# Analytical study of the impact of the mobility node on the multi-channel MAC coordination scheme of the IEEE 1609.4 standard.

Abstract

The most challenging issues in the multi-channel MAC of the IEEE 1609.4 standard is how to handle the dynamic vehicular traffic condition with a high mobility, dynamic topology, and a trajectory change. Therefore, dynamic channel coordination schemes between CCH and SCH are required to provide the proper bandwidth for CCH/SCH intervals and to improve the quality of service (QoS). In this paper, we use a Markov model to optimize the interval based on the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard. We evaluate the performance of the three-dimensional Markov chain based on the Poisson distribution for the node distribution and velocity. We also evaluate the additive white Gaussian noise (AWGN) effect for the multi-channel MAC coordination scheme of the IEEE 1609.4 standard. The result of simulation proves that the performance of the dynamic channel coordination scheme is affected by the high node mobility and the AWGN. In this research, we evaluate the model analytically for the average delay on CCHs and SCHs and also the saturated throughput on SCHs.

Keywords: MAC Multichannel, IEEE 1609.4, Dynamic channel coordination scheme, CCH/SCH interval, Markov chain three Dimensional.

1. Introduction

The vehicular ad hoc network (VANET) is an outcome of wireless technology progress in MANET. The VANET is regarded as the most appropriate network to use currently and in the future because it generates a unified vehicle strategy to resolve the traffic condition when crossing the street in a city.

IEEE 1609.4 specifies the extension to the IEEE 802.11p medium access control (MAC) for multi-channel operations [1]. According to standard, there is one control channel (CCH) and multiple service channels (SCHs). The safety and control messages are exchanged between devices in the CCH. The non-safety application services are exchanged in the SCHs [1]. According to the coordination scheme, each device should alternate between the CCH and SCHs [1]. The IEEE 1609.4 standard defines a concept of channel intervals in which frequency is divided into one CCH and six SCHs [2]. The IEEE 1609.4 standard characterizes the synchronization interval with a fixed length of 100 ms, which are divided into CCH and SCH intervals, i.e., each interval lasts for 50 ms [2]. The IEEE standard of 1609.4 synchronizes the CCH and SCH intervals to an external time reference, a global positioning system provide the universal coordinated time (UTC) [1].

In the IEEE 1609.4 specification, a WAVE provider, which could either be a roadside unit or vehicle, can initialize a Basic Service set (BSS) to provide a non-safety service [1]. Each WAVE provider advertises its presence and offers services by periodically broadcasting a WAVE service advertisement (WSA)

WSAs contain the data of the offered administrations and the system parameters important to join the promoted BSS (distinguishing proof, SCH, EDCA parameter sets, Internet arrangement, and so forth.) [1]. The IEEE 1609.4 standard suggests that each WAVE provider sends WSAs several times in the CCH interval [1]. A WAVE provider should also choose the least congested SCH for its BSS to reduce interference between nearby BSSs [1].

The results from literature show that fixed-length CCH/SCH intervals cannot effectively handle a changing traffic load dynamically [1]. In a dynamic vehicular traffic condition, a fixed-length CCH can not handle the big number of safety and packets control [1]. For example, the CCH channel is rarely used because of occasional transmissions from vehicles in scanty systems [1], while certain applications expend a lot of data transfer capacity, for example, video downloads and outline, and can't acquire adequate SCH assets because of exorbitant conflict [1]. In this way, many protocols have been aim to address a dynamic setting of CCH/SCH intervals [1] to optimize utilization of channel and improve the quality of service (QoS).

A recent study that investigated the dynamic channel coordination scheme describes a system parameter in their algorithm to analyse CCH/SCH intervals [1]. If the system parameter is not adjusted according to the dynamically changing network condition, the operation of the protocols cannot be guaranteed to work accurately under the dynamic traffic vehicular environment [1]. Furthermore, the authors used a fixed rate parameter in their algorithm to calculate the CCH/SCH interval using the default option of a typical VANET system.

In this paper, we evaluate the performance of the dynamic channel coordination scheme under a dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard. We use a Markov chain model based on the Poisson distribution for node distribution and velocity to optimize and validate the analytical model of the WSA interval, safety interval, SCH interval, and also the saturated throughput on the CCH and SCHs interval delay. We also evaluate the Doppler effect impact on the proposed dynamic coordination scheme.

This research is created as follows. In section II, we develop a number of related works. Section III, the overall system model for a system supporting the dynamic channel coordination scheme is defined and then analysed using a Markov chain. In section IV, we evaluate a performance. Finally, section V shows the conclusions and suggests future work.

2. Related Work

Evaluating dynamic adjustments of CCH and SCH intervals in how they handle a congested vehicular traffic condition is essential when discussing a multi-channel MAC of the IEEE 1609.4 standard. Wang, Q. et al. [3-5] categorized the multi-channel MAC protocol into CCH and SCH intervals. Moreover, the scheme [3-5] divides the CCH interval into the safety and WSA interval. This scheme is called the variable CCH interval (VCI). VCI optimizes the ratio between the CCH and SCH intervals [3-5] to handle the dynamic vehicular traffic condition. We used [3-5] to evaluate the performance of the proposed scheme using a three-dimensional Markov chain based on the Poisson distribution for node distribution and velocity in a multi-channel MAC of the IEEE 1609.4 standard.

In [6], J. So et al. proposed a DSRC MAC protocol to give multi-channel performance. The focus offers potentially big bandwidth to non-safety implementation provided by the roadside manufacture that does not compromise safety communication in other channels. This approach supplements the current impromptu plans when a RSU is inaccessible. In any case, every gadget must be furnished with an alternate convention in both the impromptu mode and framework mode in the MAC and system layers. Thusly, a multifaceted nature of the gadget execution incredibly increments.

Differently, D. Zhu et al. [7] proposed a multi-channel MAC convention for the dynamic change of CCH/SCH interims, called the element CCH interim (DCI). DCI works indistinguishably to VCI aside from how the WSA interim is figured. DCI ascertains the ideal WSA interim in light of the likelihood dissemination of the reservation time for an administration bundle in the CCH interim.

N. Lu et al. [8] characterized the devoted multi-channel MAC (DMMAC) to play out a versatile telecom system to diminish the crash rate and transmission delay. The objective of the exploration was to enhance the security execution of the parcel conveyance proportion. The examination had not reason an adaptive modification of a CCH interim; likewise, explanatory research were doered on the model of the aim conspire.

Most of works that study the coordination scheme in a multi-channel MAC of the IEEE 1609.4 standard did not evaluate the effect of a high mobility node and frame error caused by AWGN. This motivated us to evaluate the coordination scheme under the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard.

