Introduction

In a transportation network, vehicle breaking down or an accident on the road may block the road, and landslide or bridge collapse will make the upcoming vehicles in danger if they do not slow down. In such situations, the following vehicles or the upcoming vehicles need to be informed of the accident in order for them to take a detour to avoid the accident point or slow down to avoid the chain-accident. In the past studies, a road accident message was often broadcast through the vehicle-to-vehicle (V2V) communication by forming a Vehicular Ad Hoc Network (VANET) in different ways1,2,3,4. One common problem with broadcasting messages through V2V communication in VANETs is the collision of safety messages or the broadcast storms (BSs), which result from many vehicles relaying or broadcasting safety messages repeatedly. One cause of BSs is that messages are repeatedly disseminated among many vehicles that do not need them. One way to reduce BSs is to disseminate safety messages only to the vehicles that are influenced by the accident. Unfortunately, none of the VANET-based V2V communication methods can disseminate safety messages only to the influenced vehicles.

In order to disseminate safety messages only to the influenced vehicles, we need to know the routes of all the travelers. In an advanced TGS, travelers/ drivers are informed of the optimal routes from their origins to destinations, with the optimal routes being the dynamic shortest path. The TGS makes it possible to disseminate safety messages only to the influenced vehicles. It should be noted that there is a difference between the dynamic shortest path and the (static) shortest path. The latter tells the sequential links on the path only whereas the former also tells the arrival time at each link.

In this paper, we introduce a safety message dissemination method in a TGS that obviates a VANET and avoids broadcast storms in case of an accident in a road network. The system or method works without depending on VANET communication i.e. it avoids the need for vehicles to form an ad hoc network. With the method, safety messages are only sent to the exact vehicles that will be influenced by an accident. Thus it will greatly reduce redundant and unnecessary dissemination of messages and broadcast storms. The method presented in this paper is different from the methods in WAZE and Google Maps. The difference is explained in the subsection C in section V where the comparison of the method to the WAZE and Google Maps is presented.

The rest of the paper is organized as follows: Sect. 2 covers the literature review on the safety message broadcasting methods and the TGS. Section 3 introduces the layout of a TGS where the safety message dissemination method presented in this paper is applicable. Section 4 introduced the method for finding the optimal routes for all vehicles. Section 5 presents an example to explain how the method can be used to disseminate safety message in a TGS and to show the application of the method. Section 6 concludes the paper.

Literature review

The safety message broadcasting methods in VANETs

Probability-based method

The simple broadcasting is to send warning message to all vehicles that are approaching an accident site. All vehicles retransmit the message upon receiving a broadcast message for the first time. It has the simplest protocol yet has many repeated messages and suffers from broadcast storms. P-persistence algorithm uses a random selection method to decide which vehicle relays the warning message5,6. The probability of relay is given as Pij= Dij /R (where Dij is the distance between node i and j, R is the average transmission rage. It can reduce the number of the relay vehicles and broadcasting storm problems. Its drawback is that when the distance between any two nodes are very near, both will rebroadcast the message at the same probability, causing some broadcast storms.

The structure-free probabilistic data aggregation uses structure-free probabilistic data aggregation with a dynamic fragmentation of the road disseminate message7. It can reduce bandwidth consumption and improve information dissemination. Its weakness is that transmission may spread in all directions.

WISITPONGPHAN studied three probabilistic and timer-based broadcast suppression techniques8: weighted p-persistence, slotted 1-persistence, and slotted p-persistence schemes, to be used at the network layer. They can reduce broadcast redundancy and packet loss ratio. But messages are still disseminated in all directions at intersections, which is not good to reduce broadcasting storm problem.

Cluster-based method

In CBE-cast algorithm9, upon receiving a warning message, a vehicle responds to the sender with an ACK message. If its moving direction is the same with broadcasting node, based on the next cluster head selection algorithm, it will participate in optimal cluster head selection algorithm to become the next cluster head, which has the maximum of (Dij Vj)/R, where Vj is the speed of vehicle j. It is similar to P-persistence algorithm, with additional consideration of selecting the vehicle with higher speed when they are at the same distance. The selection of a higher speed vehicle at the same distance leads to a negative effect in disseminating message further because vehicles with higher speed are getting closer to the source vehicle than vehicles with lesser speed. In GHN algorithm10, messages are transmitted from cluster to cluster which is based on distance metric. It can slightly reduce broadcasting storm problem. The weakness is that transmission may spread in all directions.

