1 Introduction
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first, we propose a methodology to assess traffic microsimulation tools’ validity in correctly predicting global traffic behavior in the bottleneck sections of urban highways. More precisely, we focus on point-based diverges, i.e. one lane leading to two different lanes), and on extended merges, i.e. two different lanes leading to a two-lane edge reduced downstream to one lane. This methodology consists in comparing the microsimulation tools’ results with recognized analytical formulations,
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second, this methodology is applied to three existing tools. Two open-source ones, SymuVia and SUMO, and one commercial, Aimsun, are chosen for a market-representative pool. For the sake of conciseness, no more tools are considered.
2 Presentation and operation of microscopic simulation tools
2.1 How microscopic simulation tools reproduce traffic flow situations
2.1.1 Car-following models
2.1.2 Lane change models
2.1.3 Drivers’ and vehicles’ heterogeneity
2.2 Presentation of the three microscopic simulation tools
2.2.1 The need for a shared macroscopic basis
Parameter | Notation | Value |
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Free flow speed | U | 70 km/h |
Backward wave speed | W | 19.4 km/h |
Jam density (one lane) | K | 150 veh/km |
Capacity (one lane) | \(q_x\) | 2282 veh/h |
Parameter | Notation | Value |
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Desired speed (of vehicle i) | u (\(u_i\)) | 70 km/h |
Vehicle length (of vehicle i) | l (\(l_i\)) | 5 m |
Minimum relative gap | \(g_{\min }\) | 1.67 m |
Minimum relative headway | \(\tau\) | 1.23 s |
Maximum acceleration (of vehicle i) | a (\(a_i\)) | 3 m/s\({}^{2}\) |
2.2.2 SymuVia
2.2.3 Aimsun
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\(b_i\) is the maximum deceleration of vehicle i, in absolute value,
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\(b'_{i-1}\) is the estimated maximum deceleration of the leader, in absolute value,
2.2.4 SUMO
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b is the maximum deceleration, in absolute value,
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\(\sigma\) is a fixed value in \([0 ; \; 1]\) capturing the drivers imperfection, together with the random value r uniformly distributed in \([0 ; \; 1]\). Note that if equation 3 returns a negative value due to the distribution of r, a null value is returned when updating \(v_i\). Under the assumptions of 2.2.1, \(\sigma\) is set to 0 in our simulations.
3 Analytical modeling of traffic discontinuities
Definition | Notation |
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Proportion of diverging vehicles | \(\beta\) |
Downstream bottleneck capacity on lane i | \(C_i\) |
Merge/priority ratio | \(\alpha\) |
Demand (demand on lane i) | \(\lambda\) (\(\lambda _i\)) |
Effective flow (effective flow on lane i) | q (\(q_i\)) |
3.1 Point-based diverges analytical behavior
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the free-flowing operation corresponds to zone 1 and is observed when the demand \(\lambda\) does not exceed the minimum capacity of the three lanes. Then, the operation point is \((q_1 = \beta \lambda ; q_2 = (1-\beta )\lambda )\),
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else, the congested operation holds:
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if \(\beta\) is too low so that lane 2 is congested, i.e. \(\lambda _1 {:=}\beta \lambda < C_1\) and \(\lambda _2 {:=}(1-\beta )\lambda > C_2\), then the operation point is \((q_1 = \frac{1-\beta }{\beta }C_2; q_2 = C_2)\). This is graphically detailed on Fig. 3a,
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by symmetry, if \(\beta\) is too high so that lane 1 is congested, then the operation point is \((q_1 = C_1; q_2 = \frac{\beta }{1-\beta }C_1)\).
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3.2 Extended merges analytical behavior
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while the sum of the demands does not exceed the merge capacity, each demand is satisfied, and the projection function is null (i.e. the operation point is \((q_{{\text{U}}} = \lambda _{{\text{U}}}; q_{{\text{R}}} = \lambda _{{\text{R}}})\)), which corresponds graphically to zone 1,
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if the sum exceeds the merge capacity, then at least one upstream lane is congested:
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if lane R is congested and if lane U is free-flowing, then the projection function acts on the demand of lane R, which cannot be satisfied, unlike the one of lane U (i.e. the operation point is \((q_{{\text{U}}} = \lambda _{{\text{U}}}; q_{{\text{R}}} = C^{\text{m}}-\lambda _{{\text{U}}})\)), see zone 2 on Fig. 3b,
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by symmetry, we have, for zone 4, the operation point \((q_{{\text{U}}} = C^{\text{m}}-\lambda _{{\text{R}}}; q_{{\text{R}}} = \lambda _{{\text{R}}})\),
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if both lanes are congested, only one operation point is possible, and all demands are projected on it: it is such as \(q_{{\text{R}}} = \alpha q_{{\text{U}}}\), see zone 3.