3. Modelling and Analysis

In Fig. 2, we illustrate our approach to the Markov chain pattern. We used the discrete Markov chain pattern from [7,8] and extended this model by taking the variable data rate and dynamic coordination scheme on the multi-channel MAC of the IEEE 1609.4 standard. In this model, we also define the state for the nodes distribution using the Poisson distribution. We also evaluated the Doppler effect using this model. Let b(t) represents the backoff counter in time slot t, and the random process that represents the backoff stage k can be described using notation s(t), where k [MEMBER OF] m. Then, we can obtain [CW.sub.min], and m is the maximum backoff stage; therefore, [CW.sub.max] = [2.sup.m]W. Otherwise, we defined z(t) as seven groups of the distribution nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We used the transmission rate assumptions based on the maximum bandwidth in the 802.11p standard, i.e., 27 MHz. Then, the three-dimensional process {s(t), b(t), z(t)} can be modelled as a discrete-time Markov chain (DTMC).

In our model, we defined how our model deals with the real environment, called "performance anomaly" [7,8]. Based on the work from [7,8], we found the phenomenon of "performance anomaly" of the IEEE 802.11 standard, which showed startling execution corruption of the stations when utilizing high information rates or those close with the access point (AP). In this work, we evaluate the "performance anomaly" by accounting for the Doppler effect and the dynamic coordination scheme on the multi-channel MAC of the IEEE 1609.4 standard.

We defined one CCH and six SCH channels in our model. Additionally, we defined the effect of Doppler as the changing in frequency of a wave for the surveyer immigrating relative to its spring. In a vehicular environment, the Doppler effect is caused by high mobility, a dynamic topology, and a trajectory change. In this work, we evaluate the Doppler effect based on the different transmission rates and velocities in each group. We analyse the coordination scheme based on the previous scheme [3-5]. We use the Markov model to evaluate the coordination scheme under the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard.

We estimate the node distribution in each group using the Poisson and Nakagami fading distribution [11]. Next, according to the work in [11], we define the optimal CW index (CWI) as the optimum initial CW value to conform the adaptive network conditions for better fairness and higher aggregate throughput. We then found the optimal CW index (CWI) based on the distribution node in each group. Finally, we can evaluate the aggregate throughput S for the coordination scheme using the CWI result. We can also optimize the throughput based on the Doppler effect in each group of nodes using the optimum initial CW. The results in [15] showed that the change in the initial CW could increase the throughput.

3.1 Average Node Distribution

Next, we calculate the node distribution in each group using the Poisson distribution according to [12]. Firstly, we estimate the communication range under the Nakagami fading distribution.

According to [12], the Nakagami fading distribution considers that the parameters can be adjusted correspond to a variety of empirical measurements. The Nakagami-m appropriation is a likelihood circulation identified with the gamma conveyance. It has a shape measurer and a moment measurer that controls the afloat [OMEGA]. The received signal power x is probability density function (pdf) [12,13] can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for x [greater than or equal to] 0 (1)

Where [GAMMA](.) Is the Gamma function; [P.sub.r] = [P.sub.t][K/r.sup.a] is the average received power; r is the range in meters; a is a path-loss exponent; K = [G.sub.t] [G.sub.r][(c/(4[PI] [f.sub.c])).sup.2] ; C is the speed of light; [f.sub.c] = 5.9 GHz is the carrier frequency, [G.sub.t] and [G.sub.r] are a transmitter's and receiver's antennas gain, respectively, r, and m is the factor of fading [12].

From Eqn. (1), we can figure a cdf of the correspondence extend when the got power is more noteworthy than the limit [P.sub.th] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The average state of a communication area E[R] can be derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Substituting (4) into (5) and integrating above the limit, we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

To infer the normal bearer sense run E [[L.sub.CS]], where hubs can detect the bundle yet can't get it, an indistinguishable methodology from in (6) is taken after

This condition exception is for the received power [P.sub.CS], which defined as the percentage threshold [P.sub.th] as [P.sub.CS] = [.sub.p][P.sub.th], where p [MEMBER OF] [0,1]. Therefore, the expected porter sense is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

We use the same assumptions in [12] for our model analysis to estimate the average node using the Poisson distribution. According to an analytical study [12], we can discover the likelihood of having [N.sub.c] vehicles inside the scope of any labeled vehicle. The versatility model is reached out to incorporate the base wellbeing between vehicles in every path. This base separation is an arbitrary variables and relies at upon a accompanying vehicle's speed [V.sub.j] if a settled [t.sub.s] is imaginated, which is a reaction time to the driver for respond to the sudden occurrence, which can be described using the single-server queue model, as shown in Fig. 4.

According to [12], when a number of vehicles that across the defined reference point is small, the inter-arrival time ([[tau].sub.d] = 1/[[beta].sub.i]) between vehicles in the [i.sub.th] lane is larger than [t.sub.s].

In this issue, the opportunity of having [N.sub.ci] = k vehicles with a communication area of the tagged vehicles (i.e., within a distance of 2[.bar.R]) in the ith lane is based on the Poisson distribution [12] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

and the average number of vehicles about the tagged vehicle in a ith lane

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Based on [11], the optimal contention window (CW) is subject to the dynamic hub number in the system ([N.sub.ci]). Therefore, in the next section, we define the optimal contention window (CW).

3.2 Optimal CW Index (CWI)

Next, we obtain the optimal CW index (CWI) based on [11] and extend this approach by using the variable data rate based on the nodes distribution and the Doppler effect. The optimal CW index (CWI) is an optimum initial CW value to adjust the dynamic system conditions for better transient decency and higher total throughput [11]. Finally, we can evaluate the aggregate throughput S for the coordination scheme using the CWI result. Firstly, we define the aggregate throughput S as [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the time that different hubs transmit effectively aside from the labeled hub amid the mean defer time. E[p] and [R.sub.Data](t) are the normal bundle payload lengths and information rates, separately. [lambda] is the proportion of the payload size to full bundle length with the header messages.

The throughput S in the Eqn. (8) can be further simplified as in Eqn. [15]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Based on [11], the optimal CW can receive a optimum throughput with a node number of N. According to [11], the network delay is modelled more accurately when the new greateful transmission time [T.sub.s] and collision time [T.sub.c] are calculated:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [T.sub.DATA] and [T.sub.hsad] speak to the transmission duration of the MAC edge and header of the physical layer, separately, [sigma] and [T.sub.SIFS] are the propagation delay and the SIFS duration. [T.sub.RTS], [T.sub.cTs], and [T.sub.ACK] denote the transmission duration of an RTS, CTS, and ACK frames [11].

