Modeling and analysis of IEEE 1609.4 MAC in the presence of error-prone channels

Akram A. Almohammedi, Nor K. Noordin, A. Sali, Fazirulhisyam Hashim, Waheb A. Jabbar, Sabri Saeed Department of Computer and Communication Engineering, Universiti Putra Malaysia, Malaysia Wireless and Photonics Networks Laboratoratory, Universiti Putra Malaysia, Malaysia Faculty of Engineering Technology, Universiti Malaysia Pahang, Malaysia Department of Communication Systems Engineering, Taiz University, Taiz-Yemen


INTRODUCTION
Recently, with increasing the population, the number of registered vehicles has dramatically increased over all the world, and this leads to a high rate of traffic accidents on the roads. In order to prevent such accidents, an Intelligent Transportation Systems (ITSs) are needed. ITSs typically has the ability to improve the quality, effectiveness and safety of the future transportation systems. However, VANETs are the key component of ITSs which integrate wireless networks into vehicles. VANETs support three types of communications including Vehicle-to-Vehicle (V2V), Vehicle-to-Infrastructure (V2I), and Hybrid Vehicular (HV) communications. The applications of VANETs are divided into two categories, safety applications and service applications. Safety applications are used to notify drivers about the critical situation in advance. On the other hand, service applications are used for improving driving comfort and the efficiency of transportation. As a result, safety applications are delay-sensitive and have a higher priority, while service applications are throughput-sensitive and have lower priority. The US Federal Communications Commission (FCC) has allocated a frequency band of 5.9 GHz in a total bandwidth of 75 MHz under DSRC to support 7-channels each of which is 10 MHz wide and the guard band is 5 MHz wide. These channels are functionally divided into one control channel (CCH_178), and up to six are service channels (SCHs) [1][2][3]. The CCH is exclusively used to broadcast safety-critical applications and regular traffics, while the six other channels, SCHs, are dedicated to transfer service data applications. Wireless Access in Vehicular Environment (WAVE) has been designed for VANETs based on the IEEE 802.11p and IEEE 1609.x standards family. The IEEE 802.11p standard supports both the physical (PHY) and medium access control (MAC) layers of DSRC. The IEEE 1609.4 is the standard (legacy) intended to support multi-channel operation in VANETs [1][2][3]. The repeating synchronization intervals (SI) among the channels to transmit the packets are 100 ms, and each SI is evenly divided into 50 ms for CCH Interval (CCHI) and 50 ms SCH Interval (SCHI) as shown in Figure 1 [1][2][3][4][5]. For SCHs reservation in IEEE 1609.4, vehicle (provider) initially broadcasts WAVE Service Advertisement (WSA) packet on the CCH during CCHI to advertise its service and select an appropriate SCH for this service. If other vehicles (users) interest to join the service, which is advertised by a provider, will reply by Request for Service (RFS). Then, the provider replies the users by Acknowledgment (ACK) either for acceptance or rejection. Typically, packets collision may occur if more than one vehicle starts transmitting a packet simultaneously within the same time slot. Whereas, transmission error may manifest due to the complex condition of a wireless channel in VANETs such as path loss, thermal noise, channel fading, or interference from other radio resources.
The principle analysis of IEEE 802.11 Distributed Coordination Function (DCF) was introduced by Bianchi [6]. Bianchi proposed 2-D Markov Chain model to analyze the performance of MAC DCF mechanism by computing the throughput, assuming saturated traffic and error free channel. Several works such as [7][8][9] followed Bianchi's model by analyzing the throughput and delay of IEEE 802.11 DCF under saturated traffic taking into consideration frame retry limits, error-prone channels and freezing of the backoff timer. Unlike saturated traffic, the analytical model for the throughput and delay of IEEE 802.11 DCF performance under non-saturated traffic was studied by [10][11]. For the broadcast analysis in VANETs, several works such as [12][13][14] have evaluated the saturation performance of safety messages broadcast in VANETs to calculate the throughput and delay for emergency and routine messages. Different from broadcast analysis in VANETs, the unicast performance analysis of IEEE 802.11p in the presence of hidden terminals under both saturated and unsaturated traffics was presented in [15]. The analytical model of VANETs including both broadcast and unicast analysis for safety and service applications, respectively, based on Markov chain model were introduced in [16]. The authors in [16] analyzed the performance of IEEE 802.11p based MAC under non-saturated traffic and error free channels. The performance metrics of delay, packet delivery ratio and system throughput were investigated in [16]. The authors in [17][18] offered the analytical study of the IEEE 1609.4 MAC in VANETs under non-saturated condition. The performance metrics of delay, packet delivery ratio and system throughput were studied in [17][18]. However, freezing of the back-off timer and error-prone channels were not taken into consideration in [17].