In the ABM-V adaptive backoff mechanism11, the receiver estimates the expected benefit and redundancy and adaptively adjusts the backoff time by utilizing Dempster-Shafer evidence theory. The receiver with the shortest backoff time becomes the relay and rebroadcasts the packet to its neighbors. It can reduce broadcasting storm problems. In the Dynamic Broadcasting Algorithm12, nodes prepare their neighbor’s list by using hello beaconing; the algorithm calculates the waiting time for a node to rebroadcast a message by the number of neighbors and the distance between sender node and other vehicles. It reduces the redundancy of safety messages and minimizes the broadcast storm. However, the receiver needs to know the distance between its neighbors and the sender before deciding to rebroadcast, which needs extra communication between the receiver and the neighbors.

In Connected Dominating Set and Set Cover for cluster formation2, the stability of cluster formation is increased along with a reduction in rebroadcasting by allowing a cluster head to be passive when all its cluster members can receive the message from the gateway vehicles. Both algorithm can reduce the broadcast storm. However, consideration of the speed difference may often narrow the broadcast area. In both methods, the cluster/community head needs to know the distance to its neighbors to form cluster/communities, which needs extra communication between them.

In Selective Reliable Broadcast protocol (SRB)13, which belongs to cluster-based approaches, packets are forwarded only to cluster-heads. It can reduce the broadcast storm. But lots of calculation is needed on the sender to select the cluster-heads.

Modularity based Mobility Aware Community Detection Algorithm2 groups similar vehicles into communities and selects a few among them as forwarders considering their relative mobility, modularity gain, and distance.

The Distributed Clustering Scheme is a new distributed connectivity-based algorithm to form stable clusters14. It can reduce broadcasting storm problem.

In intelligent reliability-aware data dissemination (ReIDD)15, a coalition game is formulated among the vehicles by considering vehicles as the players in the game. Messages are routed to the next destination by selecting the most reliable path. Lots of calculation is needed to select the cluster-heads. It also needs extra communication among vehicles to form coalitions or clusters.

In Hierarchic Model (HM)16, by combining clustering, DSRC for V2V, and 5G for V2I, the crashed vehicle communicates with its Cluster Masters (CM), which communicates with the 5G infrastructure. The 5G base station (BS) then forwards the message to other CM or Cluster Forwarders (CF). It removes the broadcast storm. It needs periodical communication between vehicles and BS. Both methods do not apply to lane change and other CAM because it cannot differentiate different lanes.

Waiting time method

In Acknowledged PBSM17, every vehicle uses a buffer to store the alert message and the message is discarded after a certain time. It can reduce the broadcast storm. But transmission may spread in all directions.

Relative Speed Based Waiting Time Algorithm18 calculates the waiting time for each vehicle after receiving the safety/ warning messages according to the relative speed of the vehicles, the distance between the vehicles, and range of vehicles. It can reduce the broadcast storm especially in dense environment. But transmission may spread in all directions.

In Efficient-directional broadcast algorithm19,20, only the furthest receiver is responsible to retransmit the message in the same direction. The waiting time for each vehicle is given as = (1 − Dij/R) ∗maxWT, where Dij and R are the same as before defined, maxWT is the maximum waiting time. It has such goodness as long transmission range, space reuse, low redundancy, and collisions. The weaknesses are: (1) it has wrong transmission direction in case of rotation of accidental vehicle; (2) The delay problem is a major problem.

Position-based method

GL-TVAODV21 is a Group Leader (GL) based Trusted Vehicular Adhoc On-demand Distance Vector routing protocol. RSUs are taken as GL. In the absence of RSU or RSU down, the GL-TVAODV protocol selects on Slowest Moving Vehicle (SMV) and trust as the GL among the numbers of vehicles presents in that area. It can reduce the broadcast storm and remove possible malicious rebroadcasting. In RSUs based dissemination3, the victimized vehicle creates an alert message that is transmitted to the closest RSU, which is then sent to all the RSUs on that path utilizing I2I (infrastructure to infrastructure) correspondence. The RSUs signal the vehicles using light emitting diodes (LEDs) planted along the path. Both methods do not apply to lane change and other collision avoidance mechanism (CAM) because it cannot differentiate different lanes. Both also need a large amount of RSUs.

