A Mobicast Routing Protocol in Vehicular Ad-Hoc Networks

Abstract

In this paper, we present a “spatiotemporal multicast”, called a “mobicast”, protocol for supporting applications which require spatiotemporal coordination in vehicular ad hoc networks (VANETs). The spatiotemporal character of a mobicast is to forward a mobicast message to vehicles located in some geographic zone at time t, where the geographic zone is denoted as zone of relevance (ZOR). Vehicles located in ZOR at the time t must keep the connectivity to maintain the real-time data communication between all vehicles in ZOR. The connectivity is kept of all vehicles in ZOR through the vehicular ad hoc networks (VANETs). The connectivity of ZOR is lost if any vehicle in ZOR suddenly accelerates or decelerates its velocity. The temporal network fragmentation problem is occurred such that vehicle in ZOR cannot successfully receive the mobicast messages. To solve the problem, a new mobicast protocol is presented in this work to successfully disseminate mobicast messages to all vehicles in ZOR via a special geographic zone, called as zone of forwarding (ZOF). The main contribution of this work is to develop a new mobicast routing protocol to dynamically estimate the accurate ZOF to successfully disseminate mobicast messages to all vehicles in ZOR. To illustrate the performance achievement, simulation results are examined in terms of dissemination successful rate, packet overhead multiplication, packet delivery delay, and throughput.

1 Introduction

The vehicular ad hoc network (VANET) is the promising and important networking techniques for building the Intelligent Transportation System (ITS) [1]. A VANET is composed of vehicles, while each one has wireless communication device to transmit and receive emergency messages for collision warning and avoidance or broadcast advertisement messages for infotainment service. To provide the short range inter-vehicle wireless communication, Dedicated Short Range Communication (DSRC) standard is developed by ASTM [1]. The VANET is a special case of mobile ad hoc networks (MANETs) [1]. It is known that MANETs is an infrastructureless communication model without any assistance of roadside units. The VANET fundamentally has quite different properties than MANET, such that the fast changeable network topology, high mobility model, and frequent temporary network fragmentation. These new properties of VANETs increases the difficulties of designing protocols in VANETs.

A new multicast communication paradigm called a “spatiotemporal multicast” or “mobicast” was recently investigated in [2–6] which support spatiotemporal coordination in applications over wireless sensor networks (WSNs) [7–9]. The distinctive feature of mobicast is the delivery of information to all nodes that happen to be in a prescribed region of space at a particular point in time, which is necessary for VANETs to provide safety applications for drivers. However, VANETs are fundamentally different to WSNs, such as the property of mobility and rapid changed topology. It is known that VANET is composed of a set of mobile vehicles and WSN is composed of a set of static sensor nodes [10]. The topology of WSNs is stable, but the topology of VANET is rapidly changed. This key difference leads to existing mobicast protocols on WSNs can not be directly applied to VANET. Consequently, we propose a new mobicast protocol to consider the interest property of VANETs. This prescribed region is a geographic zone and is denoted zone of relevance (ZOR). The set of multicast message recipients is specified by a zone of forwarding (ZOF). This is observed that ZOR and ZOF continuously moves and evolves over time. With keeping the suitable ZOR and ZOF for a moving vehicle, the shape and size of ZOF at different time intervals greatly differs. This provides a mechanism for application developers to express their needs for spatial and temporal information dissemination through the VANETs. In this paper, the spatiotemporal character of a mobicast is to disseminate a mobicast message to all mobile vehicles that will be present at time t in the ZOR, where both the location and shape of the ZOR are a function of time over some interval (t _start,t _end). The mobicast is constructed of a series of ZORs over different intervals (t _start,t _end), and only mobile vehicles located in the ZOR in the time interval (t _start,t _end) must keep the connectivity in order to maintain the real-time data communication between all mobile vehicles in ZOR. The connectivity is kept of all mobile vehicles in ZOR through the vehicular ad hoc networks. That is, all vehicles in ZOR must receive the mobicast messages sent from a source vehicle in ZOR.

One of the challenges posed by this problem is how to develop an efficient mobicast protocol under highly changeable topology and temporal network fragmentation to guarantee that vehicles in the ZOR can successfully receive the mobicast messages in VANETs. The design difficulties is stated as follows. Most of the traffic cases, vehicle must moves at a different velocity, $\overrightarrow{v}$, in the time interval (t _start,t _end) in the road. If one vehicle of ZOR accelerates or decelerates its velocity, from $\overrightarrow{v}$ to $\overrightarrow{v^{\prime }}$, in the time interval (t _start,t _end), the connectivity of this vehicle is different. Some vehicles in ZOR may unsuccessfully receive the mobicast messages due to loss the connectivity. This condition also called as temporal network fragmentation problem. To overcome the problem, a mobicast protocol in VANETs is presented to successfully disseminate mobicast messages to all vehicles in ZOR via the vehicles of ZOF. The main contribution of this work is to develop a new mobicast protocol to accurately estimate the ZOF to achieve the high dissemination successful rate.

The rest of this paper is organized as follows. Section 2 reviews related works. Section 3 defines the system model, motivation, and describes the basic idea of our scheme. Section 4 presents the new mobicast routing protocol. Performance analysis is discussed in Section 5. Finally, Section 6 concludes this paper.

2 Related works

Protocol for supporting mobicast is not yet investigated in VANETs, but similar problems [2–6] had been investigated in wireless sensor networks (WSNs). A spatiotemporal multicast protocol, namely a mobicast, was presented in WSNs [2–6]. The spatiotemporal characteristic of a mobicast is to forward a message to all nodes that will be present at time t in the forwarding zone. Huang et al. [6] developed a mobicast routing protocol, called face-aware routing (FAR). The FAR protocol is a geometric routing protocol which provides reliable routing results. Chen et al. [2, 3] proposed a variant-egg (VE)-based mobicast routing protocol in sensornets. This VE-mobicast protocol can adaptively and efficiently determine the location and shape of the message forwarding zone.

However, all existing mobicast routing strategies are only applied to WSNs. It is observed that VANET is natively different from WSN. A VANET consists of mobile vehicles, while WSN is composed of static sensor nodes [10]. The topology of WSNs is always stable, but topology of VANETs is rapidly changed. This causes the link connectivity problem or frequent temporary network fragmentation problem in VANETs. With frequent temporal network fragmentation problem, mobicast messages may not be successfully received. VANETs incurred the frequent temporal network fragmentation problem, but this problem has never occurred in WSNs. Mobicast protocols must be carefully designed to overcome the frequent temporal network fragmentation problem in VANETs [11]. Efforts will be made in this work to develop a new mobicast protocol in VANETs.

