Methods for analyzing routing games:Information design, risk-averseness, and Braess's paradox

We study ways in which information about traffic networks can be used to achieve social objectives, such as decreasing experienced travel time. First we study how behaviour of drivers changes when the total amount of traffic changes. We give an exact characterization of this change in behaviour, which is computationally feasible to obtain. We then use insights obtained from deriving this characterization to consider the difficult problem of detecting Braess’s paradox in a network, where removal of a road leads to decreased travel time for all drivers. We give some new, efficient methods for detecting this phenomenon, and also show that in some cases the existence of Braess’s paradox in a network may be a good thing. Next we study traffic networks with potentially unpredictable travel costs. We investigate a scenario a central planner can strategically withhold information from drivers on the road to prevent congestion and benefit all road users. However, the planner’s strategy depends upon the prior beliefs about the roads that the drivers adhere to, and we study how a planner can derive these beliefs by observing the behaviour of the drivers.Finally we study the scenario where drivers are risk-averse, and can thus avoid roads that are quick on average, but can be significantly slowed in some cases

Wardrop equilibrium and Braess's paradox for varying demand

This work explores the relationship between the set of Wardrop equilibria~(WE) of a routing game, the total demand of that game, and the occurrence of Braess's paradox~(BP). The BP formalizes the counter-intuitive fact that for some networks, removing a path from the network decreases congestion at WE. For a single origin-destination routing games with affine cost functions, the first part of this work provides tools for analyzing the evolution of the WE as the demand varies. It characterizes the piece-wise affine nature of this dependence by showing that the set of directions in which the WE can vary in each piece is the solution of a variational inequality problem. In the process we establish various properties of changes in the set of used and minimal-cost paths as demand varies. As a consequence of these characterizations, we derive a procedure to obtain the WE for all demands above a certain threshold. The second part of the paper deals with detecting the presence of BP in a network. We supply a number of sufficient conditions that reveal the presence of BP and that are computationally tractable. We also discuss a different perspective on BP, where we establish that a path causing BP at a particular demand must be strictly beneficial to the network at a lower demand. Several examples throughout this work illustrate and elaborate our findings

Stochastic approximation for CVaR-based variational inequalities

In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to solve these VIs. We investigate convergence of these algorithms under various assumptions on the monotonicity of the VI and accuracy of the CVaR estimate. Our first algorithm is shown to converge to the exact solution of the VI when the estimation error of the CVaR becomes progressively smaller along any execution of the algorithm. When the estimation error is nonvanishing, we provide two algorithms that provably converge to a neighborhood of the solution of the VI. For these schemes, under strong monotonicity, we provide an explicit relationship between sample size, estimation error, and the size of the neighborhood to which convergence is achieved. A simulation example illustrates our theoretical findings

The cerebrovascular response to lower-body negative pressure vs. head-up tilt

Lower-body negative pressure (LBNP) has been proposed as a MRI-compatible surrogate for orthostatic stress. Although the effects of LBNP on cerebral hemodynamic behavior have been considered to reflect those of orthostatic stress, a direct comparison with actual orthostasis is lacking. We assessed the effects of LBNP (-50 mmHg) vs. head-up tilt (HUT; at 70°) in 10 healthy subjects (5 female) on transcranial Doppler-determined cerebral blood flow velocity (CBFv) in the middle cerebral artery and cerebral perfusion pressure (CPP) as estimated from the blood pressure signal (finger plethysmography). CPP was maintained during LBNP but decreased after 2 min in response to HUT, leading to an ~15% difference in CPP between LBNP and HUT (P ≤ 0.020). Mean CBFv initially decreased similarly in response to LBNP and for HUT, but, from minute 3 on, the decline became ~50% smaller (P ≤ 0.029) during LBNP. The reduction in end-tidal Pco2 partial pressure (PetCO2 ) was comparable but with an earlier return toward baseline values in response to LBNP but not during HUT (P = 0.008). We consider the larger decrease in CBFv during HUT vs. LBNP attributable to the pronounced reduction in PetCO2 and to gravitational influences on CPP, and this should be taken into account when applying LBNP as an MRI-compatible orthostatic stress modality.NEW & NOTEWORTHY Lower-body negative pressure (LBNP) has the potential to serve as a MRI-compatible surrogate of orthostatic stress but a comparison with actual orthostasis was lacking. This study showed that the pronounced reduction in end-tidal Pco2 together with gravitational effects on the brain circulation lead to a larger decline in cerebral blood flow velocity in response to head-up tilt than during lower-body negative pressure. This should be taken into account when employing lower-body negative pressure as MRI-compatible alternative to orthostatic stres

Assessment of middle cerebral artery diameter during hypocapnia and hypercapnia in humans using ultra-high-field MRI

In the evaluation of cerebrovascular CO2 reactivity measurements, it is often assumed that the diameter of the large intracranial arteries insonated by transcranial Doppler remains unaffected by changes in arterial CO2 partial pressure. However, the strong cerebral vasodilatory capacity of CO2 challenges this assumption, suggesting that there should be some changes in diameter, even if very small. Data from previous studies on effects of CO2 on cerebral artery diameter [middle cerebral artery (MCA)] have been inconsistent. In this study, we examined 10 healthy subjects (5 women, 5 men, age 21-30 yr). High-resolution (0.2 mm in-plane) MRI scans at 7 Tesla were used for direct observation of the MCA diameter during hypocapnia, -1 kPa (-7.5 mmHg), normocapnia, 0 kPa (0 mmHg), and two levels of hypercapnia, +1 and +2 kPa (7.5 and 15 mmHg), with respect to baseline. The vessel lumen was manually delineated by two independent observers. The results showed that the MCA diameter increased by 6.8 ± 2.9% in response to 2 kPa end-tidal P(CO2) (PET(CO2)) above baseline. However, no significant changes in diameter were observed at the -1 kPa (-1.2 ± 2.4%), and +1 kPa (+1.4 ± 3.2%) levels relative to normocapnia. The nonlinear response of the MCA diameter to CO2 was fitted as a continuous calibration curve. Cerebral blood flow changes measured by transcranial Doppler could be corrected by this calibration curve using concomitant PET(CO2) measurements. In conclusion, the MCA diameter remains constant during small deviations of the PET(CO2) from normocapnia, but increases at higher PET(CO2) value