In EB22, vehicles respond to the sender with an ACK message, which includes speed, ID, movement direction and position of the considered vehicle. The sender decides the forwarder based on the ACK. It needs three rounds of communication between the sender and the forwarder.

Hybrid approach combines distance-based and counter-based schemes23 and uses the counter-based constraint on the nodes located above the threshold to avoid excessive rebroadcasting. It is based on signal strength to decide distance without GPS. The weakness is it is difficult to set an appropriate counter.

In Broadcast Storm Suppression Algorithm (BSSA)24, the broadcast storm is suppressed by finding the ‘Farthest Infected Vehicle’ (FIV) travelling in the direction of the ESM and recovering the other infected vehicles within the region to prevent from rebroadcasting the ESM. It needs periodical communication among vehicles to record/update the farthest vehicles in range for all vehicles.

The received signal strength (RSSI) method25 includes only those neighbors in the EBN list for which the rate of change of received signal strength indicates that the vehicle is moving towards the event area. The lesser number of vehicles in the Emergency Broadcast Neighbors (EBN) list causes lesser broadcast storm ratio. It reduces broadcast storm. But the slow-moving vehicles in the same direction may not be included in the EBN list, which leads to disconnection.

Other method

In RRBCAST technique26, sender chooses the vehicle which has at least two neighbor nodes at its 1 hop as a relay node. This selection of relay cannot ensure the furthest possible transmission distance.

JAS27 makes all the nodes flood packets proportional to their RPM (Rotations per Minute), which is an effective mechanism of data exchange between nodes and RSUs. It increases connection but also increases the broadcast storm.

He et al.28 presented a method to periodically transmit rpcm broadcast message forwarding control strategy. Their method can reduce broadcasting storm problem but they didn’t explain how to realize the method in reality.

Chang et al.29 proposed the Adaptive Forwarding message and Cooperative Safe driving (AFCS) for achieving active safe driving mechanism. It can reduce broadcasting storm problem and cut relay vehicles. There is still broadcasting storms at intersections because messages are disseminated in all directions.

In DBSMA algorithm30,31, a dynamic broadcast storm mitigation algorithm is used to combat the broadcast storm problem in a vehicular network. It outperforms the Distributed Congestion Control (DCC) mechanism in reducing broadcasting storm problem. The problem with it is that transmission may spread in all directions.

Intensive Message Broadcast Protocol (IMBP)32 performs message reliability checks to confirm the message received from the sender and then uses the vehicle connected list and vehicle eliminating list for transfer of the message. It brings down message redundancy, contention, and collision. But it didn’t explain how to realize the method in reality.

Aditya et al.33 compared four schemes including probabilistic scheme, counter-based scheme, location-based scheme, and distance-based scheme in reducing broadcast storms and presented an i-table method in deciding the next hop node for packet forwarding. However, the method is not suitable for road traffic.

Raghu and Sandeep34 reviewed various techniques that focus on mitigating the broadcast storm problem in VANETs. Basheer and Bassil35 reviewed some VANET safety applications and revised the disseminating methods for V2V without infrastructure.

As has been mentioned in the introduction section, all of the above methods need to form a VANET and almost all of them focus on spreading messages endlessly from vehicles to vehicles that are not necessarily influenced by an accident or may not be relevant, which contributes to broadcast storms.

The literature review on a TGS

Thakurian4 presented the evaluation of route guidance and identified various imperfection in advanced traveler information systems (ATIS). Kühne et al.36 presented a method to provide alternative route recommendations based on real-time measurements from road near Munich, Germany. Chen et al.37 proposed an algorithm that can update the real-time optimal route at every intersection toward the destination. Lee et al.38 presented a disutility method for a route guidance system addressing travel time unreliability. Sen et al.39 incorporated travel-time variability into travelers’ path selection process by considering the mean and variance of path times. Sen40 described a method for computing default travel times for the ADVANCE implemented in Chicago. Lu et al.41 presented a method to estimate the expected travel time considering the time at risk. Li et al.42 studied vehicle proactive guidance in ride-hailing systems to reduce riders wait times and drivers idle travel distances. Ding et al.43 presented a segment travel time route guidance strategy where the sum of travel time on each segment is provided to the vehicles. Zouari et al.44 presented a method to select the followed path for vehicles when there is congestion or accident on the planned roads based on hierarchical interval type-2 fuzzy logic model and particle swarm optimization (PSO) method. Their method does not apply to an analytical DUO route choice model, where all the link/path flow and link/path time are exact, as is used in a TGS in this paper. Burkhard et al.45 studied the end user trust experience with online transit web sites. Wu et al.46 studied the role of the fuel tax rate and bus departure quantity on travel mode choice.