Some geographic routing results in VANETs are present to improve the efficiency for transmitting messages to a geographic region [12–15]. To send messages to a specific location in VANETs, Briesemeister and Hommel [14] proposed a messages disseminating mechanism, by utilizing a distance-based backoff scheme, among highly mobile vehicles. To send messages to vehicles in a geocast region, Bachir et al. [12] proposed a geocast for inter-vehicle communication based on routing schemes in [14]. This approach uses periodic broadcasts to overcome temporary network fragmentation. The re-broadcast period is calculated based on the maximum vehicle speed. Maihofer et al. [15] proposed geocast approach by keeping the message for a certain period of time when the message enters into the geocast region. Joshi et al. [13] also proposed a distributed robust geocast protocol for inter-vehicle communication to consider the problem of frequent topology changes and network fragmentation. The zone of relevance (ZOR) is first defined in [13] as a geographic region which vehicles in this region should receive the geocast messages. To enhance the reliability of receiving geocast messages under frequent changeable topology, the zone of forwarding (ZOF) is defined in [13] as the geographic region which vehicles in this region should forward the geocast messages to other vehicles in the ZOR. Note that, ZOF usually surrounds ZOR to ensure the geocast messages can be delivered to vehicles inside ZOR. A periodic retransmission mechanism is proposed in [13] to overcome the network fragmentation.

The geocast routing protocols [12–15] successfully transmit messages to a geocast region in VANETs. However, these protocols can not apply to transmit real-time messages to a dynamically prescribed region which is surrounded by a moving vehicle at time t. That is difficult to handle emergency traffic situation, such as warning notifications initiated from a suddenly braking vehicle. Considered such a vehicle, called as an event vehicle [16], we assumed that the brake system of the event vehicle is suddenly and partially failed at time t. All vehicles after the event vehicle, formed a dangerous region, encounter a dangerous condition at time t. Observe that, the event vehicle keeps on moving. At time t + 1, the location of dangerous region is different. It is observed that the dangerous region is simultaneously moving with the event vehicle. The event vehicle must continuously send warning notification to vehicles in the dangerous region to avoid the accident. Existing geocast routing protocols in VANETs can not fully support above requirements. In fact, vehicles inside the dangerous region are difficult to receive warning notifications at time t. This paper proposes a distributed mobicast routing protocol to disseminate mobicast messages to all vehicles in the prescribed dangerous region at time t. This prescribed dangerous region is a geographic zone and is denoted as ZOR _t in this work. To our knowledge, this work is the first study to develop the mobicast routing protocol in VANETs.

3 Preliminaries

This section presents the system model. The contribution and the application examples are also introduced.

3.1 System model

When a vehicle moves at a high speed, the velocity variation between each pair of vehicles is large. The distance between each pair of vehicles quickly changes from time t to time t + 1. This offers the temporal network fragmentation problem. A vehicle easily moves out of the communication range of the event vehicle and fail to receive mobicast messages. This observations shows that the stable routing is not suitable for mobicasting. Our mobicast routing protocol adopts dynamic forwarding zone to disseminate mobicast messages.

A special case of a “spatiotemporal multicast” protocol is introduced for supporting applications which require spatiotemporal coordination in VANET. This spatiotemporal multicast protocol provides applications that need to disseminate the multicast message to the “right” place (or prescribed region) at the “right” time. In a VANET, a vehicle is said as an event vehicle [16] or V _e if an abnormal condition or faulty event is detected and triggered from sensor devices and on-board unit (OBU) of the vehicle. Mobicast messages are initiated from V _e to notify nearby vehicles to avoid the accident. A prescribed region is determined by the event condition if the event is triggered. This prescribed region indicates a coverage area centered on V _e . All vehicles in this region possibly be involved the accident with V _e . To avoid the accident with V _e , these vehicles must receive the mobicast messages from V _e before the accident is occurred. For this purpose, the center of the prescribed region should be the same with location of V _e at any time; therefore, the prescribed region is moving at the same speed as V _e , and toward the same direction with V _e . Furthermore, the large or small size of the prescribed region is depended on the speed of V _e .

In the following, we define ZOR _t (zone of relevance), ZOF _t (zone of forwarding), and ZOA$_{t}^{V_{i}}$ (zone of approaching). Let V _i denote as the vehicle ID and $v_{i_{t}}$ denote as the velocity of V _i at time t, where i = {e,1,2,...,i,i + 1,...,n} throughout this paper. Event vehicle V _e is the mobicast-initiated vehicle which initiates a mobicast routing protocol to disseminate the mobicast messages to other vehicles in the ZOR _t . For instance as shown in Fig. 1, V _e is an event vehicle and $v_{e_{t}}$ is the velocity of V _e at time t.

Fig. 1

ZOR _t is the union set of ${\rm{ZOR}}_{t}^{1}\cup {\rm{ZOR}}_{t}^{2}\cup {\rm{ZOR}}_{t}^{3}\cup {\rm{ZOR}}_{t}^{4}$

ZOR _t is the prescribed region to indicate which vehicle is relevant to the event occurred on V _e and V _e should announce the condition of event to those vehicles for accident avoidance by disseminating the mobicast message.

Definition ZOR _t (zone of relevance)  Given an event vehicle V _e , ZOR _t is an elliptic region determined by V _e at time t, such that vehicle V _i must be successfully received the mobicast message from V _e at time t, where each V _i is located in the ZOR _t . In this work, ZOR _t is split into four quarters, each one is a sub-zone of relevance; they are ZOR$_{t}^{1}$, ZOR$_{t}^{2}$, ZOR$_{t}^{3}$, and ZOR$_{t}^{4}$, respectively. Let ZOR$_{t}^{q}$, q = {1,2,3,4}, denote a sub-zone of relevance in the q-th quadrant, where V _e is the circle center. Let ZOR _t be constructed by a union of four sub-zones of relevance, where ZOR _t  = $\underset{q\in \{1,2,3,4\}}{\bigcup }$ ZOR$_{t}^{q}$. The center location of ZOR _t is the same with the location of V _e , moving at the same speed as V _e , and toward the same direction with V _e .

Figure 1 shows an example of ZOR _t  = ZOR$_{t}^{1}\cup$ZOR$_{t}^{2}\cup$ZOR$_{t}^{3}\cup$ZOR$_{t}^{4}$, V _e should send the mobicast message to V ₁ and V ₂ in ZOR$_{t}^{1}$. Figure 2 gives a continuous-time example of ZOR _i , where i = t...t + 2, with the temporal network fragmentation problem. The transmission range of each vehicle is assumed to r. Initially, V _e detects an emergency event at time t to form a ZOR _t . V ₁ and V ₃ are involved by this event and indicated to receive the mobicast message by ZOR _t . V ₁ and V ₃ are located within the transmission range of V _e ; thus V _e directly disseminates the mobicast message to V ₁ and V ₃. At time t + 1, V ₂ and V ₄ approach V _e and they are indicated to receive the mobicast message by ZOR_t + 1. Observed that although V ₄ is out of transmission range of V _e , V ₄ can receive the mobicast message by relaying from V ₁. At time t + 2, V ₁ moves away from V ₄ and V ₂ moves out of transmission range of V _e ; thus V ₂ and V ₄ can not receive the mobicast message. The temporal network fragmentation problem occurred on V ₂ and V ₄. ZOF _t is introduced later to solve this problem.

Fig. 2

Operation of mobicasting

To overcome the temporal network fragmentation problem, ZOF _t is used to disseminate the mobicast message to all vehicles located in the ZOR _t . The formal definition of ZOF _t is given.

