Adquisición de Mejoras.

Definition of LP of the mobile node is introduced in [126] as an average number of nodes leaving the group within a rekeying interval. For traditional mobile net- works, such as WSN and LTE network, entrance and departure actions of portable nodes are unpredictable. Hence some key management schemes require nodes subscribing several rekeying intervals in order to calculate leaving probability. Unfortunately, security vulnerabilities appear when the system allows users to se- lect their own subscription period: a malicious user eavesdrops critical messages by asking active period longer than its real residence time.

Different from general wireless mobile networks, probability models are much easier to implement for vehicle nodes in VCS since they usually have predictable moving trajectory. For this reason, a dedicated LP calculation algorithm can be developed for VCS scenarios. According to the traffic survey [128] at a one- directional urban road, speed distribution fits normal distribution function below [129]: f(x|µ, σ ) = 1 σ √ 2πe (x−µ)2 2σ 2 (4.1)

Here, µ is the mean or expectation of the normal distribution and σ is the stan- dard deviation. With the help of the speed distribution and vehicle specifications, the key managers in VCS are able to compute the Possible Speed Range (PSR) and the Possible Departure Speed Range (PDSR). The upper boundary UPSR stands

for the maximum speed in which vehicle can reach at end of current batch interval (tBR) of Batch Rekeying (BR). Similar to UPSR, LPSR is for the minimum speed

if vehicle tries to slow down. In addition, UPSDR and LPSDR are the highest and

lowest speed for a car to leave the current RSU coverage, respectively. We assume that dremain is the distance between vehicle current position and coverage border

which is directly ahead of the vehicle. Thus, the LP PL is calculated as expressed: P_L= RU_PSDR LPSDR f(x|µ, σ )dx RU_PSR LPSR f(x|µ, σ )dx (4.2)

The SM knows the maximum positive and negative acceleration data of ve- hicle by listening to the vehicle status information inside the safety messages, thus it is easier to calculate the upper and lower boundary (Vmax&Vmin) of PSR.

For PSDR boundaries, Vdep−max stands for the maximum speed for the vehicle to

depart, two different extreme situations are classified in Fig.4.5:

Figure 4.5: Max Departure Speed Range (a) The First Departure Situation (b) The Second Situation

1. As shown in Fig.4.5(a), vehicle keep speed-up with maximum positive ac- celeration a+until the speed reaches Vmax. Keep the speed until end of batch

interval. Overall distance dremainis covered by the vehicle (shadow area on

graph).

2. Fig.4.5(b) demonstrates that the vehicle already has enough speed and dremain

is short enough so that vehicle is able to leave the region easily. Hence it speed-up with an acceleration lower then a+. It reaches Vmax at mid of tBR,

and keep the speed Vmaxuntil end of batch interval.

Figure 4.6: Min Departure Speed Range (a) The First Departure Situation (b) The Second Situation

1. As presents in Fig.4.6(a), the current speed Vcurrent is fast enough for ve-

hicle to leave the SM region, therefore the minimum speed for vehicle to leave Vdep−minis decided by decreasing speed until the end of tBR under the

assumption that the node can travel dremain(shadow region on figure).

2. The vehicle has to speed up in order to depart in tBR, therefore the node first

improve current speed from Vcurrent to Vdep−min, then keep it until the end of

batch interval. Shadow region on Fig.4.6(b) is the remaining distance.

According to the possibilities above, first situation is that the vehicle can leave the region only by driving with current speed:

V_dep−min= 2· dremain tBR

−Vcurrent (4.3)

Here assumes vehicle spends time t1to speed up to Vdep−max, equations to calcu-

late Vdep−maxare expressed below:

         V_dep−max= Vcurrent+ t1· a+

Vdep−max· (tBR− t1) + 0.5·t1· (Vdep−max+Vcurrent)

= dremain

Therefore, Vdep−maxis computed by the summarised equation: V_dep−min= Vcurrent+ a+·tBR + q 2a+(Vcurrent·tBR− dremain) + a2+·tBR2 (4.5)

To sum up, LP can be generated by using Algorithm.1: Algorithm 1 Leaving Probability Calculation

Input: : Current speed Vcurrent, distance to coverage border dremain, vehicle maximum positive

and negative acceleration a+&a−, batch interval tBR, maximum speed the vehicle can reach

Vlimit

Output: : Leaving Probability (LP): PL

1: MAX speed in tBR: Vmax−expect= Vcurrent+ a+·tBR

2: if Vmax−expect≥ Vlimitthen

3: dmaxin tBR, keep improve speed until Vlimit;

4: else

5: dmaxin tBR, keep improve speed until Vmax−expect;

6: end if

7: if dmax≥ dremainthen

8: Vdep−max= min(Vmax−expect,Vlimit);

9: else

10: Set LP for this node Pu= 0;

11: end if

12: MIN speed in tBR: Vmin−expect= Vcurrent− tBR× a−

13: if Vcurrent·tBR≥ dremainthen

14: call equation (4.3) to calculate Vdep−min

15: else

16: call equation (4.5) to calculate Vdep−min

17: end if

18: Calculate maximum and minimum possible speed of the vehicle, Vmaxand Vmin;

19: LP is calculated by employing Vdep−max, Vdepmin, Vmaxand Vmininto equation (4.2);

20: End Algorithm