None of the above literature on a TGS covers the same method as in this paper, which sends messages only to the exact vehicles that will be influenced by an accident.

Method

The technology background for a TGS

The TGS can provide travelers with real-time travel information such as optimal routes to their destinations, which is beneficial to decreasing congestion. The advanced technology on high precision positioning and fast communication is indispensable to implement a TGS. The high precision positioning technology includes Global Navigation Satellite System (GNSS), Real Time Kinematic (RTK), and Urban Continuous Operation Reference Station System (CORS). With more CORS stations constructed and put into use, the loss or deformation of positioning signals due to building obstruction can be avoided. Thus the high-precision positioning of vehicles can be obtained on all streets and highways.

The 5G communication has the characteristics of high speed (the peak speed of up to 10-20G bit/s), low latency (a delay as low as 10ms after being connected), and large connectivity (capable of millions of connections per square kilometer), high transmission rate reaching 100Mbit/s under continuous wide area coverage and high mobility, traffic density reaching over 10 M bps/m2, and mobility supporting high-speed movement at 500 km/h47. Therefore, 5G communication enables the massive signals in a TGS to be transmitted at a millisecond level.

The optimal routes provided by a real-time TGS generally follows dynamic user optimal (DUO) principle, which means the actual travel cost of an individual traveler is minimum. When traffic is in the DUO status, the actual travel times experienced by travelers departing at the same time are equal and minimal. In order to find the optimal routes on a real-size transportation network timely, the DUO needs to be solved with an efficient algorithm. This paper selected the algorithm by Xu48 to solve for the optimal route for each vehicle.

The configuration of a TGS

In the TGS, there is a transport center which is made up of three functional modules: position module, communication module, and calculation module. The compulsory positioning of electrical motorcycles has been implemented in cities in China for more than a decade. The positioning of other vehicles can be implemented in the same way. To transmit the positioning information to the transport center, the positioning system also includes network communication (mobile communication, or 5G in China), which sends the positions of vehicles to the transport center or its branch centers. To protect the privacy of a vehicle, pseudo vehicle ID will be used to identify a vehicle in the communication. A huge computer or a workstation receives the positioning information and displays the vehicle’s location on an electronic map. In this way, the transport center or its branch centers trace the real-time position of about half a million vehicles installed with global positioning systems BDS (China) in a middle to large size city in China. The communication module can be the same as the one affiliated to the position module, with an additional duty to transmit other messages such as an accident reported from an accidental vehicle to the transport center or its branch centers. The transport center or its branch centers may communicate with some selected vehicles or influenced vehicles directly via 5G. With the current mass storage and high speed of the advanced computers, the processing of the data is not an issue. With the popularization of the 5G communication and the availability of the mass storage and high speed computers, the cost is not an issue, either.

All vehicles are installed with an On-Board Unit (OBU) which has a GNSS receiver, a 5G mobile communication device, a processor, and several interfaces (e.g. Ethernet)49. The GNSS receiver receives signals from the satellites and CORS reference stations. The CORS reference stations guarantee the GNSS receiver can always receive the positioning signals even when the signals from the satellite are blocked out by big buildings. The 5G device sends the vehicle’s 3D position (latitude, longitude, and altitude), speed, acceleration, yaw, etc., to the transport center or its branch centers through 5G stations. The positions of vehicles are updated in the transport center or its branch centers every several seconds based on the messages sent from the vehicles in a city. The 5G device of a vehicle receives signals from the transport center or its branch centers when needed, which could be messages such as rerouting, stopping, etc. Vehicles are connected via the transport center or its branch centers, which has/have a connection with each vehicle through the 5G communication.