Definition ZOF _t (zone of forwarding)  Given a V _e , ZOF _t is a geographic region determined by V _e at time t, such that each vehicle V _j has the responsibility of forwarding the mobicast message sent from vehicle V _e , where V _j is located in the ZOF _t . In this work, ZOF _t is split into four quadrants, each one is a forwarding sub-zones; they are ZOF$_{t}^{1}$, ZOF$_{t}^{2}$, ZOF$_{t}^{3}$, and ZOF$_{t}^{4}$, respectively. Let ZOF$_{t}^{q}$, q = {1,2,3,4}, denote a forwarding sub-zone in the q-th quadrant, where V _e is the circle center. Let ZOF _t be constructed by a union of four forwarding sub-zones, where ZOF _t  = $\underset{q\in \{1,2,3,4\}}{\bigcup }$ ZOF$_{t}^{q}$.

Observe that, ZOF _t is the union of ZOF$_{t}^{1}\cup$ZOF$_{t}^{2}\cup$ ZOF$_{t}^{3}\cup$ZOF$_{t}^{4}$, where ZOF _t indicates which vehicle should forward the mobicast message to other vehicles located in the ZOR _t . Figure 3a shows V ₂ and V ₄ can not receive the mobicast message due to the temporal network fragmentation problem. All vehicles in ZOF _t must forward received mobicast messages, even those vehicles are not located in ZOR _t . Example of ZOF _t is illustrated in Fig. 3b, V ₅ and V ₆ are located in ZOF _t and have the responsibility of forwarding the mobicast message to V ₂ and V ₄, respectively. Normally, the size of ZOF _t may be larger or smaller than the optimal size of ZOF _t . If the size of ZOF _t is larger than the optimal size of ZOF _t , some irrelevant vehicles are asked to uselessly forward the mobicast message. If the size of ZOF _t is smaller than the optimal size of ZOF _t , the temporal network fragmentation problem is incompletely overcame. Observe that, the size of ZOF _t is difficult to predict and determined under the high speed environment, such that it easily wastes the network resources. Efforts will be made in this work to propose an efficient scheme to estimate the size of ZOF _t is near to the optimal size of ZOF _t . Therefore, zone of approaching (ZOA$_{t}^{V_{i}}$ or Z$_{t}^{V_{i}}$) is proposed herein to accurately predict the ZOF _t .

Fig. 3

a Temporal network fragmentation problem and b example of ZOF _t

Zone of approaching (ZOA$_{t}^{V_{i}}$ or Z$_{t}^{V_{i}}$) is the zone of approaching as defined below, ZOF _t is constituted by some different ZOA$_{t}^{V_{i}}$ at time t, such that the size of the ZOF _t is near to optimal size of ZOF _t . Observe that ZOA$_{t}^{V_{i}}$ is proposed herein to overcome the the temporal network fragmentation problem with the high dissemination successful rate and the lower network overhead.

Definition ZOA$_{t}^{V_{i}}$ or Z$_{t}^{V_{i}}$(zone of approaching)  Let ZOA$_{t}^{V_{i}}$ or Z$_{t}^{V_{i}}$ denote as an elliptic zone of approaching to forward the mobicast message more closed to a destined vehicle and Z$_{t}^{V_{i}}$ is initiated by vehicle V _i at time t. Any vehicle in the Z$_{t}^{V_{i}}$ has the responsibility of forwarding the mobicast message sent from vehicle V _e . Z$_{t}^{V_{i}}$ bounds the mobicast message propagation, vehicles in the Z$_{t}^{V_{i}}$ can only forward the mobicast message to other vehicles located in the Z$_{t}^{V_{i}}$. If a vehicle cannot successfully forward the mobicast message to any neighbor vehicle in the Z$_{t}^{V_{i}}$ which is more closed to the destined vehicle, a new approaching zone is initiated.

We explain how to grow a new zone of approaching Z$_{t}^{V_{i+1}}$ from an existing zone of approaching Z$_{t}^{V_{i}}$ as follows. Given two connected approaching zones Z$_{t}^{V_{i}}$ and Z$_{t}^{V_{i+1}}$, if V _i + 1 in Z$_{t}^{V_{i}}$ cannot successfully forward the mobicast message to any neighbor vehicle closed to the destined vehicle, then V _i + 1 initiates a new zone of approaching Z$_{t}^{V_{i+1}}$, where V _i + 1 is located in Z$_{t}^{V_{i}}$. Therefore, multiple zones of approaching are initiated to forward the mobicast message in the q-th quadrant, such that ZOF$_{t}^{q}$ is finally formed by all initiated zones of approaching in the q-th quadrant. Therefore, we have ZOF$_{t}^{q} = {\rm ZOR}_{t}^{q}\cup {\rm Z} _{t}^{V_{1}}\cup ...\cup {\rm Z}_{t}^{V_{i}}\cup {\rm Z}_{t}^{V_{i+1}}\cup ... \cup {\rm Z}_{t}^{V_{n}}$, where q = {1,2,3,4}. Observe that, ZOR _t is the partial ZOF _t since the mobicast message should be transmitted to all vehicles located in ZOR _t . Figure 4 gives an example of the detailed construction of ZOF$_{t}^{1}$. Both V ₂ and V ₄ cannot find out neighbors in ZOR$_{t}^{1}$, then Z$_{t}^{V_{2}}$ and Z$_{t}^{V_{4}}$ are initiated. Continually, V ₈ cannot find out neighbors in Z$_{t}^{V_{4}}$ closed to V ₅, V ₈ then initiates Z$_{t}^{V_{8}}$. In addition, V ₆ has similar condition as V ₈, V ₆ stops the forwarding since V ₆ has no any neighbor vehicle. Finally, ZOF$_{t}^{1} = {\rm ZOR}_{t}^{1}\cup {\rm Z}_{t}^{V_{2}}\cup {\rm Z}_{t}^{V_{4}}\cup {\rm Z}_{t}^{V_{8}}$.

Fig. 4

Example of multiple ZOA$_{t}^{V_{i}}$

3.2 Contribution

In this paper, zone of approaching is proposed to dynamically form the forwarding zone to overcome temporal network fragmentation problem in order to forward the mobicast message to all vehicles located in ZOR _t . In existing investigations, a fixed size of ZOF _t is adopted to solve temporal network fragmentation problem. A fixed size of ZOF _t is difficult to handle the rapid changed topology and easily wastes the unnecessary network resource. Therefore, our mobicast routing protocol uses adaptable ZOA$_{t}^{V_{i}}$ to dynamically form flexible size ZOF _t to fit current topology at each time t. The contributions are summarized as follows: (1) our mobicast protocol builds a new adaptive and dynamic shape ZOA$_{t}^{V_{i}}$ to form the ZOF _t to adaptively determine the size, shape, and location of the forwarding zone to disseminate the mobicast messages to vehicles located in the ZOR _t under highly changeable topology; (2) our mobicast protocol is a fully distributed algorithm which effectively reduces the communication overhead of constructing the ZOF _t and the mobicast message forwarding overhead; (3) our mobicast routing protocol offers high dissemination successful rate using ZOA$_{t}^{V_{i}}$. Figure 5 illustrates at time t, V ₁, V ₂, V ₃, and V ₄ are located in ZOR _t and receive the mobicast message from vehicle V _e . At time t + 1, V ₂ and V ₄ can not directly receive the mobicast messages due to temporal network fragmentation problem. Figure 5 demonstrates a mobicast example in four quarters. At time t + 1, V _e , V ₅, and V ₁ initiate Z$_{t+1}^{V_{e}},$ Z$_{t+1}^{V_{5}}$, and Z$_{t+1}^{V_{1}}$ to forward the mobicast messages to vehicles V ₄ and V ₂. In this case, ZOF$_{t+1}^{1}$ = ZOR$_{t+1}^{1}\cup$ Z$_{t+1}^{V_{1}}$, ZOF$_{t+1}^{2}$ = ZOR$_{t+1}^{2}\cup$ Z$_{t+1}^{V_{e}}$ ∪ Z$_{t+1}^{V_{5}}$, ZOF$_{t+1}^{3}=$ ZOR$_{t+1}^{3}$, ZOF$_{t+1}^{4}=$ ZOR$_{t+1}^{4}$.

