Although routing applications increasingly affect individual mobility choices, their impact on collective traffic dynamics remains largely unknown. Smart communication technologies provide accurate traffic data for choosing one route over other alternatives; yet, inherent delays undermine the potential usefulness of such information. Here, we introduce and analyze a simple model of collective traffic dynamics, which results from route choice relying on outdated traffic information. We find for sufficiently small information delays that traffic flows are stable against perturbations. However, delays beyond a bifurcation point induce self-organized flow oscillations of increasing amplitude—congestion arises. Providing delayed information averaged over sufficiently long periods of time or, more intriguingly, reducing the number of vehicles adhering to the route recommendations may prevent such delay-induced congestion. We reveal the fundamental mechanisms underlying these phenomena in a minimal two-road model and demonstrate their generality in microscopic, agent-based simulations of a road network system. Our findings provide a way to conceptually understand system-wide traffic dynamics caused by broadly used non-instantaneous routing information and suggest how resulting unintended collective traffic states could be avoided.

1.
M.
Ben-Akiva
,
A.
De Palma
, and
K.
Isam
, “
Dynamic network models and driver information systems
,”
Transp. Res. Part A: Gen.
25
(
5
),
251
266
(
1991
).
2.
A.
de Palma
,
R.
Lindsey
, and
N.
Picard
, “
Risk aversion, the value of information, and traffic equilibrium
,”
Transp. Sci.
46
(
1
),
1
26
(
2012
).
3.
R.
Lindsey
,
T.
Daniel
,
E.
Gisches
, and
A.
Rapoport
, “
Pre-trip information and route-choice decisions with stochastic travel conditions: Theory
,”
Transp. Res. Part B: Methodol.
67
,
187
207
(
2014
).
4.
A.
Rapoport
,
E. J.
Gisches
,
T.
Daniel
, and
R.
Lindsey
, “
Pre-trip information and route-choice decisions with stochastic travel conditions: Experiment
,”
Transp. Res. Part B: Methodol.
68
,
154
172
(
2014
).
5.
H.
Tavafoghi
and
D.
Teneketzis
, “Informational incentives for congestion games,” in 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (IEEE, Monticello, IL, 2017), pp. 1285–1292, ISBN 978-1-5386-3266-6.
6.
D.-M.
Storch
,
M.
Schröder
, and
M.
Timme
, “
Traffic flow splitting from crowdsourced digital route choice support
,”
J. Phys.: Complex.
1
(
3
),
035004
(
2020
).
7.
R.
Arnott
,
A.
de Palma
, and
R.
Lindsey
, “
Does providing information to drivers reduce traffic congestion?
,”
Transp. Res. Part A: Gen.
25
(
5
),
309
318
(
1991
).
8.
D.
Braess
, “
Über ein paradoxon aus der verkehrsplanung
,”
Unternehmensforschung
12
(
1
),
258
268
(
1968
).
9.
D.
Braess
,
A.
Nagurney
, and
T.
Wakolbinger
, “
On a paradox of traffic planning
,”
Transp. Sci.
39
(
4
),
446
450
(
2005
).
10.
S.
Çolak
,
A.
Lima
, and
M. C.
González
, “
Understanding congested travel in urban areas
,”
Nat. Commun.
7
(
1
),
10793
(
2016
).
11.
S.
Carrasco
,
P.
Medina
,
J.
Rogan
, and
J. A.
Valdivia
, “
Does following optimized routes for single cars improve car routing?
,”
Chaos
30
(
6
),
063148
(
2020
).
12.
J.
Thai
,
N.
Laurent-Brouty
, and
A. M.
Bayen
, “Negative externalities of GPS-enabled routing applications: A game theoretical approach,” in
2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC)
(IEEE, 2016), pp. 595–601.
13.
I.
Johnson
,
J.
Henderson
,
C.
Perry
,
J.
Schöning
, and
B.
Hecht
, “
Beautiful but at what cost?: An examination of externalities in geographic vehicle routing
,”
Proc. ACM Interact. Mob. Wearable Ubiquitous Technol.
1
(
2
),
1
21
(
2017
).
14.
A.
Festa
and
P.
Goatin
, “Modeling the impact of on-line navigation devices in traffic flows,” in
2019 IEEE 58th Conference on Decision and Control (CDC)
(IEEE, Nice, 2019), pp. 323–328.
15.
Y.
Yokoya
, “
Dynamics of traffic flow with real-time traffic information
,”
Phys. Rev. E
69
(
1
),
016121
(
2004
).
16.
S.
Scellato
,
L.
Fortuna
,
M.
Frasca
,
J.
Gómez-Gardeñes
, and
V.
Latora
, “
Traffic optimization in transport networks based on local routing
,”
Eur. Phys. J. B
73
(
2
),
303
308
(
2010
).
