Influence of driver behavior in the emergence of traffic gridlocks
aa r X i v : . [ phy s i c s . s o c - ph ] S e p September 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic
International Journal of Modern Physics Cc (cid:13)
World Scientific Publishing Company
Influence of driver behavior in the emergence of traffic gridlocks
Enrique Pazos
Instituto de Investigaci´on en Ciencias F´ısicas y Matem´aticas, Universidad de San Carlos deGuatemala, Edificio T-1, Ciudad Universitaria Z. 12Guatemala, Guatemala [email protected]
Received Day Month YearRevised Day Month YearWe present a microscopic driving algorithm that prescribes the acceleration using threeparameters: the distance to the leading vehicle, to the next traffic light and to the neareststopping point when the next traffic light is in the red phase. We apply this algorithm toconstruct decision trees that enable two driving behaviors: aggressive and careful. Thefocus of this study is to analyze the amount of aggressive drivers that are needed in orderto generate a traffic gridlock in a portion of a city with signalized intersections. At rushhour, aggressive drivers will enter the intersection regardless if they have enough time orspace to clear it. When their traffic light changes they block other drivers, thus providingthe conditions for a gridlock to develop. We find that gridlocks emerge even with veryfew aggressive drivers present. These results support the idea of promoting good drivingbehavior to avoid heavy congestion during rush hours.
Keywords : Gridlock; driver behavior; microscopic model; urban trafficPACS Nos.: 02.70.-c, 89.65.-a, 05.65.+b
1. Introduction
Traffic congestion is a problem in all mayor cities of the world. It has been studiedusing theoretical and empirical approaches with a variety of methods that includestatistical physics, numerical analysis, fluid dynamics and cellular automata, tomention a few. A comprehensive review has been done in Refs. 1, 2.One of the most widely used methods to study traffic dynamics is cellular au-tomata, from the pioneering work of Nagel and Schreckenberg to many subsequentimprovements and extensions, see Refs. 4, 5, 6, 7 and references therein. Cellularautomata have the advantage that traffic rules are stated in fairly simple formulaewhose computer implementation can run very fast. Other approach to traffic simu-lations are microscopic models, where the acceleration is given at a particular timeas a function of parameters such as distances and velocities of the neighboring vehi-cles. Some examples are the follow-the-leader models, the Newell model and theintelligent driver model. Microscopic formulations have the advantage of giving afine-grained time evolution which is a more realistic description of the motion. eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos
In this study we will use a microscopic model to analyze the dynamics of an urbantraffic scenario with signalized intersections, in which streets follow a Cartesianlay out and are single lanes with alternating senses of motion. The focus of ouranalysis is the influence of driver behavior in the emergence of gridlocks. To thisend we devised a driving algorithm that specifies the acceleration based on threeparameters which are the following distances: to the leading vehicle, to the nexttraffic light and to the nearest stopping point when the next traffic light is in thered phase. The advantage and motivation of this approach is that it enables theformulation of two driving behaviors which we call aggressive and careful . Theaggressive driver follows the leading vehicle at a safe distance but will never careabout blocking the intersection. This is a problem at rush hour congestion, speciallywhen his traffic light turns red and he has not cleared the intersection. When thishappens the aggressive driver not only is standing still but also does not allow carsin the perpendicular lane to advance, hence providing the conditions for a gridlockto develop. On the other hand, the careful driver will never block the intersection,she will wait until having enough distance headway so that she can effectively clearthe intersection without ever blocking it.We set up runs with different amounts of aggressive and careful drivers andcheck whether a gridlock develops. Since traffic is the result of many factors andinteractions, we also take into account the effects of taking a turn and the trafficlight scheme. Our main conclusion is that gridlocks emerge even when very fewaggressive drivers are present, while there is none when all drivers are careful.This papers is organized as follows: section 2 describes our proposed drivingscheme, the integration of the equations of motion, the computation of the accel-eration and the decision trees that enable the aggressive and careful behaviors.Section 3 presents the results for a freeway test case and the conditions that giverise to gridlocks in city traffic. We conclude in section 4.
