Including Right-of-Way in a Joint Large-Scale Agent-Based Dynamic Traffic Assignment Model for Cars and Bicycles

Abstract

Intersections typically account for a substantial part of the total travel time in urban areas, and an even higher share of the congested travel time, especially for bicycle traffic. Nevertheless, delays caused by yielding for cyclists or cars at intersections have previously not been modelled in large-scale bicycle traffic assignment models. This study proposes a computationally efficient large-scale applicable methodology for explicitly modelling yielding for conflicting moves at multi-modal intersections in an agent-based traffic assignment model. Nodes representing the intersections are classified into five node types that simulate potential moves across nodes differently while obeying right-of-way and preventing simultaneous conflicting moves. The methodology is implemented within a joint assignment model capable of modelling on-link congestion of both car and bicycle traffic and is applied to a large-scale case study of a Metropolitan Copenhagen network with 144,060 nodes and 572,935 links. The MATSim case study with 4,593,059 trips shows manageable computation times similar to when not modelling right-of-way at intersections. Especially for car traffic, yielding at intersections imposes considerable excess travel time. The effects are larger for trips going to the central part of the city where the inter-modal impact of conflicting bicycle traffic is identified as a major source of added travel time. The study finds that failing to model conflicting moves at intersections generally underestimates travel times and causes too much traffic to go through the urban core, highlighting the importance of joint modelling of intersections.

Appendix

1.1 A. List of Notation

$\emptyset$	The empty set.
B	A MATSim buffer. See Sect. 3.2.3 for the definition.
$\mathcal {B}_D$	Set of buffers of bundle D (diverging nodes only).
$\mathcal {B}_L$	The set of buffers of link, L.
$\beta _b$	Parameter for congested travel time in the scoring function.
$\beta _f$	Parameter for free-flow travel time in the scoring function.
$C^F_L$	The MATSim flow capacity of a link.
$\mathcal {C}_m$ (and $\mathcal {C}_n$)	The set of all conflicting moves that cause a conflict with move m (or n).
D (and $D_h$, $D_i$, $D_j$, $D_k$)	A bundle. See Sect. 2.1 for definition.
$D^-$	The bundle preceding bundle D when traversing bundles counterclockwise.
$D^+$	The bundle following bundle D when traversing bundles counterclockwise.
$D_p$ (and $D_q$)	Primary bundle (merging nodes) or bundle prioritised in previous time step
	(right and anti-priority nodes).
$D_s$	Secondary bundle (merging nodes only)
$\mathcal {D}_P$	The set of primary bundles, see Sect. 3.2.4.
$\mathcal {D}_S$	The set of secondary bundles, see Sect. 3.2.4.
l	A MATSim leg – also known as a trip in more general literature.
L	A network link.
$\ell _p$	The set of legs (trips) for plan p.
$\mathcal {L}_N^A$	Set of links of a node N that have vehicles ready to move.
$\lambda _L$	Length of link L.
m (and n)	A move across a node.
N	A network node.
$\mathcal {N}_A$	Set of all active nodes.
$\Omega$	An ordered list of buffers based on right-of-way, see Sect. 3.2.1.
$R_m$	Receiving link of move m.
$R_V$	Receiving link of vehicle V.
$\varrho _p$	Proportion of flow capacity constituted by a primary bundle (merging nodes).
$S_p$	The score of plan p.
$\bar{S}_i$	The average score across all agents in iteration i.
$\varsigma$	The MATSim stuck time (or squeeze time), see Sect. 3.1.
t	The current time in the MATSim simulation.
$t_a^l$	Actual travel time of leg l (sometimes used without l).
$t_c^l$	(Individualised) Congested travel time of leg l (sometimes used without l).
$t_f^l$	(Individualised) Free-flow travel time of leg l (sometimes used without l).
$t_m$ (and $t_{n}$)	The time that has to be exceeded before move m (or n) can be conducted.
$T_B$	Buffer time of buffer B see Sect. 3.1.
$\tau$	Time step size used in the MATSim simulation.
u	Random number in the interval [0; 1].
V	A MATSim vehicle.
$\xi$	Clearance time parameter.

1.2 B. Supplementary Figures

Fig. 7

Number of stuck events per iteration for scenarios with only cars and trucks and different values of the stuck time $\varsigma$ ($\xi = 0$)

Fig. 8

Number of stuck events per iteration for scenarios with bicycles, cars and trucks and different values of the stuck time $\varsigma$ ($\xi = 0$)

Fig. 9

The average executed score after each iteration for scenarios with only cars and trucks and different values of the stuck time $\varsigma$ ($\xi = 0$)

Fig. 10

The average executed score after each iteration for scenarios with bicycles, cars and trucks and different values of the stuck time $\varsigma$ ($\xi = 0$)

Fig. 11

Car flow differences between the uni-modal car scenario with the original node model and the tri-modal right-of-way model scenario with $\xi = 0$. Negative numbers imply lower car flows in the latter

Fig. 12

Car flow differences between the original node model and the right-of-way model with $\xi = 2$ when only including cars. Negative numbers imply lower car flows when using the right-of-way model

Fig. 13

Car flow differences for the right-of-way model with $\xi = 2$ with and without bicycles. Negative numbers imply lower car flows when including bicycle traffic

Fig. 14

Car flow differences between the uni-modal car scenario with the original node model and the tri-modal right-of-way model scenario with $\xi = 2$. Negative numbers imply lower car flows in the latter