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4 Simulation tools and traffic discontinuities operation: cross-comparison
4.1 Methodology
4.1.1 Generating the diverge operation results
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the upstream lane inflows at capacity, but as both downstream lanes capacity is \(q_x\), we need to implement, on one lane—lane 1 here—, a bottleneck of capacity \(C_1 \le q_x\) to examine the congested operation of the diverge. Thus, we produce various diverge diagrams by taking 5 values of \(C_1\) from 0 veh/h to \(q_x\), with a 25% increase from one value to another. To avoid a complete gridlock, instead of 0 veh/h, we arbitrarily chose a value of 3% \(q_x\),
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for each value of \(C_1\), one step accounts for a value of \(\beta\), from 0 to 100% with a 25% increase from one step to the next,
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for each step, 15 replications of one hour of traffic are simulated,
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every selected flow is the mean of the flow during the 15 last minutes.
4.1.2 Generating the merge operation results
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the main lane inflows at capacity,
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the on-ramp lane uniformly increases its inflow from null to capacity by 10 steps (excluding the step in which the inflow is null),
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for each step, 15 replications of one hour of traffic flow are simulated,
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to be sure a potential warm-up phase has elapsed, every selected flow is the mean of the flow during the 15 last minutes.
4.2 Entrance time headways distribution
4.3 Point-based diverge operation results
4.4 Extended merge operation results
4.4.1 Macroscopic operation results
Simulation tool | Maximum capacity drop (%) | Average capacity drop in general congestion (%) | Merge ratio |
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SymuVia | 7.04 | 6.97 | 1.00 |
Aimsun | 17.16 | 16.71 | 1.09 |
SUMO (basic mode) | 3.78 | 1.24 | 2.31 |
SUMO (zipper mode) | 1.72 | 1.13 | 1.00 |
Analytical modeling from [7] | 25.57 | 25.57 | 1 |
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The first family of behaviors gathers SUMO’s results; see Fig. 10a, b. It is characterized by the absence of significant capacity drop when congestion appears, as the downstream theoretical capacity is shared between the upstream lane and the on-ramp lane. This operation coincides with the theoretical zipper model. In the zipper mode case, the share of the downstream capacity is fair, as the merge ratio equals 1, which is the ratio of the number of lanes of the main way (one) and the one of the on-ramp way (one), what is consistent with on-field data [77]. However, as perceived in Fig. 9, in the basic mode case, the merge ratio is larger than 2. This means that more than two-thirds of the vehicles come from the on-ramp lane. Such a value is too high and unrealistic, as priority is therefore not given to the upstream lane vehicles (result 2.2).
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The second family of behaviors matches with SymuVia and Aimsun’s results; see Fig. 10c, d. In this case, the capacity drop is observed (result 2.3), even if lesser than the one predicted by [7]’s analytical model when both lanes are congested. It is worth noting that for SymuVia, the drop appears for higher values of demands. Lastly, the merge ratio is about 1, which is a consistent value as it matches the ratio of the number of lanes [77].
4.4.2 Lane changes positions distribution
5 Discussion and conclusion
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first, to ensure that this comparison was made on the same shared basis, i.e. the FD is roughly the same, we only modify the following microscopic values: the desired speed, the relative headway, and the minimum spatial gap,
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second, we propose a set of simple cases that are reproduced in the simulation tools, a point-based diverge and an extended merge,
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third, we identify the validated analytical formulations defining each test case’s expected behavior and compare them to the simulated results.
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regarding diverges operation:
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result 1.1: the macroscopic behavior is correctly reproduced,
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result 1.2: no capacity drop could be highlighted,
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result 1.3: upstream of the diverging point, no significant vehicles’ slowdown was brought out,
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regarding merges operation:
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result 2.1: the macroscopic behavior is correctly reproduced,
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result 2.2: every configuration presents an equitable sharing of the downstream supply, except SUMO’s basic mode, which presents an unrealistic one,
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result 2.4: for every configuration, the behavior of inserting vehicles is not in agreement with experimental observations. It is worth noting that this result needs to be further investigated by a comparative analysis with on-field data.
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