2. Driving algorithm
In order to account for the two different driving behaviors that we want to study, wedevised a scheme to prescribe the acceleration of every vehicle based upon the threedistances depicted in Fig. 1. In freeway traffic the main parameter that determinesthe acceleration is the distance d ( t i ) to the leading vehicle. In the model we proposehere we add two more parameters, one is the distance d TL ( t i ) to the next trafficlight and the other is the distance d STP ( t i ) to the stopping point when the trafficlight is in the red phase.Once the acceleration is known, the position and velocity of every vehicle isintegrated using the Euler method, such that x ( t i +1 ) = x ( t i ) + v ( t i ) δt, (1) v ( t i +1 ) = v ( t i ) + a ( t i ) δt, (2) t i +1 = t i + δt, (3)eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Influence of driver behavior in the emergence of traffic gridlocks d ( t i ) d STP ( t i ) d TL ( t i ) B w S w Figure 1. Schematic representation of the intersection of two perpendicular streets. Cars aredrawn as dark rectangles, the sense of motion is to the right. B w and S w are block and streetwidth, respectively, d ( t i ) is the distance to the leading vehicle at the i -th iteration, d TL ( t i ) is thedistance to the traffic light and d STP ( t i ) is the distance to the stopping location when the trafficlight is red. where x ( t i ), v ( t i ) and a ( t i ) are the position, velocity and acceleration for a givenvehicle at the i -th iteration. Similarly, the elapsed time is t i and δt is the time step.Since the acceleration values do not vary largely during the simulation, this methodis good enough to integrate the equations of motion. Acceleration modes
For each vehicle, the acceleration a ( t i ) is set by one of three acceleration modes,which we call GO, CAR IN FRONT and STOP. These modes are a way to mimichow the driver controls the vehicle in an urban traffic scenario. The motivationbehind the acceleration modes is the flexibility they provide in order to construct amodular decision tree that implements the driving behaviors we are interested in,namely the careful and the aggressive .The acceleration in each mode is set as follows: • GO: The vehicle moves with constant acceleration a go until it reaches amaximum speed v max . It is given as a ( t i ) = (cid:26) , v ( t i ) ≥ v max a go , v ( t i ) < v max . (4) • CAR IN FRONT: The vehicle moves at a speed such that it keeps a safedistance to the leading vehicle. The safe distance is the necessary spacesuch that the time elapsed from bumper to bumper as measured at a fixedlocation is δt s . The acceleration is a ( t i ) = d ( t i ) − d s ( t i ) δt δt s , (5)eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos where d ( t i ) is the distance to the leading vehicle (bumper to bumper) at atime t i (see Fig. 1) and d s ( t i ) = v ( t i ) δt s is the safe separation between thecars such that at the current speed v ( t i ) the vehicle would take a time δt s to traverse. In this mode, the cars keep the same time separation, whichwill be a larger (shorter) length when going at a faster (slower) speed. Inpractice, when taking one iteration step for the velocity, Eq. (2) reducesto v ( t i +1 ) = d ( t i ) /δt s . In other words, the speed is set to the value that isneeded to keep a time δt s to the leading vehicle. • STOP: A car will stop when the traffic light is red. The acceleration in thiscase will be a ( t i ) = − v ( t i ) d STP ( t i ) , (6)where d STP ( t i ) is the distance to the point where the car has to be at rest(see Fig. 1). By taking this approach, the car breaks smoothly, reaching zerospeed as d STP ( t i ) approaches zero. In this mode we set v ( t i ) = 0 whenever d STP ( t i ) < d min or d ( t i ) < d min . The first condition ensures that a carstops before entering an intersection and the second one avoids collisions.The fixed quantity d min is the minimum separation distance between cars.We will show in Sec. 3 that the acceleration modes reproduce the fundamentaldiagram for freeway traffic shown in Refs. 2, 12, 13. Guided by car or traffic light
The decision as to which acceleration mode is used at a given time is determinedby the values of the distances mentioned above, i.e. d ( t i ), d TL ( t i ) and d STP ( t i ). Weassume that the process of deciding which acceleration mode will be used starts bydetermining what is closer: either the leading vehicle or the traffic light at the nearestintersection. If the leading vehicle is closer, the driver will just follow it at a safedistance, regardless of the traffic light. On the contrary, if the traffic light is closer,then the driver will disregard the leading vehicle and will maneuver according to thecolor of the signal. In the first case we say that the driver is car-guided , and in thesecond case he is TL-guided (Traffic Light). This decision is made at the beginningof each iteration by comparing the distances d ( t i ) and d TL ( t i ) (see Fig. 1)if d ( t i ) (cid:26) ≤ d TL ( t i ) ⇒ car-guided > d TL ( t i ) ⇒ TL-guided . (7)Once this step is done the next ones will depend on the color of the traffic light.We consider red, yellow and green phases with duration T r , T y and T g , respectively.We use the traffic light color as the starting point of the decision trees that willimplement the two types of driving behavior, i.e. careful and aggressive.eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Influence of driver behavior in the emergence of traffic gridlocks Two types of driving behavior