Our model is extension of the existing model in [17]. Freezing of the back-off timer with the M/M/1 queue and error-prone channels are taken into considered in our model. Taking these elements into account will provide an accurate estimation of access to the channel and also avoid the overestimation of the system throughput. However, this paper focuses on analyzing two types of traffics; safety and service traffics with higher and lower priorities respectively. 1-D and 2-D Markov chain are employed to model the back-off procedures for each traffic type in the presence of error-prone channels under non-saturated conditions. Gaussian wireless error channel is adopted in this model, in which a constant channel bit error rate (BER) is supposed to be identified in advance and each bit has the same bit error probability. The performance metric PDR, average delay of safety applications and system throughput of service applications are investigated in this paper to evaluate the performance analysis of the IEEE 1609.4.  Figure 1. There are n vehicles in the network contending to access the channel based on the EDCA scheme. All vehicles are in the transmission range of each other and there are no hidden terminals in the system. However, according to the IEEE 1609.4 standard, safety and WSAs packets are only transmitted over CCH during CCHI as shown in Figure 1. If safety or WSAs packets arrive at MAC layer during the SCHI at rate , they have to queue at MAC layer buffer waiting for the subsequent CCHI to be transmitted. Thus, under heavy traffic, many packets will be queued at MAC layer buffer waiting for transmission at the beginning of the next CCHI. This will increase collision and delay of transmitted safety packets, and decrease the PDR and accordingly the performance of VANETs will be degraded. The critical solution to achieve a reliable dissemination of safety packet on the road is to mitigate the conflict when accessing the CCH. Thus, in order to mitigate the collision probability over CCH, the considered application layer has to schedule the generated packets to arrive at MAC layer with Poisson manner by delaying a time of SCHI (50 ms). Meaning that there will be two queues with the same arrival rate during the CCHI. The total of two independent Poisson process with rate is 2 . Thereby, the packet arrival rate for safety and WSAs traffic during the CCHI are denoted by and , respectively, and they follow the Poisson distribution.
Let ( ) be the random process representing the back-off timer value (0, 1, 2, … , − 1) at time slot , while The back-off state process is denoted by ( ). , and are the transmission failure probability and the probability of at least one packet in the buffer for a safety application, respectively. The state transition diagram of the 1-D Markov chain for the safety applications process is shown in Figure 2. The nonnull transition probabilities are given by: Here, the non-null transition probabilities describe the unavailability of safety packets transmission in the buffer, hence changing the station into idle ( ) state after successful transmission is as follows; . for stationary distribution, we can derive ,0 as follows: Let be the transmission probability of safety applications that a vehicle can transmit in a random chosen time slot. The vehicle can only transmit when the back-off time counter is zero ( ,0 ).
To analyze , let ( ) and ( ) be the random variables representing the back-off stage (0,1,2, … , ) and the value of the back-off timer (0,1,2, … , , − 1) for a given station at time slot , respectively. Typically, the maximum value of the back-off timer relies on the back-off stage; thereby, these random variables are not independent.
where ,0 is the initial contention window size, ,0 = ( + 1), and ′ is the maximum number of trials before the packet is dropped according to assumed to be 5. The maximum value of back-off stages is denoted by . The transmission failure probability , is constant and independent in this analysis. So, the two-dimensional ( ( ), ( )) processes are analyzed here with a discrete-time Markov chain at which the channel state changes, as shown in Figure 3. The state of this process is denoted by ( , ). Thus, the non-null transition probabilities are given by Here, the non-null transition probabilities describe the unavailability of packet transmissions in the buffer which is redirected into idle state ( ) after a successful transmission. and: Let be the transmission probability of service applications that a vehicle can transmit a service packet in a random chosen time slot. The vehicle can only transmit the packet when the back-off time counter is zero ( ,i,0 ) regardless of the back-off stage.

