This paper proposes a new method to estimate the macroscopic volume delay function (VDF) from the point speed-flow measures. Contrary to typical VDF estimation methods it allows estimating speeds also for hypercritical traffic conditions, when both speeds and flow drop due to congestion (high density of traffic flow). We employ the well-known hydrodynamic relation of fundamental diagram to derive the so-called quasi-density from measured time-mean speeds and flows. This allows formulating the VDF estimation problem with a speed being monotonically decreasing function of quasi-density with a shape resembling the typical VDF like BPR. This way we can use the actually observed speeds and propose the macroscopic VDF realistically reproducing actual speeds also for hypercritical conditions. The proposed method is illustrated with half-year measurements from the induction loop system in city of Warsaw, which measured traffic flows and instantaneous speeds of over 5 million vehicles. Although the proposed method does not overcome the fundamental limitations of static macroscopic traffic models, which cannot represent dynamic traffic phenomena like queue, spillback, wave propagation, capacity drop, and so forth, we managed to improve the VDF goodness-of-fit fromR2of 27% to 72% most importantly also for hypercritical conditions. Thanks to this traffic congestion in macroscopic traffic models can be reproduced more realistically in line with empirical observations.
Bus bunching is a well-known problem in public transport networks. It is characterized by a self-amplifying relationship between uneven distribution of rising passenger loads and deteriorating service regularity. The focus of this study is to analyse whether this negative feedback loop can be addressed by providing real-time crowding information (RTCI) on next vehicle departures at stops. We integrate a departure choice model based on stated-preference analysis of passengers' willingness to wait with RTCI. A proof-ofconcept application to a toy-network model shows that this prevents further progression of bunching effects in certain demand conditions. The RTCI usage reveals substantial benefits -in terms of relative reductions in on-board (over)crowding, headway deviations, as well as mitigated denial-of-boarding risk -in moderately saturated network. These gains may diminish though as high overcrowding eventually emerges in PT network. Nevertheless, our findings indicate that RTCI has the potential to improve travel experience and service utilisation efficiency, even without resorting to supply-side control strategies.
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