Distortion assessment for a specific road segment

(12)

We plot the packet error rate with path loss exponent as 3.25 and shadowing deviation as 4.0 as Figure 3. The transmission range here is defined as 300m with packet error rate as 0.5.

Figure 3: The packet error rate under shadowing model.

3.3. Distortion assessment for a specific road segment

To discover whether a road segment is vital for video packet delivery in the proposed algorithm or not, depends on the possible video distortion created. The goal is to find a road path which leads to the minimum video distortion to deliver video packets.

Considering the nature of VANET, the possibility of network disconnection may be caused by the dynamics of vehicles and the unexpected driving behaviors. Although researchers have adopted the idea of carry-and-forward to handle this unpleasant situation, the strict packet delivery deadline requirement makes this approach not really work well in video streaming. Therefore we modified the rate-distortion

formula mentioned above to add this impact in:

(13)

where is the distortion led by network disconnection, and is the corresponding packet dropping probability (because there is no route at that moment).

Figure 4: A model used for hop-by-hop distortion calculation.

The scenario of video packet delivery could be expressed as Figure 4. is the expiration probability due to the queuing delay at vehicle ni, and is the packet dropping probability between vehicle n_i and vehicle n_i+1 caused by failed MAC retransmissions. We combine and to stand for the overall packet dropping probability when the network is connected, and denote it as

(14) and are the packet arrival rate and remaining available time of the incoming packet for vehicle ni. To take the road traffic behavior into account, we also

consider the probability of the road connectivity for road segment based on the traffic statistics. We then calculate the video distortion for a given road segment by the model.

3.3.1. Probability of road connectivity

According to [6], [23] and [24], we assume the inter-vehicle distance follows an exponential distribution. If the average vehicular density is for the road segment

, then the disconnected probability is

(15) where is the road length, and the value of shows the number of hops needed to pass through . Although the transmission range and the packet receiving probability of shadowing model are variables, we still use to estimate the connectivity of a road segment for simplicity.

3.3.2. Probability of MAC retransmission error

This study computes the packet failure probability by two factors: radio fading and packet collision. Given an inter-vehicle distance d, the packet error probability from radio fading is derived from equation (11). To calculate the packet collision probability, a simplified scenario as depicted in Figure 5. Suppose that vi is the current video sender, vi-1, vi-2, …, are the predecessor senders, and vi+1, v_i+2…, are the successor senders (i.e., white cars). The rest vehicles in v_i’s transmission range only broadcast HELLO messages periodically (i.e., red cars).

Suppose the HELLO time interval is , then the corresponding frequency

is:

(16)

There are two conditions to cause the collision: (1) one of v_i’s neighbor nodes transmits during vi’s RTS period or (2) one of vi+1’s neighbor nodes transmits during v_i+1’s CTS period. This study assumes that a successfully RTS/CTS transaction can perfectly occupy the wireless channel, where no other vehicles can transmit packets during the channel occupation time. Therefore, for vehicle v_i+1, only the neighbor nodes of vi+1 outside vi’s transmission range should be considered (i.e., the vehicles inside gray area in Fig.6). Based on above observation, the collision probabilities for a sending RTS frame and a responding CTS frame can be calculated accordingly.

Suppose that the packet arrivals in VANETs are Poisson distributions no matter for video packet or HELLO message. Given a vehicular density ρ_ij and a hop distance

between any two sequential video sender vehicles, the accumulated packet arrival rate from v_i’s neighbor nodes can be derived as:

(17) where is the video packet arrival rate. and are the number of neighboring vehicles with and without video traffic respectively.

Figure 5: Illustration of the scenario used for the packet collision probability calculation.

and

. The collision probability for a sending RTS frame is:

(18) where is the time spent to transmit a RTS frame. We then calculate the collision probability for a responding CTS frame according to Figure 6. The accumulated packet arrival rate is:

(19) and the collision probability is:

(20) where is the time spent to transmit a CTS frame. Finally, we combine the two probabilities and have the overall collision probability as:

(21)

Figure 6: The space coverage of the RTS frame and the CTS frame

The transmission failure probability of RTS/CTS transaction and DATA/ACK

(22) and

(23)

Figure 7: The retransmission scheme of IEEE 802.11 DCF.

To calculate the probability a video data frame will be dropped by MAC, we need to study the operation of the IEEE 802.11 DCF retransmission mechanism. The IEEE 802.11 DCF standard presents a retransmission approach, a frame must be transmitted successfully in a specific attempt limit or it will be discarded. Figure 7 shows the retransmission scheme. ssrc is known as Station Short Retry Count and slrc is known as Station Long Retry Count, they are with respect to the retry limits ShortRetryLimit and LongRetryLimit. ssrc is for the frames which are less than or equal to the RTSThreshold, and slrc is for the frames which are longer than the RTSThreshold.