Every vehicle chooses its departure time and destination by sending the departure time and destination to the transport center or its branch centers via the 5G device at the origin zone in advance. Pseudo vehicle ID is used to identify a vehicle to protect the privacy of the vehicle. The position module and communication module of the transport center or its branch centers receives the data on the departure times and destinations from all the vehicles/travelers and adds them together to obtain the time-dependent origin-destination (OD) demand. The calculation module calculates the most optimal route for each vehicle to its destination. The optimal route and the alternative routes for each vehicle is stored in the transport center or its branch centers until the vehicle reaches its destination. Meanwhile, the message of the optimal route and the alternative routes is sent from the communication module to each vehicle and is stored in the OBU of the vehicle. The majority of the travelers travel on a regular basis and the optimal route and the alternative routes is stored. Once there is change on the time-dependent OD demand, the optimal route and the alternative routes is updated.

In normal cases, vehicles run on the optimal routes to their destinations. The transport center or its branch centers monitor each vehicle’s movement. The position module collects each vehicle’s information sent from the vehicles through 5G. The calculation module calculates and predicts each vehicle’s path and trajectory. If it finds a vehicle has broken down (or an accident) through 5G, it will determine the vehicles that will be influenced by the accident, which can be found based on the optimal routes stored in the transport center or its branch centers. The influenced vehicles are those vehicles with their original optimal routes passing the accident position during the lasting time of the accident. Recalculation is not needed in looking up the influenced vehicles so the delay is avoided. The communication module will then send safety messages to the influenced vehicles through 5G. The influenced vehicles might be the following vehicles or any vehicles that plan to traverse the same street during the lasting time of the accident. The following vehicles in the same street will receive the safety messages and stop to avoid potential crashing. The vehicles that had planned to enter the street will use the alternative routes stored in their OBUs based on the safety messages. The alternative routes can be other optimal routes for other vehicles departing the same origin at the same departure time. Even if there are vehicles not following the optimal routes, as long as the majority of the travelers travel on the optimal routes, the above safety message dissemination method will function normally.

The layout of a TGS for a small network is shown in Fig. 1.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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The layout of a TGS for a small network.

Algorithm for calculating optimal routes

As mentioned in the above section, the calculation module calculates the most optimal route and the alternative route for each vehicle to its destination based on time-dependent OD demand. In this section, the model and solution algorithm for finding optimal routes are introduced.

The optimal routes for vehicles/travelers can be obtained by solving a DUO route choice problem. Some definitions on the DUO problem are given in Table 1.

Table 1 Some definitions on the DUO problem.
Full size table

In this paper, when the superscript is too long, it can also be put into a pair of square parenthesis after the variable.

The discrete variational inequality (VI) DUO route choice model is defined as

$$\:\sum\:_{r,s,p}\sum\:_{k=1}^{{K}_{0}}{\eta\:}_{p,\:k}^{rs*}\left({f}_{p,\:k}^{rs}-{f}_{p,\:k}^{rs*}\right)\ge\:0.$$
(1)

where * means the path flow and path time is estimated at the optimal status. Equation (1) is the definition of the IV. It states that for any OD \(\:rs\) at any \(\:k\), if the departure flow is positive over route \(\:p\), the travel time \(\:{\eta\:}_{p,\:k}^{rs}\) for route \(\:p\) must equal the minimal travel time. In other words, at equilibrium, the actual cost of flows departing at any time through any used path is equal and minimum and no flows can reduce its cost by unilaterally changing its departure time and route choice.

The recursive formula for the path time is as follows

$$\:{\eta\:}_{p,\:k}^{ri}={\eta\:}_{p,\:k}^{r\left(i-1\right)}+{\tau\:}_{a}\left[k+{\eta\:}_{p,\:k}^{r\left(i-1\right)}\right]\:\forall\:\:p,\:r,\:i;i=1,\:2,\:\cdots\:,\:s.$$
(2)

where \(\:p=\left(r,\:\cdots\:,\:s\:\right)\), \(\:x\in\:{\Theta\:}\),. \(\:{\Theta\:}\) is the feasible region defined by the following constraints:

Path flow conservation constraint:

$$\:\sum\:_{p}{f}_{p,\:k}^{rs}={f}_{k}^{rs}\:\:\:\:\:\forall\:\:k,\:r,\:s.$$
(3)

(3) states that the sum of the path flow at an interval of each OD equals the time-dependent demand of the OD at the interval.