According to Eqn. (8), we can simplify Eqn. (10) using CW and [partial derivative]S/[partial derivative]CW = 0 and then neglecting the stuffs that is less than or equals to the third-order stuff 1/[CW.sup.3]

[partial derivative]S/[partial derivative]CW=[N.T.sub.SLOT]/2.[CW.sup.2] + 2[(N - 1).sup.2].[T.sub.SLOT].CW +(N - 1)([4T.sub.SLOT] - [2T.sub.c] - [2T.sub.EIFS])[N.sup.2] +(N - l)([2T.sub.EIFS] - [2T.sub.DIFS] - [14T.sub.SLOT])N +(N -1)([2T.sub.DIFS]+ [10T.sub.SLOT])N (10)

We can obtain the optimal CW by solving Eqn. (11) as

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

Consequently, we can calculate the result of the CW from (12)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and is referred to as the CW Index (CW I).

3.3 Throughput Analysis

We use the three-dimensional Markov chain model to evaluate and analyse the throughput. First, according to the work in [3-5], we can obtain the probability of successful transmission [P.sub.SUC], where a channel collision occurs with a probability of [P.sub.COL] or the channel is idle with a probability of [P.sub.idls]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

According to [10], [W.sub.i,k] denotes the backoff window for a station in gathering i at backoff arrange k. In the routine DCF instrument utilizing bearer sense numerous entrance with impact shirking (CSMA/CA), all stations in any gathering i have a similar starting (at backoff organize 0) backoff window [w.sub.i,0] for all i = 1, 2, 3, 4, 5, 6, and 7 [10].

We use the same assumptions with [10] at the point when the channel is sit out of gear amid the DCF interframe space (DIFS), where every station chooses an arbitrary backoff counter among [0, [w.sub.i,0] - 1] slots and sits tight for the comparing number of spaces before endeavoring to get to the remote medium. The estimation of the backoff counter is decremented by one at whatever point an opening is detected as sit. On the off chance that there are transmissions from different stations amid this period, the backoff counter commencement is suspended [10]. At that point, when the channel gets to be distinctly sit without moving, the station continues its backoff procedure after a DIFS sit out of gear period [10]. At the point when the backoff counter esteem achieves zero, the station transmits the pending edge [10].

Then, we evaluate the transition state probability in figure 3. We have seven groups of nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. Therefore, we define z(t) that represents the group of nodes i, where 1 [less than or equal to] i [less than or equal to] N. In this paper, we rework the probability of successful transmission [P.sub.SUC], where a channel collision occurs with the probability of [P.sub.col] or the channel is idle with a probability of [P.sub.idls]. The state of the Markov chain is denoted as (i, k, l), 1 [less than or equal to] i [less than or equal to] N, 0 [less than or equal to] k [less than or equal to] m, 0 [less than or equal to] l [less than or equal to] [w.sub.i,k] - 1, where i, k, and l represent group i, the backoff stage k, and the backoff counter value l, respectively. Let [t.sub.z] represent the conditional transmission probability of nodes in zone z as N group zones. We define m as the maximum backoff stage. Additionally, [W.sub.max] represents the maximum contention window, and [W.sub.z] represents the minimum contention window size [CW.sub.MIN] associated in zone z. We define E[X] as the mean time of transmission data of the tagged point in area z. We define E[[Tx.sub.suc,z]] as the mean duration of successful transmission of the tagged point in area z. Furthermore, we derived from [10] by considering the Doppler effect:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15a)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15b)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15c)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15d)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15e)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15f)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15g)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15h)

An unsuccessful (re)transmission attempt can occur due to collision of this station with at least one of the n - 1 remaining stations, which has the probability of [p.sub.col] [14]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

An error frame occurs with probability [P.sub.s] due to the channel fading and/or noise. Because both events are independent, the probability of node collision in each zone i, [p.sub.C,i] can be expressed as [10,14]

p = [P.sub.c,i] = 1 - (1 - [p.sub.col])(1 - [p.sub.e]) = [p.sub.col] + [p.sub.s] - [p.sub.col] [p.sub.s] (17)

where [P.sub.s] = 1 - [(1 - [p.sub.s]).sup.L] and [P.sub.s] = E [[R.sub.b] ([gamma])]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Next, we determine [tau] as the transmission probability where a station conducts the success transmission at the slot. By using the random distribution node and considering the AWGN, we calculate the transmission probability [tau] of each station.

Because transmission occurs only in states (k, 0), the probability [tau] of a station transmitting in a random chosen slot able be showed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Then, probability [b.sub.i,k,l] for 0 < i [less than or equal to] (m + f) can be given simply as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Then, we can obtain the probability [tau] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Combining the equation above, we obtain [[tau].sub.i]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

Next, we define [P.sub.tr] as the opportunity of at least one point in transmission in the cognationed duration, and [P.sub.s] is the symbol error rate (SER). In this work, we use the same assumptions with [14] by taking the frame error probability [P.sub.s] into the calculation.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

Moreover, the saturated throughput in each zone is obtained using [15], which is the average payload of information that able be transmitted in a duration slot on a SCH channel by considering the effect of bit error, and the Doppler effect can be calculated by the following formula.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

Where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

where

y = [OMEGA][E.sub.B]/[N.sub.0] is the fading of average SNR, [OMEGA] is the gain of channel, and p is the fading correction parameter, where p = [J.sub.0](2[pi][f.sub.d][T.sub.b]). Additionally, [f.sub.d] denotes the Doppler spread.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

c represents the velocity of waves in the medium.

[v.sub.[gamma]] represents the velocity of the receiver relative to the medium.

[v.sub.s] represents the velocity of the source relative to the medium.

[f.sub.0] denotes the source frequency ([f.sub.0] =5.9 GHz).

From Equations (19), (20), (21), and (24), we can obtain the formula of the saturated throughput as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

Finally, the aggregate throughput can be defined from [15] as the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

Based on Luo [17], the effect of gain is more urgent in IEEE 802.11p because the velocity. In 802.11p systems, when a 10-MHz bandwidth is brought, the Doppler spectrum with velocities of 10.8 km/h and 216 km/h is approximately 59 Hz and 1.18 kHz, respectively. In this work, the simulated velocities of the vehicles are between 80-120 km/h.

In the next section, we evaluate and simulate the coordination scheme, which considers the Doppler effect.

4. Performance Evaluation

Using MATLAB, we evaluate the performance of the Markov model for the coordination scheme based on the IEEE 1609.4 standard. We simulate the scenario with the 119 vehicle nodes, the velocities of the vehicles are between 80-120 km/h, the packet length is 2000 bytes, and there are seven groups of distributed nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. The channel configuration uses the variable value for the control and administration channel interims. The protect interim esteem is 4 ms. Table I shows every one of the parameters utilized as a part of our recreation. While certain parameters remain settled, others are fluctuated to watch any changed conduct of the system.

4.1 Performance Evaluation of the Probability of WSA Packet Transmission

We use the three-dimensional Markov chain model to determine the probability of the WSA packet transmission that is affected by the reservation channel CCH contention models and the anomalous performance due to the different transmission rates in each zone. The probability of the WSA packet transmission is calculated based on two variables, i.e., the transmission rate and the number of distribution nodes in each zone. The influence of these two variables on the probability of the WSA packet transmission on the DCF model were simulated using MATLAB. In this work, we have different transmission rates, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also consider the Nakagami propagation model to analyse the performance results.