Fig. 5

Link disconnection due to the velocity variation

3.3 Application examples

Many interesting and useful applications on VANETs can be supported by our mobicast routing protocol, such as emergency event [17], online game [18], and video advertisement [19]. Our mobicast routing protocol can be effectively used for those VANETs applications for emergency warning, online game invitation, and video advertisement, as illustrated in Fig. 6. Figure 6a shows vehicle V _e has the control failure problem for a short period of time, and warning messages are sent to all nearby vehicles to avoid accident. By our mobicast routing protocol, warning messages can be sent to vehicles in the warning area to avoid accident. Figure 6b shows an online game application, vehicle V _e can invite those nearby vehicles to be game-playing members for a longer period of time. Our mobicast routing protocol can make sure that the game information can disseminate to all members in the ZOR _t .

Fig. 6

Two mobicast application examples (a, b)

4 Mobicast routing protocol

This section presents the mobicast routing protocol. The mobicast routing protocol is split into three phases; (1) ZOR _t creation phase, (2) message dissemination phase, and (3) ZOA$_{t}^{V_{i}}$ growing phase. In the ZOR _t creation phase, ZOR _t is initiated by a V _e if an event is detected and triggered by the OBU of V _e . The region of ZOR _t is determined according to the condition of event. Then, V _e performs the messages dissemination phase. In the message dissemination phase, mobicast messages are disseminated to other vehicle V _i located in the ZOR _t . If the mobicast message can not be disseminated caused by the temporal network fragmentation problem, then ZOA$_{t}^{V_{i}}$ growing phase is executed. In the ZOA$_{t}^{V_{i}}$ growing phase, many ZOA$_{t}^{V_{i}}$ are initiated to dynamically cover ZOF _t in order to ensure all vehicles in the ZOR _t can successfully received the mobicast message. The detailed operation is developed as follows.

4.1 ZOR _t creation phase

The main task of this phase is to identify an elliptic region, ZOR _t , by V _e . In this work, the shape of ZOR _t assumes to be the elliptic due to the nature of vehicle driving. The result is quit different from similar results in WSNs [4–6] by adopting the circular shape. When V _e suddenly occurs an event, the coverage region is determined by the velocity and direction of V _e . Observe that, the coverage region of ZOR _t , in this investigation, is an ellipse as explained.

Theorem 1

The shape of ZOR _t for an event vehicle V _e is an ellipse.

Proof

Let $D_{V_{i}},_{V_{j}}$ denote the distance from V _i to V _j . Consider an example in Fig. 7a, vehicle V _e , $V_{B^{1}}$, $V_{B^{2}}$, ..., $V_{B^{x}}$, ..., $V_{B^{n}}$ are moving with the same direction and velocity, then event vehicle V _e suddenly accelerates its velocity and moves forward to a new location $V_{e}^{\prime }$, the distance between $V_{B^{1}}$ and V _e is shifted from $D_{V_{e},V_{B}1}$ to $D_{V_{e}\prime ,V_{B}1}$, and the distance between $V_{B^{2}}$ and V _e is shifted from $D_{V_{e},V_{B}2}$ to $D_{V_{e}\prime ,V_{B}2}$. Let $D_{V_{B}1,V_{B}2}$ be Δ, $D_{V_{e},V_{B}1}$ be $\overrightarrow{u}$, and $D_{V_{e},V_{e}\prime }$ be $\overrightarrow{v}$. Observe that, Δ is a very tiny distance. The increased distance for $V_{B^{1}}$ is $D_{V_{e}\prime ,V_{B}1}-D_{V_{e},V_{B}1}=|(\overrightarrow{v}+ \overrightarrow{u})|-|\overrightarrow{u}|=|\overrightarrow{v}|$. The increased distance for $V_{B^{2}}$ is $D_{V_{e}\prime ,V_{B}2}-D_{V_{e},V_{B}2}$, where $D_{V_{e},V_{B}2}=D_{V_{e},V_{B}1}\times \sec \delta _{1}$ and $D_{V_{e}\prime ,V_{B}2}=D_{V_{e}\prime,V_{B}1}\times \sec \theta _{1}$, then $D_{V_{e}\prime ,V_{B}2}-D_{V_{e},V_{B}2} = (| \overrightarrow{v}+\overrightarrow{u}|)\times \sec \theta _{1}-| \overrightarrow{u}|\times \sec \delta _{1}$, and $\theta _{1}=\tan ^{-1} \frac{\Delta }{|\overrightarrow{v}+\overrightarrow{u}|}$ and $\delta _{1}=\tan ^{-1}\frac{\Delta }{|\overrightarrow{u}|}$. Therefore, $D_{V_{e}\prime ,V_{B}2}-D_{V_{e},V_{B}2} = (|\overrightarrow{v}+ \overrightarrow{u}|)\times \sec (\tan^{-1}\frac{\Delta }{|\overrightarrow{v} +\overrightarrow{u}|})-|\overrightarrow{u}|\times \sec (\tan ^{-1}\frac{ \Delta }{|\overrightarrow{u}|})$. Observe that, $|\overrightarrow{v}|>(| \overrightarrow{v}+\overrightarrow{u}|)\times \sec (\tan ^{-1}\frac{\Delta }{ |\overrightarrow{v}+\overrightarrow{u}|})-u\times \sec (\tan ^{-1}\frac{ \Delta }{|\overrightarrow{u}|})$, it means that the increased distance for $V_{B^{1}}$ is greater than $V_{B^{2}}$, while vehicle V _e moves to location $V_{e}^{\prime }$. Then, we can deduce that the increased distance of $V_{B^{x}}$ is $D_{V_{e}\prime ,V_{B}x}-D_{V_{e},V_{B}x}=(| \overrightarrow{v}+\overrightarrow{u}|)\times \sec \theta _{2}-| \overrightarrow{u}|\times \sec \delta _{2}$, and $\theta _{2}=\tan ^{-1}$ $\frac{(x-1)\Delta }{|\overrightarrow{v}+\overrightarrow{u}|}$ and $\delta _{2}=\tan ^{-1}\frac{(x-1)\Delta }{|\overrightarrow{u}|}$. Therefore, $D_{V_{e}\prime ,V_{B}x}-D_{V_{e},V_{B}x}=(|\overrightarrow{v}+ \overrightarrow{u}|)\times \sec(\tan ^{-1}\frac{(x-1)\Delta }{| \overrightarrow{v}+\overrightarrow{u}|})-|\overrightarrow{u}|\;\times\; \sec$ $(\tan ^{-1}\frac{(x-1)\Delta }{|\overrightarrow{u}|})$. Let $| \overrightarrow{d_{x}}|$ denote as the increased distance for $V_{B^{x}}$, then $|\overrightarrow{d_{x}}|=D_{V_{e}\prime ,V_{B}i}-D_{V_{e},V_{B}i}$. Observe that, we accumulate the increased distance $\overrightarrow{u}+ \overrightarrow{d_{x}}$ around vehicle V _e , where $\overrightarrow{u}$ is the projection of $D_{V_{e},V_{B}x}$ onto $D_{V_{e}},_{V_{B}1}$, the equation is,

