvements of MC pricing with fewer unpopular aspects. One claimed improvement of MinRev tolls is the ability to maintain fixed tolls while flows change. We show that single-power-law congestion costs are sufficient (but not always necessary) conditions for the stability (flow independence) of Minimal-Revenue (MinRev) tolls in transportation networks, so long as the links that are actually used do not change. This is particularly important because the usual Bureau of Public Roads (BPR) cost function recommended as a good representation of real road traffic, has this single power-law congestion cost. For cases of elastic demand, these MinRev tolls do not achieve the full economic efficiency of Marginal-Cost (MC) tolls. However, they may still prove desirable because of greater stability, greater simplicity, lower out-ofpocket costs, and greater perceived equity. Furthermore, in cases of major congestion problems, where all links are used, the MinRev tolls are totally stable, i.e. totally independent of flows; also, if demand is relatively insensitive to price, the flows are nearly equal to the optimal flows obtained by MC pricing. The discussion is based on the equilibrium assignment method, with tolls to encourage System Optimal (SO) flows rather than User Optimal (UO) flows. Results are obtained for general networks, and also illustrated with a very simple example.

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Section: Summary For Inelastic Demand and Power Law Congestion Costsmentioning

confidence: 99%

Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function

Penchina¹

2009

TOTJ

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“…This illustrates the robustness of the phenomenon, given that our simulations are in two dimensions and three-dimensional effects are expected to be significant in the experiments. We note that different aspects of the paradox have been considered in fluid networks, but only for macroscopic (i.e., nonmicrofluidic) systems and while modeled by ad hoc flow 5 equations [37][38][39]. Analogs of the paradox have also been studied in several other areas, including electrical, mechanical, biological, and contemporary traffic networks [40][41][42][43][44].…”

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confidence: 99%

Braess’s paradox and programmable behaviour in microfluidic networks

Case

Liu

Kiss

et al. 2019

Nature

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Microfluidic systems are now being designed with precision to execute increasingly complex tasks. However, their operation often requires numerous external control devices due to the typically linear nature of microscale flows, which has hampered the development of integrated control mechanisms. We address this difficulty by designing microfluidic networks that exhibit a nonlinear relation between applied pressure and flow rate, which can be harnessed to switch the direction of internal flows solely by manipulating input and/or output pressures. We show that these networks exhibit an experimentally-supported fluid analog of Braess's paradox, in which closing an intermediate channel results in a higher, rather than lower, total flow rate. The harnessed behavior is scalable and can be used to implement flow routing with multiple switches. These findings have the potential to advance development of built-in control mechanisms in microfluidic networks, thereby facilitating the creation of portable systems that may one day be as controllable as microelectronic circuits. † Microfluidics' promise to operate as autonomous microscale networks where fluids can be transported, mixed, reacted, separated, and processed is no longer limited by experimental fabrication challenges but instead by difficulties to create built-in controls [1][2][3]. The development of the modern microelectronics that form the basis of computer microprocessors was ultimately determined by the creation of integrated circuits, with all components fabricated on the same substrate. Microfluidics have already reached a level of integration in which networks with thousands of components, including control devices, are built on a single compact chip. However, in contrast with electronic integrated circuits, existing onchip fluid control devices still need to be actuated externally. For example, microfluidic circuits fabricated from flexible polydimethylsiloxane (PDMS) can now incorporate a large number of control valves, which nevertheless have to be operated using control fluids through a control layer that lays on top of the working fluid network [4,5]. As a result, microfluidics are still predominantly controlled by external hardware despite significant efforts over the past twenty years to develop systems with new control schemes [6][7][8][9][10]. The construction of systems that forgo the current reliance on external hardware is crucial to further the development of portable microfluidic systems for pressing applications, ranging from point-of-care diagnostics and health monitoring wearables to analysis kits for field research [11][12][13][14]. This requires developing next-generation integrated circuits in which not only the control devices but also the operation of those devices is integrated on-chip. The development of such a level of integration has been fundamentally limited by the fact that, at the microscale, fluid flows tend to respond lin- † The final version of this paper was published early to pressure changes and thus cannot be easily ampl...

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Braess's Paradox and Power-Law Nonlinearities in Five-Arc and Six-Arc Two-Terminal Networks

Cited by 2 publications

References 9 publications

Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function

Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function

Braess’s paradox and programmable behaviour in microfluidic networks

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