Failure and collision probabilities
The transmission failure probabilities , and , of safety and service packets are respectively derived as follows: where , and , denote the probability of frame error for safety and service packets, respectively.
where , _ , , _ , , _ , and , _ denote the Frame Error Rate (FERs) for safety and WSA/RFS/ACK frames error, respectively. The probability of these errors can be computed from bit error probability (i.e. BER) as follows [9]: where , , and represents the size of safety and WSA/RFS/ACK frames respectively. The probabilities of collision for safety , and service , packets are respectively defined as follows: then, From (7), (18), and (23), we can solve the two unknown variables, , , , and , by using numerical techniques in order to calculate the transmission and failure probabilities for safety and service applications respectively.

Time analysis for safety and WSA transmission
In every time slot during the contention-based MAC scheme (CCH), the state of the channel could be idle , , successful transmission, collision transmission or failure transmission due to the frame error. Thus, the probabilities of channel states are expressed by (24).
where , and , represent the successful transmission probabilities of safety and service packets, respectively.
However, assuming that the service data packet size is constant, then the time slot duration to transmit a service data packet over the SCH based on the contention-free MAC scheme is expressed by In this model, the Poisson distribution model is assumed, in which the inter arrival time is exponentially distributed. Then, from the average duration of the logical time slot , the load equation of queue probability, and for safety and service applications is given respectively by [10]: The packet delivery ratio (PDR) of the safety application is derived as the probability of having a successful transmission during a given time slot over the average number of vehicles transmitting packets in a generic time slot; The average time slot of a safety packet to execute the back-off is given by . Thereby, the average total service time [ ] of a safety packet, which experiences the average back-off duration, can be estimated by In this model, each vehicle is modelled as an M/M/1 queue with an infinitive buffer size, service rate , and the packet arrival rate 2 . In 1609.4 standard, the CCHI and SCHI have the same duration (50 ms for each interval), thereby, the average arrived packets are equal. However, safety packets which are generated during SCHI have to delay by ℎ . Therefore, the average delay of safety packets [ ] including queuing and transmission delays is expressed by However, the retry limit is considered in the model analysis of the WSAs packets in order to meet the IEEE 802.11p specifications. Thus, the maximum back-off stage for the WSA packet to be transmitted in this model is denoted by m. If the WSA packet faces m collisions in the previous stages, and therefore this packet will be dropped if it experiences another collision. Then, the WSA packet drop probability , expressed by For service applications, when the vehicles successfully exchange the WSA packets over CCH, they will tune to the selected SCH during SCHI to transfer service data. The maximum time that vehicles use to According to the 1609.4 standard, the number of service channel is six, thus, the maximum transmission slots can be utilized is 6Q. Finally, the aggregate throughput of the service packets , is evaluated by considering the number of selected transmission slots, and thus, it can be estimated by [17],

MODEL VALIDATION
We use MATLAB to carry out the numerical results, while the extensive simulations are conducted to validate the proposed analytical model using NS-2.34. The simulation scenario includes 100 vehicles with a GPS and a single-radio WAVE communication device. The speed of vehicles is 60 km/h. The value of bit error rate for the channel condition is assumed to be 10 −5 , which is one of the most affected and sensitive values for the channel BER in a comparatively noisy, channel fading and unreliable wireless environment [20][21]. The typical parameters values for both analytical model and simulations are summarized in Table 1 as obtained from [17]. The safety packet arrival rate is varied up to 100 packets/second (pps), while the service packet arrival rate and the number of vehicles n are fixed, = 50 and = 30 ℎ . Performance metrics such as average delay and PDR of safety packets, as well as the network throughput of service packets are investigated in this section.  Figure 4 displays the performance of the IEEE 1609.4 MAC in VANETs under various safety packet arrival rate . In fact, the value of collision probability increases with increasing the packet arrival rate or the number of vehicles in the network. The reason for this can be attributed to the fact that in the heavy packet arrival rate (traffic load), more broadcasting packets are exchanged, leading to a higher collision probability. In addition, due to the lack of ACK and exponential back-off mechanisms in safety packets broadcast, vehicles with broadcast mode attempts to transmit a packet after the last packet being broadcasted constantly, which results in higher collision probability. According to these facts, we observe the PDR of safety packets in Figure 4(b) and the throughput of service packets in Figure 4(d) decrease with increasing the packet arrival rat in the network. We also notice in Figure 4(c) that the WSA packets drop probability significantly increases with increasing safety packet arrival rate. Figure 4(a) shows that the average delay of safety packets increases linearly with increasing packet arrival rate. This observation explains that the average service time [ ] = is directly proportional to the packet arrival rate. Explicitly, as the packet arrival rate increases, the packets queue and service time increase as well and this certainly lead to longer delay for packets to be transmitted. In addition, with more safety packets being broadcasted, the back-off time occurs more frequently and the overall back-off time increases for each vehicle in the network due to more frequent freezing of the back-off timer.  Figure 4 clearly shows that the results of the proposed model outperform the results of the existing model, although the BER is considered in the proposed model. This is due to the freezing of the back-off timer mechanism that is taken into consideration in the proposed model. This mechanism always keeps the vehicles aware of the channel status to apply the freezing of the back-off timer when there is a collision in the channel to reduce the collision probability, especially when the packet arrival rate increases in the network. In addition, the simulation results in Figure 4 are close to the analytical results, which validate the accuracy of the proposed model.

CONCLUSION
This paper has proposed analytical models based on 1-D and 2-D Markov chain for safety and service applications, respectively, to evaluate the performance of the IEEE 1609.4 MAC in in the presence of error prone channels. The result displays the effect of the packet arrival rate on the network performance. The network performance degrades with increasing the safety packet arrival rate. The study also shows that the results of the proposed model outperform the results of the existing model in terms of average delay and PDR of safety packets over CCH, and network throughput of service packets over SCHs.