$$\begin{array}{lll} \int_{\theta =0,x=1}^{\theta =\frac{\pi }{2},x=n}|\overrightarrow{u}|&+&((| \overrightarrow{v}+\overrightarrow{u}|)\times \sec \left(\tan ^{-1}\displaystyle\frac{ (x-1)\Delta }{|\overrightarrow{v}+\overrightarrow{u}|}\right)\nonumber\\ &-&|\overrightarrow{u} |\times \sec (\tan ^{-1}\displaystyle\frac{(x-1)\Delta }{|\overrightarrow{u}|})dxd\theta ). \end{array}$$

(1)

Fig. 7

The shape of ZOR _t for an event vehicle is an approximate ellipse (a, b)

The result of this integration in polar coordinates is given in Fig. 7b. From $\overrightarrow{d_{1}}$ to $\overrightarrow{d_{n}}$, the result shows a quarter of shape because we only accumulate from 0 to $\frac{\pi }{2}$. If we accumulate the increased distance $\overrightarrow{ d_{i}}$ from 0 to 2π, we can have an approximate ellipse. Therefore, our mobicast routing protocol adopts the ellipse as the size of ZOR _t . □

Example is given in Fig. 8. The size of ZOR _t is determined according to the velocity of V _e . In this paper, each vehicle can acquire location information via location information provider, such as the GPS [20]. Let $(x_{t}^{V_{i}},y_{t}^{V_{i}})$ denote as the location of V _i at time t. Each vehicle V _i sends its location $(x_{t}^{V_{i}},y_{t}^{V_{i}})$ and velocity information $v_{i_{t}}$ to its neighbors through the hello message (V _i , $(x_{t}^{V_{i}},y_{t}^{V_{i}})$, $v_{i_{t}}$) . Let N(V _i ) denote the set of neighboring vehicles of V _i , where N(V _i ) does not include V _i . Let P _L and P _R denote as the left apex P _L and the right apex P _R of the elliptic region (ZOR _t ). Example is given in Fig. 8. We always assume a vehicle is located at P _x , where x = L or R. Our mobicast protocol tries to disseminate the mobicast message to a virtual vehicle located at P _x , even no real vehicle exists at P _x . This way makes sure that the mobicast message can be disseminated to all vehicle located in ZOR _t . The procedure of the ZOR _t creation phase is given herein.

• S1 Event vehicle V _e acquires the location $(x_{t}^{V_{e}},y_{t}^{V_{e}})$ and velocity $v_{e_{t}}$ from its OBU.

• S2 The ellipse region of ZOR _t is determined by $Z_{t}(V_{i})= \frac{(x_{t}^{Vi}-x_{t}^{Ve})^{2}}{a^{2}}+\frac{(y_{t}^{Vi}-y_{t}^{Ve})^{2}}{ b^{2}}-1=0$, where a is the major axis of the ellipse, $a=v_{e_{t}}\times \frac{1}{10}\times l_{m},$ l _m is the average length of vehicle, and b is the minor axis of the ellipse, which is determined by the width of lane.

• S3 The V _e broadcasts the mobicast control packet P _m (V _e , Z _t (V _e ), m), where P _m is the control packet to control the dissemination of mobicast message, V _e is the ID of current vehicle, Z _t (V _e ) describes the region of ZOR _t , and m is the content of mobicast message. After V _e broadcasting the P _m , message dissemination phase is executed.

Fig. 8

Creation of ZOR _t

In the Step 2, we assume the event is occurred from the brake system. Therefore, the major axis a is set as $v_{e_{t}}\times \frac{1}{10}\times l_{m}$ to provide driver to have the enough reaction time. Actually, the value of the major axis a is depended on different kind of the events. For instance, if the event is the game invitation, the major axis a is related to the relative distance to game invited members. As shown in Fig. 8, the ZOR _t is determined by $Z_{t}(V_{i})=\frac{ (x_{t}^{Vi}-x_{t}^{Ve})^{2}}{a^{2}}+\frac{(y_{t}^{Vi}-y_{t}^{Ve})^{2}}{b^{2}} -1=0$. Vehicles located in the ZOR _t should receive the mobicast messages from V _e .

4.2 Message dissemination phase

In the message dissemination phase, vehicle V _j receives the mobicast control packet P _m from V _i and then forwards packet P _m if V _j is in the ZOR _t . Otherwise, V _j drops P _m . The mobicast control packet P _m is continuously disseminated until P _m approaches to the apex P _x , where x = L or R. The procedure of the message dissemination phase is described below.

• S1 If V _j directly receives P _m from V _i and the location of V _j is $(x_{t}^{V_{j}},y_{t}^{V_{j}})$ , then packet P _m is forwarded from V _j if $Z_{t}(V_{j})=\frac{ (x_{t}^{V_{j}}-x_{t}^{V_{_{e}}})^{2}}{a^{2}}+\frac{ (y_{t}^{V_{j}}-y_{t}^{V_{_{e}}})^{2}}{b^{2}}-1\leq 0$. Otherwise, V _j drops P _m and terminates the mobicast message dissemination.

• S2 Vehicle V _j decides the packet forwarding depended on the distance between V _i and apex P _x , x = L or R. Let $d_{V_{i},P_{x}}$ denote the distance from vehicle V _i to apex P _x , x = L or R. If $d_{V_{i},P_{x}}>$ r, V _j disseminates the mobicast message toward apex P _x , where r is the transmission range. Each vehicle V _i |Z _t (V _i ) ≤ 0 must forward the mobicast message toward P _x until $d_{V_{i},P_{x}}<r$, where x = L or R. Observe that, the greater part of vehicles in ZOR _t received the mobicast message implies that the dissemination of mobicast messages is successfully done. The apex P _x is P _R or P _L depended on the current location in ZOR$_{t}^{q}$. Let P _x  = P _R if V _j is in ZOR$_{t}^{1}$ or ZOR$_{t}^{4}$. Let P _x  = P _L if V _j is in ZOR$_{t}^{2}$ or ZOR$_{t}^{3}$.

• S3 Vehicle V _j dynamically verified the efficacy of dissemination before V _j broadcasts P _m if $d_{V_{i},P_{x}}>r$. An effective dissemination is to disseminate the mobicast message closed to apex P _x , where x = L or R. A dissemination is called as an effective dissemination if the following two conditions are satisfied; (C1) there at least exists one neighbor V _k  ∈ N(V _j ) for V _j , where Z _t (V _k ) ≤ 0 and (C2) $d_{V_{k},P_{x}}-d_{V_{j},P_{x}}<0$. The condition Z _t (V _k ) ≤ 0|V _k  ∈ N(V _j ) means that the neighbor V _k is in ZOR _t and the condition $d_{V_{k},P_{x}}-d_{V_{j},P_{x}}<0$ means that the location of V _k is closed to P _x than that of V _j . If the above two conditions are satisfied, then go to Step 4. Otherwise the ZOF _t expansion phase is executed.