Fig. 4 shows the probability of WSA packet transmission with the optimum initial contention window (CW) based on the nodes distribution in each zone, where the probability of the WSA packet transmission is better than that without determining the optimum initial contention window (CW).

We found that the probability of WSA packet transmission with the optimum initial contention window (CW) enhanced the performance results with a mean of approximately 24.67%.

4.2 Performance Evaluation of the Average Transmission Delay of Service Packets

In this work, we evaluate the analytical model for the average transmission delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for the proposed coordination scheme under node mobility and frame error caused by AWGN. In our model, different transmission rates were used, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also consider the Nakagami propagation model to analyse the performance results. It was assumed that the node had the highest data rates on a certain channel with service packet lengths of up to 2000 bytes.

By using [3-5], we can obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

where [G.sub.1] shows the number of reservations made on the CCH amid the WSA interim, and [G.sub.2] is the quantity of administration bundles transmitted on all Nsch SCHs amid the SCH interim [3-5].

Fig. 5 shows the optimal [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] under different groups with different transmission rates and node velocities in each group. We also evaluated service packets based on the frame error caused by the AWGN. We found that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] increases correspondingly with increases in the transmission rate and node velocity. The average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] significantly increases, which is caused by the distribution node in each group.

Moreover, the frame error caused by the AWGN influences the service packet data and will correspondingly increase the average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

4.3 Performance Evaluation of the Average Transmission Delay of Service Packets

To analyse and perform the saturated throughput on the SCHs, a three-dimensional Markov chain model was used. In this work, we used different transmission rates in each groups, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also considered the error frame caused by the AWGN. In this work, we used the Nakagami propagation model to analyse the saturated throughput. We also used the same assumptions as those in [6-8] for the saturated throughput on the SCHs caused by the SCH interval, the mean interval that transmits a service packet on SCH, the number of SCHs, and the payload of the service packet. In this model, we also considered the different transmission rates and node velocity in each group to analyse the saturated throughput on the SCHs.

Fig. 6 shows the optimum saturated throughput on SCHs that considered the error frame caused by the AWGN noise. We found that the saturated throughput on the SCHs reduce correspondingly as the error frame increases, which is caused by the AWGN. Moreover, as the transmission rate and node velocity increase, the saturated throughput on the SCHs also increases.

5. Conclusion and Future Work

We evaluated the performance of the dynamic channel coordination scheme that is affected by the high mobility node and additive white Gaussian noise (AWGN). We found that the probability of the WSA packet transmission with the optimum initial contention window (CW) based on the nodes distribution in each zone is better than that without determining the optimum initial contention window (CW). We found that the probability of the WSA packet transmission with the optimum initial contention window (CW) enhanced the performance results with a mean of approximately 24.67%.

Furthermore, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] increased as the transmission rate and node velocity increased. The average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] significantly increased due to the nodes distribution in each group. Moreover, the frame error caused by the AWGN influenced the service packet data and correspondingly increased the average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Additionally, the saturated throughput is influenced by the increase in the transmission rate and node velocity. Similar to the average delay, the frame error caused by the AWGN influenced the service packet data, which corresponds with the saturated throughput on the SCHs.

Later on, we plan to augment the 3D Markov model evaluation with the influence of the hidden nodes problem in relation to the node mobility performance on the IEEE 1690.4 standard.

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[9] Duck-Yong Yang, Tae-Jin Lee, Jin Bong Chang, and Sunghyun Choi, "Performance Enhancement of Multirate IEEE 802.11 WLANs with Geographically Scattered Stations," IEEE Transactios on Mobile Computing, Vol. 5, No.7, July 2006. Article (CrossRef Link)

[10] Tom H. Luan, Xinhua Ling, and Xuemin (Suherman) Shen, "MAC in Motion : Impact of Mobility on the MAC of Drive-Thru Internet," IEEE Trans. Mobile Computing, vol. 11, no. 2, pp. 305-319, February 2012. Article (CrossRef Link)

[11] Shi Chun, Dai Xianhua, Liang Pigyuan, and Zhang Han "Adaptive Access Mechanism with Optimal Contention Window Based on Node Estimation Using Multiple Theresholds," IEEE Transactions Wireless Communicatios, Vol. 11, No. 6, June 2012. Article (CrossRef Link)

[12] Khalid Abdel Hafeez, Lian Zhao, Bobby Ma, and Jon W. Mark, "Performance Analysis and Enhancement of the DSRC for VANET's Safety Applications," IEEE Transactions on Vehicular Technology, Vol. 62, No. 7, September 2013. Article (CrossRef Link)

[13] He J., Tang Z., Yang Z., Cheng W., Chou C.T, " Performance Evaluation of Distributed Access Scheme in Error-Prone Channel, in Proc. of IEEE TENCON 2002, pp. 1142-1145, October 2002. Article (CrossRef Link)

[14] Bianchi, G.; "Performance analysis of the IEEE 802.11 distributed coordination function," Selected Areas in Communications, IEEE Journal on, vol.18, no.3, pp.535-547, Mar 2000. Article (CrossRef Link)

[15] Doan Perdana and Riri Fitri Sari, "Mobility Models Performance Analysis using Random Dijkstra Algorithm and Doppler Effect for IEEE 1609.4 Standard," International Journal of Simulation, Systems, Science, and Technology, United Kingdom Simulation Society Article (CrossRef Link)

[16] Luo, T., Wen, Z., Li. J, Chen, H.H, "Saturation Throughput Analysis of WAVE Networks in Doppler Spread Scenarios IET Communcations," special on Vehicular Ad Hoc and Sensor Networks, September 2009. Article (CrossRef Link)

Doan Perdana (1), Ray-Guang Cheng (2), Riri Fitri Sari (3)

(1) Telecommunication Engineering, School of Electrical Engineering, Telkom University, Bandung City- Indonesia,

(2) Department of Electronics and Computer Engineering, National Taiwan University of Science and Technology, Taipei-Taiwan, (3) Department of Electrical Engineering, Faculty of Engineering, University of Indonesia, Depok - Indonesia

[e-mail: doanperdana@telkomuniversity.ac.id, crg@mail.ntust.edu.tw, riri@ui.ac.id]

(*) Corresponding author: Doan Perdana

Received September 9, 2016; accepted November 25, 2016; published January 31, 2017

Doan Perdana received his BSc and MSc degrees in Telecommunication Engineering, from the Institute of Technology Telkom in 2004 and 2012, respectively. He is currently pursuing his doctorate in the Electrical Engineering Department, University of Indonesia. His interests include Telecommunication Systems and Computer Engineering.