We focus our attention on the traffic flux and speed attained when individual driversbehave in one of two ways, which we call the aggressive and the careful types,following Ref. 11. The distinction between them occurs when the driver has tomake a decision at the same time that he is approaching the intersection of twoperpendicular streets. We assume that the traffic flow at the intersection is controlledby a traffic light and that all streets have a single lane with a fixed sense of motion.When the vehicle density is high, there is a chance that some drivers will blockthe intersection, either moving slowly or standing still completely. If the potentiallyblocking driver, has enough green light time to clear the intersection, then he justgoes through it at a low speed. The problem arises when the traffic light changesfrom green to yellow and red while the car is still traversing the intersection. At thispoint the vehicles waiting on the perpendicular lane have now the green light, butthey will not be able to move because the intersection is blocked, thus increasingcongestion.We define the careful driving behavior or careful type as that in which the driverwill never block the intersection. The careful driver achieves this by waiting to haveenough distance headway to the leading vehicle so that she can effectively clear theintersection. The aggressive type is the opposite. This driver will follow the leadingvehicle at a safe distance but he will not have any consideration about obstructingan intersection whatsoever.From now on, for clarity, we will drop the time dependence from the distancesconsidered.2.3.1.
The aggressive type
The decision trees for this driving conduct are shown in Fig. 2. In the car-guided treethe acceleration mode is basically CAR IN FRONT. The STOP mode is reachedwhen three conditions are met: the light is red, the leading vehicle has entered theintersection ( d > d
STP ) and the driver has not entered it yet ( d STP ≤ B w ). Here, theaggressive conduct is manifest when the condition d STP ≤ B w is false, which meansthat the driver is already going through the intersection and he will continue tomove. The TL-guided tree is straightforward. The aggressive behavior is expressedwhen the light changes to red while the driver is already on the intersection ( d STP ≤ B w ). The yellow light plays a role in this tree through the variable Y count , whichis the remaining time before the signal turns to red. The condition d TL /v < Y count tries to mimic the judging criterion that the driver uses to evaluate whether he hastime to clear the intersection in the time that remains of yellow light.2.3.2. The careful type
The decision trees for this behavior are illustrated in Fig. 3. The car-guided oneis very simple: the driver either stops or follows the vehicle ahead regardless ofeptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos car-guided color? CAR IN FRONT d < d
STP ? d STP ≤ B w ? STOPgreen , yellowred YESNO YES NO
TL-guided color? GO d STP ≤ B w ? STOP d TL /v < Y count ?red YESNO yellow
YESNO green
Figure 2. The aggressive behavior decision tree for a driver guided by the leading vehicle (leftpanel) and by traffic light (right panel). car-guided color? d < d
STP ? CAR IN FRONTSTOP
YESNO
TL-guided color? d > d TL + ℓ + d min ? GOSTOP d TL /v < Y count ? d > d TL + ℓ + d min ?greenyellowred YESNOYESNO YESNO
Figure 3. The careful behavior decision tree for a driver guided by the leading vehicle (left panel)and by traffic light (right panel). the traffic light phase. The carefulness shows here in the fact that there is a singlecondition to go into STOP mode, which is that the driver has not entered theintersection. This ensures that in the careful behavior the driver will always stopbefore going through the intersection. In the TL-guided panel, the driver executesmore evaluations before crossing an intersection. If the signal is green she goes toGO mode only if she has enough space to accommodate herself after clearing theintersection completely ( d > d TL + ℓ + d min ), where ℓ is the length of the car. Weconsider that a car blocks the intersection if any fraction of its length is over it. Redlight means unconditional stop. In yellow phase the driver still evaluates whethershe has enough time and space to safely clear the intersection altogether.