Link inflow conservation constraint:

$$\:\sum\:_{rs}{u}_{a,\:k}^{rs}={u}_{a}^{k\:\:\:\:\:}\forall\:\:a,\:k,\:r,\:s.$$
(4)

(4) states that the sum of the inflow of all OD entering a link at an interval equals the inflow of the link at an interval.

Link outflow conservation constraint:

$$\:\sum\:_{rs}{v}_{a,\:k}^{rs}={v}_{a}^{k}\:\:\:\:\forall\:\:a,\:k,\:r,\:s.$$
(5)

(5) states that the sum of the outflow of all OD leaving a link at an interval equals the outflow of the link at an interval.

Node flow conservation constraint:

$$\:\sum\:_{a\in\:B\left(j\right)}{v}_{a,\:k}^{rs}=\sum\:_{a\in\:A\left(j\right)}{u}_{a,\:k}^{rs}\forall\:\:j\ne\:r,\:s;\:k,\:r,\:s.$$
(6)

where\(\:\:A\left(j\right)\) is the set of links after\(\:\:j\) and \(\:B\left(j\right)\) is the set of links before\(\:\:j\). (6) states that the sum of the flow entering a node equals the flow exiting the node at an interval.

Link flow propagation constraint:

$$\:{u}_{a,\:k}^{rs}={v}_{a}^{rs}\left[k+{\tau\:}_{a}^{k}\right]\forall\:\:a,\:k,\:r,\:s.$$
(7)

(7) states that the inflow entering a link at an interval will leave the link at a later interval.

Path-link flow incidence constraint:

$$\:{u}_{a}^{rs}\left(n\right)=\sum\:_{r,s,p}\sum\:_{k=1}^{{K}_{0}}{f}_{p,\:k}^{rs}{\delta\:}_{rsa}^{pkn}\:\forall\:\:a,\:n,\:\:r,\:s.$$
(8)

where \(\:{\delta\:}_{rsa}^{pkn}\) =1 if travelers departing origin \(\:r\) at interval \(\:k\) heading for destination \(\:s\) on path \(\:p\) arrives at link \(\:a\) during the \(\:nth\) interval; =0, otherwise. (8) states that the inflow of a link from OD \(\:rs\) at interval \(\:n\) equals the sum of the path flow from the OD arriving at the link at interval \(\:n\).

Nonnegative constraint:

$$\:{f}_{p,\:k}^{rs}\ge\:0,\:{u}_{a,\:k}^{rs}\ge\:0\:\forall\:\:k,\:r,\:s,\:a,\:p.$$
(9)

(9) is nonnegative constraint.

The VI DUO model is equivalent to the following optimization problem under relaxation

$$\:\underset{\varvec{f}}{{min}}Z=\sum\:_{n=1}^{n=K}\sum\:_{a}\left\{{\int\:}_{0}^{\sum\:_{rs}\sum\:_{k=1}^{{K}_{0}}\sum\:_{p}{f}_{p}^{rs}\left[n-{\eta\:}_{p}^{ri}\left(k\right)\right]{\delta\:}_{rsa}^{pkn}}{\tau\:}_{a}^{k}\left(\omega\:\right)d\omega\:\right\}.$$
(10)

(10) is the objective function of the equivalent optimization problem at each relaxation of the VI.

The algorithm for solving the above ideal route-based DUO route choice model is given by48, interested readers should refer to the paper for a detailed explanation of the algorithm.

Application and results

The application of the method

In this section, we show the safety message dissemination method in the case of the example network in Fig. 2. In the first sub-section, first, we use relaxation with a gradient projection algorithm to solve for the optimal routes for all vehicles. Second, we provide alternative routes for vehicles that are influenced by an accident. In the second sub-section, we analyze the ability of the method in reducing broadcast storms by comparing it with a simple broadcast method and other methods in VANETS.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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An illustration network.