Ray-Guang Cheng PhD is a Professor of Electronic and Computer Engineering of National Taiwan University Science and Technology. He received his B.E, M.E, and PhD degrees in Communication Engineering from National Chiao-Tung University, Taiwan, ROC, in 1991, 1993, and 1996, respectively. His current research interests include machine-to-machine communications, multi-hop cellular networks, and network architecture for radio over fibres.

Riri Fitri Sari PhD is a Professor of Computer Engineering in the Electrical Engineering Department of Universitas Indonesia. She received her BSc degree in Electrical Engineering from Universitas Indonesia. She completed her MSc in Software System and Parallel Processing from the University of Sheffeld, UK. She was awarded her PhD in Computer Science from the University of Leeds, UK. Riri Fitri Sari is a senior member of the Institute of Electrical and Electronic Engineers (IEEE).

The most challenging issues in the multi-channel MAC of the IEEE 1609.4 standard is how to handle the dynamic vehicular traffic condition with a high mobility, dynamic topology, and a trajectory change. Therefore, dynamic channel coordination schemes between CCH and SCH are required to provide the proper bandwidth for CCH/SCH intervals and to improve the quality of service (QoS). In this paper, we use a Markov model to optimize the interval based on the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard. We evaluate the performance of the three-dimensional Markov chain based on the Poisson distribution for the node distribution and velocity. We also evaluate the additive white Gaussian noise (AWGN) effect for the multi-channel MAC coordination scheme of the IEEE 1609.4 standard. The result of simulation proves that the performance of the dynamic channel coordination scheme is affected by the high node mobility and the AWGN. In this research, we evaluate the model analytically for the average delay on CCHs and SCHs and also the saturated throughput on SCHs.

Keywords: MAC Multichannel, IEEE 1609.4, Dynamic channel coordination scheme, CCH/SCH interval, Markov chain three Dimensional.

1. Introduction

The vehicular ad hoc network (VANET) is an outcome of wireless technology progress in MANET. The VANET is regarded as the most appropriate network to use currently and in the future because it generates a unified vehicle strategy to resolve the traffic condition when crossing the street in a city.

IEEE 1609.4 specifies the extension to the IEEE 802.11p medium access control (MAC) for multi-channel operations [1]. According to standard, there is one control channel (CCH) and multiple service channels (SCHs). The safety and control messages are exchanged between devices in the CCH. The non-safety application services are exchanged in the SCHs [1]. According to the coordination scheme, each device should alternate between the CCH and SCHs [1]. The IEEE 1609.4 standard defines a concept of channel intervals in which frequency is divided into one CCH and six SCHs [2]. The IEEE 1609.4 standard characterizes the synchronization interval with a fixed length of 100 ms, which are divided into CCH and SCH intervals, i.e., each interval lasts for 50 ms [2]. The IEEE standard of 1609.4 synchronizes the CCH and SCH intervals to an external time reference, a global positioning system provide the universal coordinated time (UTC) [1].

In the IEEE 1609.4 specification, a WAVE provider, which could either be a roadside unit or vehicle, can initialize a Basic Service set (BSS) to provide a non-safety service [1]. Each WAVE provider advertises its presence and offers services by periodically broadcasting a WAVE service advertisement (WSA)

WSAs contain the data of the offered administrations and the system parameters important to join the promoted BSS (distinguishing proof, SCH, EDCA parameter sets, Internet arrangement, and so forth.) [1]. The IEEE 1609.4 standard suggests that each WAVE provider sends WSAs several times in the CCH interval [1]. A WAVE provider should also choose the least congested SCH for its BSS to reduce interference between nearby BSSs [1].

The results from literature show that fixed-length CCH/SCH intervals cannot effectively handle a changing traffic load dynamically [1]. In a dynamic vehicular traffic condition, a fixed-length CCH can not handle the big number of safety and packets control [1]. For example, the CCH channel is rarely used because of occasional transmissions from vehicles in scanty systems [1], while certain applications expend a lot of data transfer capacity, for example, video downloads and outline, and can't acquire adequate SCH assets because of exorbitant conflict [1]. In this way, many protocols have been aim to address a dynamic setting of CCH/SCH intervals [1] to optimize utilization of channel and improve the quality of service (QoS).

A recent study that investigated the dynamic channel coordination scheme describes a system parameter in their algorithm to analyse CCH/SCH intervals [1]. If the system parameter is not adjusted according to the dynamically changing network condition, the operation of the protocols cannot be guaranteed to work accurately under the dynamic traffic vehicular environment [1]. Furthermore, the authors used a fixed rate parameter in their algorithm to calculate the CCH/SCH interval using the default option of a typical VANET system.

In this paper, we evaluate the performance of the dynamic channel coordination scheme under a dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard. We use a Markov chain model based on the Poisson distribution for node distribution and velocity to optimize and validate the analytical model of the WSA interval, safety interval, SCH interval, and also the saturated throughput on the CCH and SCHs interval delay. We also evaluate the Doppler effect impact on the proposed dynamic coordination scheme.

This research is created as follows. In section II, we develop a number of related works. Section III, the overall system model for a system supporting the dynamic channel coordination scheme is defined and then analysed using a Markov chain. In section IV, we evaluate a performance. Finally, section V shows the conclusions and suggests future work.

2. Related Work

Evaluating dynamic adjustments of CCH and SCH intervals in how they handle a congested vehicular traffic condition is essential when discussing a multi-channel MAC of the IEEE 1609.4 standard. Wang, Q. et al. [3-5] categorized the multi-channel MAC protocol into CCH and SCH intervals. Moreover, the scheme [3-5] divides the CCH interval into the safety and WSA interval. This scheme is called the variable CCH interval (VCI). VCI optimizes the ratio between the CCH and SCH intervals [3-5] to handle the dynamic vehicular traffic condition. We used [3-5] to evaluate the performance of the proposed scheme using a three-dimensional Markov chain based on the Poisson distribution for node distribution and velocity in a multi-channel MAC of the IEEE 1609.4 standard.

In [6], J. So et al. proposed a DSRC MAC protocol to give multi-channel performance. The focus offers potentially big bandwidth to non-safety implementation provided by the roadside manufacture that does not compromise safety communication in other channels. This approach supplements the current impromptu plans when a RSU is inaccessible. In any case, every gadget must be furnished with an alternate convention in both the impromptu mode and framework mode in the MAC and system layers. Thusly, a multifaceted nature of the gadget execution incredibly increments.

Differently, D. Zhu et al. [7] proposed a multi-channel MAC convention for the dynamic change of CCH/SCH interims, called the element CCH interim (DCI). DCI works indistinguishably to VCI aside from how the WSA interim is figured. DCI ascertains the ideal WSA interim in light of the likelihood dissemination of the reservation time for an administration bundle in the CCH interim.