3. Results and discussion
We implemented the above schemes using the C++ programming language. Thesetup consists of a grid-like city where all streets meet at perpendicular intersectionsin a Cartesian fashion. The extent of the city is 10 blocks in both x and y directions.Each street contains only a single lane, the sense of which alternates according to( − i ˆx and ( − j ˆy for the x and y directions, respectively. The variables i and j are numbering integers in the interval [0 , Influence of driver behavior in the emergence of traffic gridlocks a go free acceleration 1 m/s ℓ car length 5 m d min minimum distance between cars 2 m δt s safe time interval between cars 3 s δt time step 0.1 s v max maximum (free) speed 11 m/s T r red light phase 30 s T y yellow light phase 5 s T g green light phase 25 s B w block width 90 m S w street width 10 m Single lane with green lights
In order to test our driving algorithm, we present first some results for a simplifiedsetting. Using the city layout, let’s consider the situation in which cars travel along aunique street only, and all traffic lights are set to green during the whole simulation.This setting mimics the conditions of a continuous road of length L with periodicboundary conditions. We set L = 20( B w + S w ) (see Fig. 1), corresponding to a totallength L = 2 km, according to the values listed in Table 1.We randomly distribute a number of vehicles N with zero initial velocity alongthe street. This defines the density ρ = N/L . The cars start moving according to therules outlined in Sec. 2. We follow their motion for a three-hour simulated period,during which we compute the instantaneous average speed ¯ v ( t k ) over all vehicles atintervals of 1 s according to ¯ v ( t k ) = 1 N N X j =1 v j ( t k ) , (8)where v j ( t k ) is the speed of the j -th vehicle at a time t k . Now we take the last300 s of the simulation and compute the time averaged speed V = P k ¯ v ( t k ) / V .Knowing ρ and V the traffic flow is given as Q = ρV . By taking the last 300 s of athree-hour simulation we make sure that the transient part of the dynamics is overand we are left with the steady state.The results are shown in Fig. 4. We plot the traffic flow Q (panel A) and theaverage velocity V (panel B) versus the vehicle density ρ . We consider the twoextreme cases: one where all drivers are aggressive and the other where all drivers arecareful. Our results for the aggressive type are in agreement with the fundamentaldiagrams in Refs. 6, 1, 10, 2, 14, 15. The traffic flow Q exhibits a linear growthat low densities, reaching a maximum when the safe separation is d s = v max δt s .This corresponds to a critical density ρ cr = 1 / ( ℓ + d s ) ≈
11 vehicles/km. Fromthis point the flow decreases linearly until the density is ρ max = 1 / ( ℓ + d min ) ≈ eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos A t r a ff i c f l o w Q [ v eh i c l e s / h ] density ρ [vehicles / km]% aggressive1000 0 10 20 30 40 50 0 40 80 120 160 B a v e r age v e l o c i t y V [ k m / h ] density ρ [vehicles / km]% aggressive1000 Figure 4. Fundamental diagram for a single lane. Traffic flow Q (panel A) and average velocity V (panel B) vs. vehicle density ρ . The curves show the fundamental diagram for the two drivingmodes, namely, aggressive and careful.
143 vehicles/km. When density reaches ρ max all vehicles are at their minimumseparation d min , thus they cannot be any closer and Q goes to zero.In the case where all drivers are careful (0% aggressive), the traffic flow exhibitsa different behavior. It starts increasing linearly at low densities, as in the previouscase, but it drops to a constant value over a wide range of densities. This is dueto the fact that careful drivers try to stop at every intersection if they don’t haveenough space to position themselves without blocking the intersection after crossingit. This behavior is desired at higher densities, thus it is not optimal for lower ones.Since we are interested in urban traffic and congestion at high densities we do notperform further optimization for the careful type at lower densities.The fact that the aggressive type behavior reproduces the fundamental diagramfor freeway traffic validates our ad-hoc driving algorithm formulation, which is qual-itatively similar to those presented in Refs. 16, 10. Other feature we found in oursimulations is the existence of stop-and-go waves, which are a well-known propertyof freeway traffic. City with turning vehicles and traffic lights
We consider a square city of size 10 ×