In the network shown in Fig. 2, there are 24 links, each being a one-lane street with a length of 0.5 miles. There are 9 nodes, node 2 to node 8 each representing an intersection, node 1 being the origin zone, and node 9 being the destination zone. One O-D pair 1–9 is considered. The total demand from the origin zone 1 to the destination zone 9 is assumed as 360 vehicles. These vehicles depart from origin zone 1 from 7:20 am to 7:50 am (so the departure horizon is 30 min), heading for destination zone 9 along optimal routes between OD pair 1–9. The free flow speed is 25 miles/hour. The following linear travel time function is used to enforce the first-in-first-out (FIFO) condition: \(\:{\tau\:}_{a}^{k}={L}_{a}/{s}_{f}+0.3{x}_{a}^{k}\), where \(\:{L}_{a}\) and \(\:{s}_{f}\) are the length of link \(\:a\) and the free flow speed, \(\:{x}_{a}^{k}\) is the number of vehicles on link \(\:a\) at time \(\:k\). There are thirty departure time intervals, each lasting 60 s. The OD flows are 12 vehicles per minute.

The relaxation with gradient projection algorithm by Xu48 was used to solve for the optimal routes for all vehicles. The work is supposed to be done in the calculation module of the transport center or its branch centers when implementing the program in reality. Part of the optimal routes are shown in Table 2. It should be noted that here our purpose in this paper is to apply an algorithm to find the optimal routes to be used in a TGS. Our purpose is not to present and prove a novel algorithm for solving the DUO model.

In normal cases when there is no accident, vehicles run on the optimal routes to reach their destinations (this means a vehicle will enter or leave a street at a specified time). For example, as is shown in the first row of Table 2, among the 12 vehicles departing origin 1 in the minute of 7:20, 3 of them traverse link 5 at the 1st minute which is 7:20, traverse link 15 at the 2nd minute which is 7:21, traverse link 23 at the 3rd minute which is 7:22, final traverse link 24 at the 4th minute which is 7:22, etc. At 7:28, there was a vehicle breaking down in link 13 as shown in Fig. 2.

Table 2 Part of the optimal routes.
Full size table

The accident lasted for 5 min before the accidental vehicle was towed away from the street. The message of the accident was sent from the accidental vehicle to the transport center through 5G communication. The transport center determined the vehicles that would be influenced by the accident. It also looked up the vehicles with their original optimal routes passing link 13 during the lasting time of the accident which was from 7:28 to 7:32. The communication module then sent safety messages or rerouting messages through 5G to the influenced vehicles, which are the vehicles that had planned to enter link 13 from 7:28 to 7:32. They will use the alternative routes stored in their OBUs upon receiving the safety messages.

As can be seen from the table, the following vehicles in link 13 at 7:28 (highlighted in yellow) are 4 vehicles departing origin 1 at the 7th minute which is 7:27. They received a safety message sent from the transport center through 5G and stopped to avoid potential crashing. The vehicles that had planned to traverse link 13 during the lasting time of the accident (highlighted in red) include 3 vehicles departing origin 1 at the 8th, 9th, 10th, 11th, and 12th minute, or 7:28, 7:29, 7:30, 7:31, and 7:32, respectively. They would arrive at link 13 at 7:29, 7:30, 7:31, 7:32, and 7:33, respectively, when the accident still blocked the street but was directed to alternative routes stored in their OBUs. The alternative routes were link 5, link 15, link 23, and link 24 sequentially (highlighted in green). After the accidental vehicle was towed, link 13 was free to use and traffic was back to normal. Only 19 vehicles that were influenced by the accident received the safety message. All the other vehicles that were not affected by the accident were not informed of the messages. So there was no broadcast storm in this sense.