N. Lu et al. [8] characterized the devoted multi-channel MAC (DMMAC) to play out a versatile telecom system to diminish the crash rate and transmission delay. The objective of the exploration was to enhance the security execution of the parcel conveyance proportion. The examination had not reason an adaptive modification of a CCH interim; likewise, explanatory research were doered on the model of the aim conspire.

Most of works that study the coordination scheme in a multi-channel MAC of the IEEE 1609.4 standard did not evaluate the effect of a high mobility node and frame error caused by AWGN. This motivated us to evaluate the coordination scheme under the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard.

3. Modelling and Analysis

In Fig. 2, we illustrate our approach to the Markov chain pattern. We used the discrete Markov chain pattern from [7,8] and extended this model by taking the variable data rate and dynamic coordination scheme on the multi-channel MAC of the IEEE 1609.4 standard. In this model, we also define the state for the nodes distribution using the Poisson distribution. We also evaluated the Doppler effect using this model. Let b(t) represents the backoff counter in time slot t, and the random process that represents the backoff stage k can be described using notation s(t), where k [MEMBER OF] m. Then, we can obtain [CW.sub.min], and m is the maximum backoff stage; therefore, [CW.sub.max] = [2.sup.m]W. Otherwise, we defined z(t) as seven groups of the distribution nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We used the transmission rate assumptions based on the maximum bandwidth in the 802.11p standard, i.e., 27 MHz. Then, the three-dimensional process {s(t), b(t), z(t)} can be modelled as a discrete-time Markov chain (DTMC).

In our model, we defined how our model deals with the real environment, called "performance anomaly" [7,8]. Based on the work from [7,8], we found the phenomenon of "performance anomaly" of the IEEE 802.11 standard, which showed startling execution corruption of the stations when utilizing high information rates or those close with the access point (AP). In this work, we evaluate the "performance anomaly" by accounting for the Doppler effect and the dynamic coordination scheme on the multi-channel MAC of the IEEE 1609.4 standard.

We defined one CCH and six SCH channels in our model. Additionally, we defined the effect of Doppler as the changing in frequency of a wave for the surveyer immigrating relative to its spring. In a vehicular environment, the Doppler effect is caused by high mobility, a dynamic topology, and a trajectory change. In this work, we evaluate the Doppler effect based on the different transmission rates and velocities in each group. We analyse the coordination scheme based on the previous scheme [3-5]. We use the Markov model to evaluate the coordination scheme under the dynamic vehicular traffic condition with high mobility nodes in the multi-channel MAC of the IEEE 1609.4 standard.

We estimate the node distribution in each group using the Poisson and Nakagami fading distribution [11]. Next, according to the work in [11], we define the optimal CW index (CWI) as the optimum initial CW value to conform the adaptive network conditions for better fairness and higher aggregate throughput. We then found the optimal CW index (CWI) based on the distribution node in each group. Finally, we can evaluate the aggregate throughput S for the coordination scheme using the CWI result. We can also optimize the throughput based on the Doppler effect in each group of nodes using the optimum initial CW. The results in [15] showed that the change in the initial CW could increase the throughput.

3.1 Average Node Distribution

Next, we calculate the node distribution in each group using the Poisson distribution according to [12]. Firstly, we estimate the communication range under the Nakagami fading distribution.

According to [12], the Nakagami fading distribution considers that the parameters can be adjusted correspond to a variety of empirical measurements. The Nakagami-m appropriation is a likelihood circulation identified with the gamma conveyance. It has a shape measurer and a moment measurer that controls the afloat [OMEGA]. The received signal power x is probability density function (pdf) [12,13] can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for x [greater than or equal to] 0 (1)

Where [GAMMA](.) Is the Gamma function; [P.sub.r] = [P.sub.t][K/r.sup.a] is the average received power; r is the range in meters; a is a path-loss exponent; K = [G.sub.t] [G.sub.r][(c/(4[PI] [f.sub.c])).sup.2] ; C is the speed of light; [f.sub.c] = 5.9 GHz is the carrier frequency, [G.sub.t] and [G.sub.r] are a transmitter's and receiver's antennas gain, respectively, r, and m is the factor of fading [12].

From Eqn. (1), we can figure a cdf of the correspondence extend when the got power is more noteworthy than the limit [P.sub.th] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The average state of a communication area E[R] can be derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Substituting (4) into (5) and integrating above the limit, we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

To infer the normal bearer sense run E [[L.sub.CS]], where hubs can detect the bundle yet can't get it, an indistinguishable methodology from in (6) is taken after

This condition exception is for the received power [P.sub.CS], which defined as the percentage threshold [P.sub.th] as [P.sub.CS] = [.sub.p][P.sub.th], where p [MEMBER OF] [0,1]. Therefore, the expected porter sense is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

We use the same assumptions in [12] for our model analysis to estimate the average node using the Poisson distribution. According to an analytical study [12], we can discover the likelihood of having [N.sub.c] vehicles inside the scope of any labeled vehicle. The versatility model is reached out to incorporate the base wellbeing between vehicles in every path. This base separation is an arbitrary variables and relies at upon a accompanying vehicle's speed [V.sub.j] if a settled [t.sub.s] is imaginated, which is a reaction time to the driver for respond to the sudden occurrence, which can be described using the single-server queue model, as shown in Fig. 4.

According to [12], when a number of vehicles that across the defined reference point is small, the inter-arrival time ([[tau].sub.d] = 1/[[beta].sub.i]) between vehicles in the [i.sub.th] lane is larger than [t.sub.s].

In this issue, the opportunity of having [N.sub.ci] = k vehicles with a communication area of the tagged vehicles (i.e., within a distance of 2[.bar.R]) in the ith lane is based on the Poisson distribution [12] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

and the average number of vehicles about the tagged vehicle in a ith lane

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Based on [11], the optimal contention window (CW) is subject to the dynamic hub number in the system ([N.sub.ci]). Therefore, in the next section, we define the optimal contention window (CW).

3.2 Optimal CW Index (CWI)

Next, we obtain the optimal CW index (CWI) based on [11] and extend this approach by using the variable data rate based on the nodes distribution and the Doppler effect. The optimal CW index (CWI) is an optimum initial CW value to adjust the dynamic system conditions for better transient decency and higher total throughput [11]. Finally, we can evaluate the aggregate throughput S for the coordination scheme using the CWI result. Firstly, we define the aggregate throughput S as [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the time that different hubs transmit effectively aside from the labeled hub amid the mean defer time. E[p] and [R.sub.Data](t) are the normal bundle payload lengths and information rates, separately. [lambda] is the proportion of the payload size to full bundle length with the header messages.

The throughput S in the Eqn. (8) can be further simplified as in Eqn. [15]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Based on [11], the optimal CW can receive a optimum throughput with a node number of N. According to [11], the network delay is modelled more accurately when the new greateful transmission time [T.sub.s] and collision time [T.sub.c] are calculated:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [T.sub.DATA] and [T.sub.hsad] speak to the transmission duration of the MAC edge and header of the physical layer, separately, [sigma] and [T.sub.SIFS] are the propagation delay and the SIFS duration. [T.sub.RTS], [T.sub.cTs], and [T.sub.ACK] denote the transmission duration of an RTS, CTS, and ACK frames [11].

