Macroscopic network-level traffic models: Bridging fifty years of development toward the next era

Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

“…The aggregated modeling of urban networks has a long history dating back to Godfrey (1969), and numerous theories and models have been published since; see Johari et al (2021) for a recent review and reference therein. The starting point for all macroscopic urban models is the reservoir (or bathtub) model for cities, which simply states the conservation of Q(t), the number of vehicles inside the network at time t:…”

“…To fill this gap, section 2 below uses the framework proposed in Jin (2020) to derive analytical solutions of the tripbased model and to characterize its steady state, which coincides with the accumulation-based model independently of the trip-length distribution. Perhaps a more important gap in the literature is that the stochastic nature of arrival flows has been completely neglected, at least when it comes to analytical formulations; see Johari et al (2021). Section 3 fills this gap by drawing the analogy with the M/G/∞ queue and shows that accumulations exhibit a much larger variance than predicted by the M/G/∞ queue, due to the nonlinear dynamics imposed by the MFD.…”

Effect of the Trip-Length Distribution on Network-Level Traffic Dynamics: Exact and Statistical Results

“…He points out that extracting dynamic behavior from the model is possible for slow-varying demands, providing the foundations for the macroscopic modeling of cities. Despite some confusion in the literature (Jin, 2020, Johari et al, 2021, Batista et al, 2021b, Martínez and Jin, 2021, Johari et al, 2022, the role played by the exponential distribution in this model surfaced in the literature not until Arnott (2013) who considers it an unrealistic assumption. As it turns out, this important observation that (3) follows from assuming exponentially distributed trip lengths, appears to have its origins in Vickrey (1991) although it was not published until Vickrey (2020) as described in Jin (2020).…”

“…To fill this gap, section 2 below uses the framework proposed in Jin (2020) to derive analytical solutions of the trip-based model and to characterize its steady state, which coincides with the accumulation-based model independently of the trip-length distribution. Perhaps a more important gap in the literature is that the stochastic nature of arrival flows has been completely neglected, at least when it comes to analytical formulations; see Johari et al (2021). Section 3 fills this gap by drawing the analogy with the M/G/∞ queue and shows that accumulations exhibit a much larger variance than predicted by the M/G/∞ queue, due to the nonlinear dynamics imposed by the MFD.…”

Partitioning of urban networks with polycentric congestion pattern for traffic management policies: Identifying protected networks

“…Recently, studies have confirmed that urban traffic networks can be managed efficiently by implementing perimeter control policies (Keyvan‐Ekbatani et al., 2012), which are designed to limit the number of vehicles entering the busiest part of a network to avoid over‐saturated conditions, based on the notion of network macroscopic fundamental diagram (MFD or NMFD) (Geroliminis & Daganzo, 2008; Johari et al., 2021). Such NMFD‐based policies rely on relationships between traffic variables (i.e., flow vs. density) measured at the network level in a protected network (PN) or restricted zone (RZ; PN or RZ is conceptually similar to pricing cordon).…”