The analysis of the broadcast storm reduction

As a comparison, we now analyze what will happen if a simple broadcast method in a VANET is used to broadcast the safety message. For analysis, the number of vehicles in each street at each interval needs to be known. Figure 3 shows the number of vehicles on each link at each interval during the lasting time of the accident based on the above calculation. At 7:28 when the accident happened, there are 48 vehicles on all the used 12 streets (streets where there are vehicles). There are 48 vehicles on all the used 12 streets at 7:29, 7:30, 7:31, and 7:32, respectively. The area of the network is 1609 m by 1609 m square. The broadcast frequency of dedicated short range communication (DSRC) is 10 Hz or 10 times per second. The broadcast range of DSRC is 300–1000 m. With the simple broadcast method, each of the 48 vehicles will broadcast the safety message once. Conservatively speaking, a vehicle will receive the messages rebroadcast by other vehicles on the same street. So the average number of messages a vehicle received is 48/12 = 4, where 48 is the total number of messages broadcast by 48 vehicles, and 12 is the number of streets where there are vehicles. This will happen in less than 3 s if we assume the latency of the broadcast is 2 s. At 7:29, 12 new vehicles enter the network. For them to know the accident, the safety message will have to be broadcast again. What happened at 7:28 will repeat. Similarly, what happened at 7:28 will repeat at 7:30, 7:31, and 7:32. If the vehicles broadcast the message once a minute during the 5 min when the accident lasts, conservatively speaking, a vehicle will receive 4 messages rebroadcast by other vehicles on the same street in a minute. For 48 vehicles, there are 192 (= 48* 4) messages received and rebroadcast in a minute, and there are 960 (= 192* 5) messages received and rebroadcast during the 5 min when the accident lasts. If the vehicles broadcast the message twice a minute during the 5 min when the accident lasts, there are 1920 (= 960* 2) messages received and rebroadcast during the 5 min when the accident lasts., and so on. Most of the vehicles do not need the message because their optimal routes do not include the street where the accident happened. So there is a lot of unnecessary and redundant rebroadcast. As analyzed in the previous subsection, only 19 vehicles that were influenced by the accident received the safety message by the method presented in this paper.

The comparison of the results of broadcasting messages to all vehicles versus selectively transmitting messages only to relevant vehicles in this example is shown in Fig. 4. As can be seen in the figure, with the same broadcast frequency (The time of broadcast in a minute), the number of rebroadcast messages with the simple broadcast method is 50 times more than the method presented in this paper. Other methods may lessen to some extent the congestion and collision of broadcast but will not thoroughly remove the unnecessary and redundant rebroadcast. Only the method presented in this paper can thoroughly remove the unnecessary and redundant rebroadcast.

Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Number of vehicles on each link at each interval during the lasting time of the accident (7:28 − 7:32).

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
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The comparison of the results of broadcasting messages.

The comparison of the method to WAZE and Google Maps

It is noticeable that the well-known applications like WAZE and Google Maps achieve similar functionality using cellular networks, suggesting new routes only to vehicles that will pass by the accident location. However, there are two differences between the method presented in the paper and in WAZE and Google Maps. One is that the shortest path in WAZE and Google Maps is based on distance and the congestion effect caused by traffic flow is not considered. In the method presented in the paper, the dynamic shortest path is based on travel time and the congestion effect caused by traffic flow is considered by the DUO model. The other is that the message in WAZE and Google Maps is shown on the map for all travelers and the travelers need to watch the map for the possible information from time to time. If the travelers find the message is useful to them they will use the message. If the travelers find the message is not useful to them they will ignore the message. In either case, the travelers need to watch the map proactively and continually to see the message. However, driving and watching the map is a dangerous behavior and is likely to cause road accidents. In the method presented in the paper, travelers do not need to watch the map. The message will be sent to the relevant travelers via the 5G from the transport center. All the travelers not influenced by the accident will receive no message. Only the relevant travelers receive the message and the speaker of the receiver of the travelers will broadcast the message in everyday language. The traffic safety is not affected.

Conclusions

In the past studies, a road accident message was often broadcast through the V2V by forming a VANET and the corresponding safety message broadcasting methods often lead to broadcast storms. This study presented a method to broadcast accident messages in a TGS that obviates a VANET and broadcast storms. Unlike current safety message broadcasting methods in VANETs (the majority of the literatures in this paper belong to safety message broadcasting methods in VANETs), most of which disseminate messages to as many vehicles as possible, this method does not form a VANET. It sends messages only to the exact vehicles that will be influenced by an accident. The selection of influenced vehicles in this study is consistent with drivers’ route choice behavior, i.e., they are on the dynamic shortest paths from their origins to destinations. It greatly reduces redundant and unnecessary dissemination of messages to irrelevant vehicles and obviate broadcast storms.

The method presented in this paper requires high-precision positioning technology such as massive construction of CORS and 5G communication base stations. It also requires vehicles to be equipped with a 5G device, a processor, and several interfaces. Also needed is a transport center or its branch centers made up of three functional modules: position module, communication module, and calculation module. With the popularization of the 5G communication and the availability of the mass storage and high speed computers, the processing of the data and the cost is not an issue. Thus this paper has presented a safety message dissemination method in a TGS in the near future when vehicles are equipped with the above devices.