According to Eqn. (8), we can simplify Eqn. (10) using CW and [partial derivative]S/[partial derivative]CW = 0 and then neglecting the stuffs that is less than or equals to the third-order stuff 1/[CW.sup.3]

[partial derivative]S/[partial derivative]CW=[N.T.sub.SLOT]/2.[CW.sup.2] + 2[(N - 1).sup.2].[T.sub.SLOT].CW +(N - 1)([4T.sub.SLOT] - [2T.sub.c] - [2T.sub.EIFS])[N.sup.2] +(N - l)([2T.sub.EIFS] - [2T.sub.DIFS] - [14T.sub.SLOT])N +(N -1)([2T.sub.DIFS]+ [10T.sub.SLOT])N (10)

We can obtain the optimal CW by solving Eqn. (11) as

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

Consequently, we can calculate the result of the CW from (12)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and is referred to as the CW Index (CW I).

3.3 Throughput Analysis

We use the three-dimensional Markov chain model to evaluate and analyse the throughput. First, according to the work in [3-5], we can obtain the probability of successful transmission [P.sub.SUC], where a channel collision occurs with a probability of [P.sub.COL] or the channel is idle with a probability of [P.sub.idls]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

According to [10], [W.sub.i,k] denotes the backoff window for a station in gathering i at backoff arrange k. In the routine DCF instrument utilizing bearer sense numerous entrance with impact shirking (CSMA/CA), all stations in any gathering i have a similar starting (at backoff organize 0) backoff window [w.sub.i,0] for all i = 1, 2, 3, 4, 5, 6, and 7 [10].

We use the same assumptions with [10] at the point when the channel is sit out of gear amid the DCF interframe space (DIFS), where every station chooses an arbitrary backoff counter among [0, [w.sub.i,0] - 1] slots and sits tight for the comparing number of spaces before endeavoring to get to the remote medium. The estimation of the backoff counter is decremented by one at whatever point an opening is detected as sit. On the off chance that there are transmissions from different stations amid this period, the backoff counter commencement is suspended [10]. At that point, when the channel gets to be distinctly sit without moving, the station continues its backoff procedure after a DIFS sit out of gear period [10]. At the point when the backoff counter esteem achieves zero, the station transmits the pending edge [10].

Then, we evaluate the transition state probability in figure 3. We have seven groups of nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. Therefore, we define z(t) that represents the group of nodes i, where 1 [less than or equal to] i [less than or equal to] N. In this paper, we rework the probability of successful transmission [P.sub.SUC], where a channel collision occurs with the probability of [P.sub.col] or the channel is idle with a probability of [P.sub.idls]. The state of the Markov chain is denoted as (i, k, l), 1 [less than or equal to] i [less than or equal to] N, 0 [less than or equal to] k [less than or equal to] m, 0 [less than or equal to] l [less than or equal to] [w.sub.i,k] - 1, where i, k, and l represent group i, the backoff stage k, and the backoff counter value l, respectively. Let [t.sub.z] represent the conditional transmission probability of nodes in zone z as N group zones. We define m as the maximum backoff stage. Additionally, [W.sub.max] represents the maximum contention window, and [W.sub.z] represents the minimum contention window size [CW.sub.MIN] associated in zone z. We define E[X] as the mean time of transmission data of the tagged point in area z. We define E[[Tx.sub.suc,z]] as the mean duration of successful transmission of the tagged point in area z. Furthermore, we derived from [10] by considering the Doppler effect:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15a)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15b)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15c)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15d)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15e)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15f)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15g)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15h)

An unsuccessful (re)transmission attempt can occur due to collision of this station with at least one of the n - 1 remaining stations, which has the probability of [p.sub.col] [14]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

An error frame occurs with probability [P.sub.s] due to the channel fading and/or noise. Because both events are independent, the probability of node collision in each zone i, [p.sub.C,i] can be expressed as [10,14]

p = [P.sub.c,i] = 1 - (1 - [p.sub.col])(1 - [p.sub.e]) = [p.sub.col] + [p.sub.s] - [p.sub.col] [p.sub.s] (17)

where [P.sub.s] = 1 - [(1 - [p.sub.s]).sup.L] and [P.sub.s] = E [[R.sub.b] ([gamma])]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Next, we determine [tau] as the transmission probability where a station conducts the success transmission at the slot. By using the random distribution node and considering the AWGN, we calculate the transmission probability [tau] of each station.

Because transmission occurs only in states (k, 0), the probability [tau] of a station transmitting in a random chosen slot able be showed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Then, probability [b.sub.i,k,l] for 0 < i [less than or equal to] (m + f) can be given simply as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Then, we can obtain the probability [tau] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Combining the equation above, we obtain [[tau].sub.i]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

Next, we define [P.sub.tr] as the opportunity of at least one point in transmission in the cognationed duration, and [P.sub.s] is the symbol error rate (SER). In this work, we use the same assumptions with [14] by taking the frame error probability [P.sub.s] into the calculation.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

Moreover, the saturated throughput in each zone is obtained using [15], which is the average payload of information that able be transmitted in a duration slot on a SCH channel by considering the effect of bit error, and the Doppler effect can be calculated by the following formula.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

Where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

where

y = [OMEGA][E.sub.B]/[N.sub.0] is the fading of average SNR, [OMEGA] is the gain of channel, and p is the fading correction parameter, where p = [J.sub.0](2[pi][f.sub.d][T.sub.b]). Additionally, [f.sub.d] denotes the Doppler spread.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

c represents the velocity of waves in the medium.

[v.sub.[gamma]] represents the velocity of the receiver relative to the medium.

[v.sub.s] represents the velocity of the source relative to the medium.

[f.sub.0] denotes the source frequency ([f.sub.0] =5.9 GHz).

From Equations (19), (20), (21), and (24), we can obtain the formula of the saturated throughput as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

Finally, the aggregate throughput can be defined from [15] as the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

Based on Luo [17], the effect of gain is more urgent in IEEE 802.11p because the velocity. In 802.11p systems, when a 10-MHz bandwidth is brought, the Doppler spectrum with velocities of 10.8 km/h and 216 km/h is approximately 59 Hz and 1.18 kHz, respectively. In this work, the simulated velocities of the vehicles are between 80-120 km/h.

In the next section, we evaluate and simulate the coordination scheme, which considers the Doppler effect.