Every time a RTS/CTS transaction failure is occurred, the ssrc is increased by 1, and a DATA/ACK transaction failure will increase the slrc by 1. The increment of the contention window size is caused from both transaction failures. If a RTS/CTS transaction can be completed successfully, then the ssrc will be reset to 0. In the same

way, successful DATA/ACK transaction also let the slrc be reset to 0. Frames will be dropped if then ssrc exceeds the ShortRetryLimit or the slrc exceeds the LongRetryLimit.

So we can calculate the probability that the video packet can be sent out successfully by taking such retransmission scheme into account. After applying conditional probability, we have:

In this subsection, the probability of packet deadline expiration will be investigated.

That is, the possibility the packet sojourn time at a vehicle will exceed the remaining available time. The first step here is to calculate the packet service time. To estimate the service time adequately, the impacts from binary exponential backoff (BEB) is considered.

Figure 8 depicts the BEB algorithm, every time a packet cannot be transmitted successfully, the current backoff stage of the station node will be increased by 1, and its contention window (CW) size will be doubled until the window size reaches the . The contention window size will be reset to only if the MAC decides

Figure 8: Possible contention window size by applying binary exponential backoff algorithm.

to discard the packet or the packet can be successfully sent out. The following equation can be used to compute the contention window size:

(26) where is the current backoff stage and is the maximum backoff stage. Between two consecutive contention window decrements, the time interval, which can be formulated as the sum of a constant slot time T_slot and an extra delay time E[T_freeze] caused by the surrounding packet transmission [33].

(27)

is the probability if there is at least one neighboring vehicle transmits packet during a single slot time, this could be derived by applying the simplified scenario shown as Figure 5.

(28)

where

and

. In addition, p_s is the probability that a transmitting neighboring vehicle can finish the packet transmission during a slot time period without any contending transmissions simultaneously: needed to discover the transmission failures for RTS/CTS transaction and DATA/ACK transaction. In this thesis, and are set as the same as and , to match the ns2’s implementation [21].

In the proposed approach, the service time is divided into 3 parts to analysis: (1) time for successful transmission ; (2) time for unsuccessful RTS/CTS transmission ; (3) time for unsuccessful DATA/ACK transmission .

By considering all the possible retransmission cases, the average service time for successful transmission is derived as follow:

time for a given retransmission case which sums up the time cost of random backoffs, RTS/CTS handshakes and DATA/ACK handshakes: can help us to reduce the equation representation. Considering the question: find the number of non-negative integer solutions for the equation

We know Inclusion-Exclusion Principle can be applied to solve the question. So the following function is defined to stand for the answer.

authors all assumed the packet queues are M/G/1 queues that means the inter-packet arrival following Poisson distribution. In reality, the Poisson arrival assumption probably is not true. For example, a video frame comes at , and which is separated into packets according to the frame size, so the packet queue instantly has new packets; the next video frame may come at and makes the queue instantly have new packets, etc. However, for the computation simplicity, we still follow the M/G/1 assumption to calculate the packet expiration probability. By the Pollaczek-Khinchin (P-K) formula, the packet waiting time can be expressed as

and Consequently, the distortion for the whole road segment can be further expressed as:

where is the set of all possible hop lengths by considering the vehicle placement:

(45) For the vehicle , if its best forwarder is just meters away from itself ( is the average inter-vehicle distance according to the average vehicular density

for the road segment ), then we averagely think the best forwarder of the vehicle should be also away from itself meters. If the best forwarder vehicle of the vehicle is meters away, two times of the average inter-vehicle distance by Gamma distribution, then we also think averagely the best

forwarder of the vehicle should be also away from itself meters. By analogy, after considering the average distance to each neighbor in transmission range, the distance which leads to minimum distortion will be picked. Figure 9 gives an illustration.

Figure 9: The average distance to each neighbor vehicle in transmission range.

An example is given here to explain the procedure to find the best forwarding distance. We suppose the road density for the road segment is 50 vehicles per kilometer, so the inter-vehicle distance is 20 meters, and then we have . Using each of the entry of as the parameter for the modified distortion model, the corresponding packet dropping probabilities for the entire road segment can be calculated as Figure 10.

Figure 10: An example of total packet dropping probability

Because the minimum total packet dropping probability is led if the hop distance is

160 meters, hence 160 meters will be designated in the distortion estimation, and treated as the best forwarding distance.