17.
J. L.
Horowitz
, “
The stability of stochastic equilibrium in a two-link transportation network
,”
Transp. Res. Part B: Methodol.
18
(
1
),
13
28
(
1984
).
18.
J.
Wahle
,
A.
Lúcia C Bazzan
,
F.
Klügl
, and
M.
Schreckenberg
, “
Decision dynamics in a traffic scenario
,”
Physica A
287
(
3–4
),
669
681
(
2000
).
19.
W.-X.
Wang
,
B.-H.
Wang
,
W.-C.
Zheng
,
C.-Y.
Yin
, and
T.
Zhou
, “
Advanced information feedback in intelligent traffic systems
,”
Phys. Rev. E
72
(
6
),
066702
(
2005
).
20.
Y.
(Marco) Nie
, “
Equilibrium analysis of macroscopic traffic oscillations
,”
Transp. Res. Part B: Methodol.
44
(
1
),
62
72
(
2010
).
21.
T.
Imai
and
K.
Nishinari
, “
Optimal information provision for maximizing flow in a forked lattice
,”
Phys. Rev. E
91
(
6
),
062818
(
2015
).
22.
B.
Schöfer
,
M.
Matthiae
,
M.
Timme
, and
D.
Witthaut
, “
Decentral smart grid control
,”
New J. Phys.
17
(
1
),
015002
(
2015
).
23.
M.
Jose Peroza Marval
,
J.
Chen
,
L.
Wosinska
, and
A.
Fumagalli
, “Adaptive routing based on summary information mitigates the adverse impact of outdated control messages,” in
2011 13th International Conference on Transparent Optical Networks
(IEEE, Stockholm, Sweden, 2011), pp. 1–4.
24.
R.
Smock
, “
An iterative assignment approach to capacity restraint on arterial networks
,”
Highway Res. Board Bull.
347
,
60
66
(
1962
).
25.
D.
Branston
, “
Link capacity functions: A review
,”
Transp. Res.
10
(
4
),
223
236
(
1976
).
26.
K.
Nagel
and
M.
Schreckenberg
, “
A cellular automaton model for freeway traffic
,”
J. Phys. I
2
(
12
),
2221
2229
(
1992
).
27.
T. A.
Domencich
and
D.
McFadden
, Urban Travel Demand: A Behavioral Analysis: A Charles River Associates Research Study, Number 93 in Contributions to Economic Analysis (North-Holland Publishing Co./American Elsevier, Amsterdam/New York, 1975), ISBN: 978-0-444-10830-2.
28.
D.
Helbing
, “Dynamic decision behavior and optimal guidance through information services: Models and experiments,” in Human Behaviour and Traffic Networks, edited by M. Schreckenberg and R. Selten (Springer, Berlin, 2004), pp. 47–95, ISBN: 978-3-662-07809-9.
29.
R. D.
Driver
, Ordinary and Delay Differential Equations (Springer, New York, NY, 1977), ISBN: 978-1-4684-9467-9, OCLC: 863868406.
30.
V.
Krall
,
M. F.
Burg
,
M.
Schröder
, and
M.
Timme
, “Number fluctuations induce persistent congestion,”
Findings
(published online).
31.
H. S.
Mahmassani
and
R.
Jayakrishnan
, “
System performance and user response under real-time information in a congested traffic corridor
,”
Transp. Res. Part A: Gen.
25
(
5
),
293
307
(
1991
).
32.
J.
Liu
,
S.
Amin
, and
G.
Schwartz
, “Effects of information heterogeneity in Bayesian routing games,” arXiv:1603.08853 (2016).
33.
T.
Shing Tai
and
C. H.
Yeung
, “
Global benefit of randomness in individual routing on transportation networks
,”
Phys. Rev. E
100
(
1
),
012311
(
2019
).
34.
C.-Y.
Chan
, “
Advancements, prospects, and impacts of automated driving systems
,”
Int. J. Transp. Sci. Technol.
6
(
3
),
208
216
(
2017
).
35.
J. B.
Michael
,
D. N.
Godbole
,
J.
Lygeros
, and
R.
Sengupta
, “
Capacity analysis of traffic flow over a single-lane automated highway system
,”
ITS J.
4
(
1–2
),
49
80
(
1998
).
36.
M. R.
Roussel
, “Delay-differential equations,” in Nonlinear Dynamics (Morgan & Claypool Publishers, 2019), pp. 12–14, ISBN: 978-1-64327-464-5.
37.
V.
Krall
,
M. F
Burg
,
F.
Pagenkopf
,
H.
Wolf
,
M.
Timme
, and
M.
Schröder
, “Supplementary material for `Obscuring digital route-choice information prevents delay-induced congestion',” (1.0.0) (Zenodo,
2021
).
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