10 blocks, each block being a B w + S w squareper side. The total road length is L = 200( B w + S w ), which amounts to 20 km. Thedensity ρ and average velocity V are defined in the same way as in section 3.1.Initially a number of vehicles N are randomly distributed on all streets. Allinitial velocities are zero. We consider three driving behavior configurations for the N drivers: all aggressive, half aggressive-half careful and all careful. We will namethese configurations by the percentage of aggressive drivers they have, i.e. 100-, 50-and 0%-aggressive, respectively. For each configuration we consider that there isa probability that a driver will take a turn at the next intersection. Ideally, theeptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Influence of driver behavior in the emergence of traffic gridlocks A t r a ff i c f l o w Q [ v eh i c l e s / h ] B
50% aggressive drivers 0 100 200 300 0 25 50 75 100 125 C
0% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 D a v e r age v e l o c i t y V [ k m / h ] density ρ [vehicles / km]100% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 E density ρ [vehicles / km]50% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 F density ρ [vehicles / km]0% aggressive drivers Figure 5. Traffic flow (top row) and average velocity (bottom row) for the three configurationsof aggressive and careful drivers using sync-mode traffic lights. amount of turns a driver will take depends solely on the departure and destinationpoints within the city. In reality it is influenced by other factors such as trafficincidents along the way, a preferred route or the driver’s empirical knowledge of thestate of the city traffic. To cover a wide range of turning probabilities we set upa series of runs, each with a fixed probability to take a turn. For instance, a runwith 0% turning probability means that all drivers will just go straight ahead, theamount of cars in each lane will remain constant throughout the simulated time.The probabilities considered here are 0, 10, 25, 50 and 75%. For the type of citywe are analyzing, i.e. streets consisting of a single lane with alternating and uniquesenses, a trip from one location to another can be accomplished by taking turns in10 to 25% of the traversed intersections.Traffic lights are set up in two different ways: synchronized (sync-) and random(rand-) modes. In sync-mode all traffic lights change at the same time. Initially, thelights are in green phase for both senses along the x -direction, consequently theyare in red phase for both senses along the y -direction. The duration of the threephases is the same for all traffic lights (see Table 1). In rand-mode each traffic lightis out of phase by a random fraction of the cycle. The extent of the cycle is still thesame for all traffic lights but now the shifting sequence has been randomly ordered. Gridlock
Figure 5 shows traffic flow and average velocity for urban traffic using the threedriving behavior configurations, the five turning probabilities and traffic lights insync-mode. Figure 6 shows similar results but setting traffic lights to rand-mode.eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos A t r a ff i c f l o w Q [ v eh i c l e s / h ] B
50% aggressive drivers 0 100 200 300 0 25 50 75 100 125 C
0% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 D a v e r age v e l o c i t y V [ k m / h ] density ρ [vehicles / km]100% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 E density ρ [vehicles / km]50% aggressive drivers 0 5 10 15 20 0 25 50 75 100 125 F density ρ [vehicles / km]0% aggressive drivers Figure 6. Traffic flow (top row) and average velocity (bottom row) for the three configurationsof aggressive and careful drivers using rand-mode traffic lights.
The effect of turning is evident for sync-mode traffic lights. In rand-mode, turningprobabilities make no significant differences for both the flow and the average ve-locity. Our results are similar to those reported in Ref. 14 for urban traffic withsignalized intersections.The cases with 100% aggressive drivers give higher fluxes at lower densities andtraffic lights in sync-mode. This is no surprise, since sync-mode enables half of thecity grid to momentarily behave as free roads during the green phase. However,the high flux is cut down abruptly to zero when a critical density is reached. Thissharp change from a finite value to zero flow signals a total gridlock, meaning thatall vehicles are standing still without moving. This constitutes a first order phasetransition.