• S4 If Z _t (V _k ) ≤ 0|V _k  ∈ N(V _j ) and $d_{V_{k},P_{x}}-d_{V_{j},P_{x}}<0$, V _j broadcasts packet P _m (V _j , Z _t (V _j ), m). Before V _j broadcasts P _m , V _j waited for a random backoff time R _time, such that

  $$ R_{\rm time}=\frac{d_{V_{j},P_{x}}}{d_{V_{i},P_{x}}}\times r_{\rm time}\text{,} $$

  where r _time is a random time. If V _j receive the same P _m from N(V _i ) during R _time time period, then V _j does not broadcast, otherwise V _j broadcasts P _m if R _time of V _j is timeout. The use of random backoff time R _time is to prevent the broadcast storm problem [21]. A vehicle V _i closed to P _x has the high priority to forward. The reachability of P _m in Z _t (V _i ) can be improved, since if some neighbors of V _i are failed to receive the mobicast message from V _i , the other neighbors of V _i may re-broadcast P _m .

Figure 9 gives an example of the message dissemination phase in ZOR$_{t}^{2}$. Vehicle V ₁ broadcasts P _m (V ₁,Z _t (V ₁),m) to V ₂ and V ₃. The random backoff time R _time of V ₂ and V ₃ is$\frac{d_{V_{2},P_{L}}}{d_{V_{1},P_{L}}}\times r_{\rm time}$ and $\frac{d_{V_{3},P_{L}}}{d_{V_{1},P_{L}}}\times r_{\rm time}$, respectively. If R _time of V ₃ < that of V ₂, V ₃ broadcasts P _m (V ₃,Z _t (V ₃),m). Thus, V ₂ receives P _m (V ₃,Z _t (V ₃),m) from V ₃, then stop the broadcasting. Similarly, V ₄ receives the mobicast control message and try to broadcast; however, V ₄ can not find any neighbor closed to P _L in ZOR _t . The mobicast message can not be forwarded to V ₅ to produce the temporal network fragmentation problem, V ₄ must perform ZOA$_{t}^{V_{i}}$ growing phase.

Fig. 9

Random backoff time is depended on distance to P _L

4.3 ZOA$_{t}^{V_{i}}$ growing phase

To solve the temporal network fragmentation problem, ZOA$_{t}^{V_{i}}$ growing phase is needed. The goal of ZOA$_{t}^{V_{i}}$ growing phase is to raise the possibility of sending the mobicast message toward P _x , where x = L or R. The ZOA$_{t}^{V_{i}}$ is initiated to create ZOF _t from vehicle V _i at time t to expand the dissemination area. When the temporal network fragmentation problem is occurred, ZOA$_{t}^{V_{i}}$ growing phase is executed to ensure vehicles in the ZOR _t can successfully receive the mobicast message, a series of new created elliptic shape ZOA$_{t}^{V_{i}}$ are produced if V _i cannot send out the mobicast message. The procedure of the ZOA$_{t}^{V_{i}}$ growing phase is developed.

• S1 To raise the possibility of sending the mobicast message from V _i toward P _x , a reference vehicle V _j  ∈ N(V _i ) is necessary to ensure the mobicast message can be forwarded. To reduce the hop number from V _i to P _x , the reference vehicle V _j is chose as the next node of V _i , where V _j has the minimal distance to P _x than all other vehicles in N(V _i ); that is, $d_{V_{j},P_{x}}<d_{V_{k\in N(V_{i})},P_{x}}$.

• S2 Vehicle V _i initiates a new elliptic ZOA$_{t}^{V_{i}}$ to include the reference vehicle V _j , where V _i is located at one of focuses of ZOA$_{t}^{V_{i}}$ and the coordinate of the center of ZOA$_{t}^{V_{i}}$ is (h,k). Observe that, reference vehicle V _j is a possible alternative path to forward the mobicast message closed to P _x . The reference vehicle V _j should be included in ZOA$_{t}^{V_{i}}$. The ZOA$_{t}^{V_{i}}$ is created by the function $A_{t}(V_{i})=\frac{(x_{t}^{Vi}-h)^{2}}{a^{\prime 2}}+\frac{(y_{t}^{Vi}-k)^{2} }{b^{\prime 2}}-1=0,$ where major axis a ^′ is determined by $\frac{d_{Vi,P_{x}}}{\alpha \times v_{i}}$, and minor axis b ^′ is determined by $\frac{\alpha \times v_{i}}{d_{V_{i},P_{x}}}$, where α is a constant which is used to adjust v _i . Major axis a ^′ and minor axis b ^′ control the shape of ZOA$_{t}^{V_{i}}$. Different shape of ZOA$_{t}^{V_{i}}$ can raise different possibility to find successful route to P _x or reduce the number of growing new ZOA$_{t}^{V_{i}}$. This discussion will be explained later. After a ^′ and b ^′ are determining, (h,k) can be deduced by the locations of V _i and V _j as follows,

  $$ \left\{ \begin{array}{l} \displaystyle\frac{(x_{t}^{V_{j}}-h)^{2}}{a^{\prime 2}}+ \displaystyle\frac{(y_{t}^{V_{j}}-k)^{2}}{ b^{\prime 2}}\leq 1, \\ \\ \sqrt{(x_{t}^{V_{i}}-h)^{2}+(y_{t}^{V_{i}}-k)^{2}}=\sqrt{a^{\prime 2}-b^{\prime 2}}. \end{array} \right. $$

  For instance of ZOA$_{t}^{V_{i}}$ as illustrated in Fig. 10a, let c denote as the distance between V _i and O(h,k), and the distance between V _j and two focuses represent as r ₁ and r ₂, respectively. According to the ellipse nature, $r_{1}+r_{2}=2a^{ \prime }$ is known, then $c=\sqrt{a^{\prime 2}-b^{\prime 2}}$. The length of c is $\sqrt{(x_{t}^{V_{i}}-h)^{2}+(y_{t}^{V_{i}}-k)^{2}}$, so we have $\sqrt{(x_{t}^{V_{i}}-h)^{2}+(y_{t}^{V_{i}}-k)^{2}}=c=\sqrt{a^{\prime 2}-b^{\prime 2}}$.

• S3 The V _i broadcasts the ZOA$_{t}^{V_{i}}$ growing packet E _m (V _i , A _t (V _i ), P _m ) after waiting for the random backoff time R _time of V _i . Packet E _m (V _i , A _t (V _i ), P _m ) is a control packet to control the growing of ZOA$_{t}^{V_{i}}$, where V _i is the ID of current vehicle, A _t (V _i ) is the region of ZOA$_{t}^{V_{i}}$, and P _m is the mobicast control packet. The mobicast message is disseminated through ZOA$_{t}^{V_{i}}$ to P _x . It is possible to forward the mobicast message to a dead-end vehicle. A vehicle is said as a dead-end vehicle if the vehicle does not have any other neighbors except for V _i . Therefore, the dead-end vehicle cannot re-forward the mobicast message to any neighboring vehicles. If the mobicast message reaches to a dead-end vehicle, the dead-end vehicle cannot re-forward the mobicast message, then V _i should know that the mobicast message reaches to a dead-end vehicle. If V _i does not receive E _m from any neighbor but N(V _i ) ≠ { ∅ } for the period of maximum R _time after V _i sending out E _m message, it implies that all neighbors of V _i are dead-end vehicles, where $N\left( N(V_{i})\right) =\{V_{i}\}$. If all neighbors of V _i cannot send out the mobicast message, then V _i replies $d_{V_{i},P_{x}}=\infty$ to previous vehicle to notify that a dead-end situation is occurred. The path passed V _i surely cannot be chose due to $d_{V_{i},P_{x}}=\infty$. Then, go to Step 1 to find another path closed to P _x . Example is given in Fig. 10b, V _k is a dead-end vehicle and V _i tries to find another path toward P _x .