4. Performance Evaluation

Using MATLAB, we evaluate the performance of the Markov model for the coordination scheme based on the IEEE 1609.4 standard. We simulate the scenario with the 119 vehicle nodes, the velocities of the vehicles are between 80-120 km/h, the packet length is 2000 bytes, and there are seven groups of distributed nodes according to their transmission rate, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. The channel configuration uses the variable value for the control and administration channel interims. The protect interim esteem is 4 ms. Table I shows every one of the parameters utilized as a part of our recreation. While certain parameters remain settled, others are fluctuated to watch any changed conduct of the system.

4.1 Performance Evaluation of the Probability of WSA Packet Transmission

We use the three-dimensional Markov chain model to determine the probability of the WSA packet transmission that is affected by the reservation channel CCH contention models and the anomalous performance due to the different transmission rates in each zone. The probability of the WSA packet transmission is calculated based on two variables, i.e., the transmission rate and the number of distribution nodes in each zone. The influence of these two variables on the probability of the WSA packet transmission on the DCF model were simulated using MATLAB. In this work, we have different transmission rates, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also consider the Nakagami propagation model to analyse the performance results.

Fig. 4 shows the probability of WSA packet transmission with the optimum initial contention window (CW) based on the nodes distribution in each zone, where the probability of the WSA packet transmission is better than that without determining the optimum initial contention window (CW).

We found that the probability of WSA packet transmission with the optimum initial contention window (CW) enhanced the performance results with a mean of approximately 24.67%.

4.2 Performance Evaluation of the Average Transmission Delay of Service Packets

In this work, we evaluate the analytical model for the average transmission delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for the proposed coordination scheme under node mobility and frame error caused by AWGN. In our model, different transmission rates were used, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also consider the Nakagami propagation model to analyse the performance results. It was assumed that the node had the highest data rates on a certain channel with service packet lengths of up to 2000 bytes.

By using [3-5], we can obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

where [G.sub.1] shows the number of reservations made on the CCH amid the WSA interim, and [G.sub.2] is the quantity of administration bundles transmitted on all Nsch SCHs amid the SCH interim [3-5].

Fig. 5 shows the optimal [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] under different groups with different transmission rates and node velocities in each group. We also evaluated service packets based on the frame error caused by the AWGN. We found that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] increases correspondingly with increases in the transmission rate and node velocity. The average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] significantly increases, which is caused by the distribution node in each group.

Moreover, the frame error caused by the AWGN influences the service packet data and will correspondingly increase the average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

4.3 Performance Evaluation of the Average Transmission Delay of Service Packets

To analyse and perform the saturated throughput on the SCHs, a three-dimensional Markov chain model was used. In this work, we used different transmission rates in each groups, i.e., 3, 6, 12, 27, 12, 6, and 3 Mbps. We also considered the error frame caused by the AWGN. In this work, we used the Nakagami propagation model to analyse the saturated throughput. We also used the same assumptions as those in [6-8] for the saturated throughput on the SCHs caused by the SCH interval, the mean interval that transmits a service packet on SCH, the number of SCHs, and the payload of the service packet. In this model, we also considered the different transmission rates and node velocity in each group to analyse the saturated throughput on the SCHs.

Fig. 6 shows the optimum saturated throughput on SCHs that considered the error frame caused by the AWGN noise. We found that the saturated throughput on the SCHs reduce correspondingly as the error frame increases, which is caused by the AWGN. Moreover, as the transmission rate and node velocity increase, the saturated throughput on the SCHs also increases.

5. Conclusion and Future Work

We evaluated the performance of the dynamic channel coordination scheme that is affected by the high mobility node and additive white Gaussian noise (AWGN). We found that the probability of the WSA packet transmission with the optimum initial contention window (CW) based on the nodes distribution in each zone is better than that without determining the optimum initial contention window (CW). We found that the probability of the WSA packet transmission with the optimum initial contention window (CW) enhanced the performance results with a mean of approximately 24.67%.

Furthermore, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] increased as the transmission rate and node velocity increased. The average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] significantly increased due to the nodes distribution in each group. Moreover, the frame error caused by the AWGN influenced the service packet data and correspondingly increased the average delay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Additionally, the saturated throughput is influenced by the increase in the transmission rate and node velocity. Similar to the average delay, the frame error caused by the AWGN influenced the service packet data, which corresponds with the saturated throughput on the SCHs.

Later on, we plan to augment the 3D Markov model evaluation with the influence of the hidden nodes problem in relation to the node mobility performance on the IEEE 1690.4 standard.

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Doan Perdana (1), Ray-Guang Cheng (2), Riri Fitri Sari (3)

(1) Telecommunication Engineering, School of Electrical Engineering, Telkom University, Bandung City- Indonesia,

(2) Department of Electronics and Computer Engineering, National Taiwan University of Science and Technology, Taipei-Taiwan, (3) Department of Electrical Engineering, Faculty of Engineering, University of Indonesia, Depok - Indonesia

[e-mail: doanperdana@telkomuniversity.ac.id, crg@mail.ntust.edu.tw, riri@ui.ac.id]

(*) Corresponding author: Doan Perdana

Received September 9, 2016; accepted November 25, 2016; published January 31, 2017

Doan Perdana received his BSc and MSc degrees in Telecommunication Engineering, from the Institute of Technology Telkom in 2004 and 2012, respectively. He is currently pursuing his doctorate in the Electrical Engineering Department, University of Indonesia. His interests include Telecommunication Systems and Computer Engineering.

Ray-Guang Cheng PhD is a Professor of Electronic and Computer Engineering of National Taiwan University Science and Technology. He received his B.E, M.E, and PhD degrees in Communication Engineering from National Chiao-Tung University, Taiwan, ROC, in 1991, 1993, and 1996, respectively. His current research interests include machine-to-machine communications, multi-hop cellular networks, and network architecture for radio over fibres.

Riri Fitri Sari PhD is a Professor of Computer Engineering in the Electrical Engineering Department of Universitas Indonesia. She received her BSc degree in Electrical Engineering from Universitas Indonesia. She completed her MSc in Software System and Parallel Processing from the University of Sheffeld, UK. She was awarded her PhD in Computer Science from the University of Leeds, UK. Riri Fitri Sari is a senior member of the Institute of Electrical and Electronic Engineers (IEEE).

Table 1. Simulation Parameters Parameters Values Number of CCH 1 Number of SCHs 4 Group of nodes 7 Service packet length 2000 bytes [CW.sub.min] 32 [CW.sub.max] 1024 WSA/RFS 160 bits + PHY header ACK 112 bits + PHY header Slot time 20 [micro]s SIFS 10 [micro]s DIFS 50 [micro]s Number of vehicles 119 nodes Velocity of vehicles 80-120 km/h

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Title Annotation: | medium access control |
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Author: | Perdana, Doan; Cheng, Ray-Guang; Sari, Riri Fitri |

Publication: | KSII Transactions on Internet and Information Systems |

Article Type: | Report |

Date: | Jan 1, 2017 |

Words: | 5987 |

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