1, 6, 18
The cause of this lies in the distinctive feature of the aggressivetype: the driver can block the intersection box. At low densities such behavior isof little or no consequence. But as soon as the streets become crowded and thedrivers that are waiting to clear the intersection are actually blocking the streetperpendicular to their motion, the traffic collapses and nobody can move.Gridlocks emerge in sync- and rand-modes and for all turning probabilities when-ever we have 100% and 50% aggressive drivers, as can be seen in panels A, B, Dand E in Figs. 5 and 6. The only cases in which gridlock is avoided is with 0% ag-gressive drivers. The main feature of the careful driver is that she will never blockthe intersection. She will wait until there is enough space ahead to actually traverseand clear the intersection. In cases of high vehicle densities, this behavior keeps thetraffic flowing, as can be seen in panels C and F in Figs. 5 and 6.There is always traffic flow in the 0% aggressive configuration. It goes to zeroeptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic
Influence of driver behavior in the emergence of traffic gridlocks t r a ff i c f l o w Q [ v eh i c l e s / h ]
1% aggressive drivers% turning010255075 0 100 200 300 0 25 50 75 100 125 1503% aggressive drivers 0 100 200 300 0 25 50 75 100 125 150 t r a ff i c f l o w Q [ v eh i c l e s / h ] density ρ [vehicles / km]6% aggressive drivers 0 100 200 300 0 25 50 75 100 125 150density ρ [vehicles / km]12% aggressive drivers Figure 7. Traffic flow for small fractions of aggressive drivers and rand-mode traffic lights. Grid-locks are formed with as little as 1-3% aggressive drivers. only at high densities, when vehicles approach their allowed minimum separation.We do not find any traffic jam when all drivers are careful. This poses the question:how many aggressive drivers are needed in order to produce a gridlock? We exploredthis situation performing runs with 1, 3, 6, 12 and 25% aggressive drivers, the trafficflow for these cases (25% not shown) are presented in Fig. 7. We can see that trafficjams arise with as little as 1-3% aggressive drivers. In the 1% case, gridlocks aremore frequent with increasing turning probability. In the 3% case, only the 10%probability turning curve is free from gridlocks until ρ ≈
60 vehicles/km, for higherturning probabilities gridlocks are present.The effect of a higher turning probability is translated into a decrease in flow forthe sync-mode traffic lights setting (Fig. 5). In rand-mode it has no noticeable effecton the flow (panels A and D in Fig. 6). It makes the gridlock onset appear at lowerdensities (panels B and E) and correlates with a smaller flow for 0% aggressivedrivers (panels C and F). This can be understood noticing that an aggressive driverthat takes a turn into a congested lane, can end up blocking the intersection, insteadof just going ahead had it not turned.We chose to simulate a three-hour period of congested traffic, which is enough tocollapse the flow even with a small number of aggressive drivers. The time it takesfor a gridlock to appear depends on the vehicle density. The higher the density theeptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic Enrique Pazos sooner it emerges. We can say that a traffic jam could be avoided if higher densitiesdissolve quickly, instead of lasting for as long as three hours. Consequently, thesystem would have a higher tolerance to aggressive drivers, requiring larger amountsof them for a gridlock to happen. We therefore take the three-hour period as a worstcase scenario.
4. Conclusion
We have formulated a microscopic traffic model that simulates the decision makingprocess for two kinds of driving behaviors. The formulation is based on the valuesof three parameters at a given instant of time. These parameters are the followingdistances: to the leading vehicle, to the next traffic light and to the nearest stoppingpoint when the next traffic light is in the red phase. More complex decision treescan be formulated making use of additional parameters. This would account for amore realistic driving behavior. For instance, the driver could base her decision ofgoing through the intersection not only on the location of her leading vehicle butalso on the location of the next one ahead.We have shown the importance of individual driving behavior in the collectiveproperties of traffic flow, specifically in the phase transition from congested flow toa traffic jam or gridlock. In practice it is impossible to have the ideal situation ofattaining zero aggressive drivers; however, the less they are, the better the chancesto keep traffic flowing at rush hours.Gridlocks arise even when very few aggressive drivers are present. Around 3%is enough to collapse the traffic flow. This is a very important lesson in promotinggood driving behavior, since very few aggressive drivers can create chaos, it is evenmore important that everybody do their best not to be one of them.Rand-mode traffic lights give more similar fluxes and speeds regardless of turn-ing frequency. This is because rand-mode does not enable a preferred direction ofmotion as sync-mode does by shifting all traffic lights at the same time. Random-ization makes the flow insensitive to turning frequency, making gridlocks appear ata more defined value of density. We consider that rand-mode is the scheme thatbest represents the traffic light conditions in the portion of Guatemala City called
Centro Hist´orico .Several aspects of city traffic have been studied with cellular automata.
15, 19–22
Our results support their findings in the sense that drivers who do not follow goodconduct rules tend to worsen the traffic. Here we offer a different approach to accountfor driver behavior.Future work includes the effects of the extent of the traffic light cycle and theuse of different cycle lengths for different intersections.
Acknowledgments
Motivation and inspiration for this paper came from the many hours lost in trafficduring rush hours in Guatemala City.eptember 30, 2020 17:6 WSPC/INSTRUCTION FILE traffic
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