• S4 If V _k directly receives E _m from V _i and the location of V _k is $(x_{t}^{V_{k}},y_{t}^{V_{k}})$, then packet E _m is forwarded from V _k if $A_{t}(V_{k})=\frac{(x_{t}^{V_{k}}-h)^{2}}{ a^{\prime 2}}+\frac{(y_{t}^{V_{k}}-k)^{2}}{b^{\prime 2}}-1\leq 0$. Otherwise, V _k drops E _m .

• S5 If V _k has only one neighbor V _i , N(V _k ) = {V _i }, that means V _k can not send out the mobicast message, then V _k sets $d_{V_{k},P_{x}}=\infty$ at time t, V _k does not broadcast at time t.

• S6 Vehicle V _k broadcasts E _m after waiting for time period of R _time of V _k , if at least one neighbor V _l  ∈ N(V _k ) for V _k exists, where A _t (V _l ) ≤ 0 and $d_{V_{l},P_{x}}-d_{V_{k},P_{x}}<0$, then go to Step 3 until the mobicast messages can be transmitted toward P _x . Otherwise go to Step 1.

Fig. 10

a Growing of ZOA$_{t}^{V_{i}}$ and b a dead-end example

Let’s discuss with the shape of ZOA$_{t}^{V_{i}}$ mentioned in Step 2. The shape of ZOA$_{t}^{V_{i}}$ is depended on value of $d_{V_{i},P_{x}}$. Figure 11a shows that the shape of ZOA$_{t}^{V_{1}}$ is narrow if a ^′ > b ^′. The shape of ZOA$_{t}^{V_{3}}$ is wide if a ^′ < b ^′ as shown in Fig. 11b. Different shape of ZOA$_{t}^{V_{i}}$ has the different impact of the mobicast message dissemination. If the shape of ZOA$_{t}^{V_{i}}$ is narrow, the mobicast message dissemination has the minimal number of hops to P _x and the reduced number of ZOA$_{t}^{V_{i}}$ growing. If the shape of ZOA$_{t}^{V_{i}}$ is wide, more possible paths to P _x can be discovered.

Fig. 11

The shape of ZOA$_{t}^{V_{i}}$ is different depended on different distance to P _x (a, b)

Figure 12 gives an example to illustrate event vehicle V _e disseminates the mobicast messages to all vehicles in ZOR _t . Event vehicle V _e broadcasts P _m (V _e , Z _t (V _e ), m) to V ₁, V ₂, and V ₃. Vehicle V ₃ broadcasts P _m (V ₃, Z _t (V ₃) , m) to V ₄, then V ₄ finally broadcasts P _m (V ₄, Z _t (V ₄), m), since $d_{V_{4},P_{R}}<r$. Vehicle V ₂ cannot forward P _m closer to P _L , then V ₂ chooses a reference vehicle V ₇ to initiate ZOA$_{t}^{V_{2}}$ by V ₇. Then, V ₂ broadcasts packet E _m (V ₂, A _t (V ₂), P _m ), and V ₇ receives E _m from V ₂ and re-broadcasts E _m (V ₇, A _t (V ₇), P _m ) to V ₈ since $d_{V_{8},P_{L}}<d_{V_{7},P_{L}}$. Then, V ₈ re-broadcasts E _m (V ₈, A _t (V ₈), P _m ) and V ₈ has a neighboring V ₅ in ZOR _t . Observe that, V ₅ has the minimum R _time in N(V ₈) because V ₅ is located in the ZOR _t . However, V ₅ still cannot forward P _m closer to P _L , then V ₅ initiates ZOA$_{t}^{V_{5}}$ by V ₉ and broadcasts E _m (V ₅, A _t (V ₅), P _m ). Then, V ₉ re-broadcasts E _m (V ₉, A _t (V ₉), P _m ) to V ₆. Finally, V ₆ receives E _m from V ₉. Furthermore, the mobicast message can be disseminated through different quadrants. Figure 13 shows the mobicast message is disseminated to ZOR$_{t}^{3}$ from 1-st quadrant because no any neighboring vehicle of V _e exists in 3-rd quadrant.

Fig. 12

An example of mobicast operation

Fig. 13

The mobicast message is disseminated to ${\rm{ZOR}}_{t}^{3}$

5 Simulation results

Our paper presents a mobicast protocol. To evaluate our mobicast protocol, our mobicast routing protocol is simulated compared to a forwarding without ZOA$_{t}^{V_{i}}$ scheme. This is because that our mobicast protocol is the first mobicast result in VANETs. In our simulation, the forwarding without ZOA$_{t}^{V_{i}}$ scheme means that the mobicast message is broadcasting in ZOR _t without the assistance of ZOA$_{t}^{V_{i}}$ during the mobicasting. All these protocols are mainly implemented using the NCTUns 4.0 simulator and emulator [22]. The physical and MAC layer in this simulation is adopted the 802.11b protocol. The system parameters are given below. To discuss the effect of the network density (ND) of a VANET, our simulator considers a 2000×20 m² highway scenario with various numbers of vehicles, ranging from 40 to 400. With the same road area, the ND is changed due to the different number of vehicles. The communication radius of each vehicle is 100 m. Each vehicle knows its location information from the location provider (GPS). The velocity, v, of each vehicle is assumed from 10 to 100 km/h. The simulation time of each round is 300 seconds. Each simulated result is obtained from 100 rounds. The performance metrics to be observed are:

• The dissemination successful rate (DSR) is the number of vehicles located in ZOR _t which can successfully receive the mobicast messages from event vehicle V _e , divided by the total number of vehicles in ZOR _t .

• The packet overhead multiplication (POM) is the total number of packets that all vehicles transmit transmitted used in our mobicast protocol (with the assistance of ZOA$_{t}^{V_{i}}$), divided by the total number of packets that all vehicles transmit not used in our mobicast protocol (without the assistance of ZOA$_{t}^{V_{i}}$).

• The packet delivery delay (PDD) is the average time that a mobicast message is sent from event vehicle V _e to vehicle V _i in ZOR _t .

• The throughput (TP) is the total number of data packets the vehicle V _i receives from event vehicle V _e in ZOR _t per second.

It is worth mentioning that an efficient mobicast routing protocol in a VANET is achieved with a high DSR, low POM, low PDD, and high TP. In the following, we illustrate our simulation results for dissemination successful rate (DSR), packet overhead multiplication (POM), packet delivery delay (PDD), and throughput (TP) from several aspects.

5.1 Dissemination successful rate (DSR)

The simulation results of the DSR under various NDs and velocities are shown in Fig. 14. Figure 14a shows the observed DSR under various NDs, where the maximum velocity, v, is 50, 80, and 100 km/h, respectively. A mobicast routing protocol with the high dissemination successful rate implies that the value of its DSR was high. The DSR was low if v was high for various NDs. It was observed that DSR was very low under v = 100 km/h since it is easily moved out the transmission range of IEEE 802.11b. In addition, the higher the ND is, the higher the DSR will be. For each case, the curve of the DSR of v = 100 km/h was lower than that of v = 80 km/h, and the curve of the DSR of v = 80 km/h was lower than that of v = 50 km/h. Considered a pair of two high speed moving vehicles (even if v = 100 km/h) and its velocity variation is small, then it can successfully work for mobicasting. On the contrary, given a pair of two low speed moving vehicles and its velocity variation is large, then it cannot obtain the better of DSR. In average, the velocity variation becomes large if the maximum velocity is large. When the velocity is larger than 90 km/h, DSR drops if its velocity variation is large. Figure 14a shows that the ND is larger than 0.9, DSR does not grow up. This is because that the network contention and collision are occurred in the high density network. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol can improve the DSR as illustrated in Fig. 14a.

Fig. 14

Performance of dissemination successful rate vs. a network density and b velocity

Figure 14b shows the observed DSR under various velocity v, with the ND fixed at 0.3, 0.5, and 0.8. In general, the DSR drops as the v increases because the rapid changed topology and frequent happened temporal network fragmentation problem. The temporal network fragmentation problem is frequently occurred when the ND is low. Therefore, DSR was low when ND was low. For each case, the curve of the DSR of ND = 0.3 was lower than that of ND = 0.5, and the curve of the DSR of ND = 0.5 was lower than that of ND = 0.8. As shown in Fig. 14b, compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol significantly improves DSR by using ZOA$_{t}^{V_{i}}$.

5.2 Packet overhead multiplication (POM)

The simulation results of the packet overhead multiplication (POM) is shown in Fig. 15. The higher the value of POM is, the larger the number of packets will be. Figure 15a shows the performance of the average POM vs. various NDs, where the maximum velocity v are 50, 80, and 100 km/h. Forwarding without ZOA$_{t}^{V_{i}}$ scheme cannot offer extra packets to solve the temporal network fragmentation problem, the average POM of forwarding without ZOA$_{t}^{V_{i}}$ scheme is near to 1. The average POM of protocol ranges from 1.5 to 4.5 under various maximum velocities v. In general, POM was low if ND was high. The average POM of v = 50 < that of v = 80 < that of v = 100. Observe that when the ND is higher than 0.9, POM not keep to decrease due to network contention and collision problems. Figure 15b shows the observed POM under various velocity v, with the NDs fixed at 0.3, 0.5, and 0.8, respectively. In general, the POM grows up as the velocity v increases. The average POM of ND = 0.8 < that of ND = 0.5 < that of ND = 0.3. For each case, the higher the ND is, the lower the POM will be.

Fig. 15

Performance of packet overhead multiplication vs. a network density and b velocity

5.3 Packet delivery delay (PDD)

The simulation results of the PDD under various NDs and v are given in Fig. 16. Figure 16a shows the observed PDD under various NDs, where v = 50, 80, and 100 km/h. A mobicast routing protocol with the high dissemination successful rate implies that the value of its PDD was low. The PDD was high if v was high for various NDs. In general, the PDD drops as the ND increases. The average PDD of v = 50 < that of v = 80 < that of v = 100. As the ND is lower than 0.3, event vehicle V _e may not find any neighbors to forward the mobicast message. Event vehicle V _e will carry the mobicast message and try to forward the mobicast message to a new incoming vehicle. If ND is low, PDD is greatly growing since the mobicast message can not be sent out by multi-hop transmission. When the ND is higher than 0.9, PDD still not decrease due to network contention and collision problems. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol can improve the PDD.

Fig. 16

Performance of packet delivery delay vs. a network density, b velocity, and c packet size

Figure 16b shows the observed PDD under various velocity v, with the ND fixed at 0.3, 0.5, and 0.8. In general, the PDD grows up as the velocity v increases. The average PDD of ND = 0.8 < that of ND = 0.5 < that of ND = 0.3. For each case, the higher the ND is, the lower the PDD will be. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol can provide the better of PDD for various velocities.

Figure 16c illustrates the observed PDD under various packet sizes ranging from 32 to 320 bytes, with the velocity v fixed at 50 km/h and the NDs are 0.3, 0.5, and 0.8, respectively. The PDD drops as the packet size decreases. The average PDD of ND = 0.8 < that of ND = 0.5 < that of ND = 0.3. The higher the ND is, the lower the PDD will be. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol improves PDD under various packet sizes.

5.4 Throughput (TP)

Figure 17 shows the simulation results of the throughput (TP) for our mobicast routing protocol. The result of throughput is obtained by running the video advertisement application. The higher the value of TP is, the higher network utilization will be. Figure 17a shows the performance of the throughput vs. various NDs, where the maximum velocity v are 50, 80, and 100 km/h. The throughput was high where the ND was high under the velocity of 50, 80, and 100 km/h. The average TP of v = 100 < that of v = 80 < that of v = 50. Observe that when the ND is higher than 0.9, throughput does not increase since the network contention and collision problem. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol can improve the TP when ND is low.

Fig. 17

Performance of throughput vs. a network density and b velocity

Figure 17b illustrates the observed TP under various velocity v, with the NDs fixed at 0.3, 0.5, and 0.8. In general, the TP decreases as the velocity v increases. The average PDD of ND = 0.3 < that of ND = 0.5 < that of ND = 0.8. For each case, the higher the ND is, the higher the TP will be. Compared to forwarding without ZOA$_{t}^{V_{i}}$ scheme, our mobicast routing protocol improves TP for various velocities.

In summary, it was observed that the efficient mobicast routing protocol is achieved by having the results of average DSR < 0.6, average PDD < 500 ms, and average TP < 500 kbps. The dissemination successful rate (DSR) can be improved over 50%, compared to the forwarding without ZOA$_{t}^{V_{i}}$ scheme. However, the average POM of our protocol is less than 3.0.

6 Conclusion

In this paper, we present a new “spatiotemporal multicast” protocol for supporting applications which require spatiotemporal coordination in vehicular ad hoc networks (VANETs). The main result of this work is to develop a new mobicast routing protocol to dynamically estimate the accurate ZOF to successfully disseminate mobicast messages to all vehicles in ZOR. To overcome the temporal network fragmentation problem, we have developed a new algorithm by extending some adaptive ZOA$_{t}^{V_{i}}$ to significantly improve the dissemination successful rate, even if the connectivity of ZOR is temporally lost due to any vehicle in ZOR suddenly accelerates or decelerates its velocity. Finally, the simulation results illustrated our performance achievements in terms of dissemination successful rate, packet overhead multiplication, packet delivery delay, and throughput. Observe that, the dissemination successful rate can be improved over 50%, compared to a similar data dissemination scheme without using our mobicast protocol. Future work involves developing a multi-mobicast routing protocol which supports applications of multiple event vehicles in VANETs.