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Table 1 Symbols

From: Hello scheme for vehicular ad hoc networks: analysis and design

Symbol

Definition

L

Road length

R

Transmission range of a node

λ

Vehicle arrival rate

v i

Velocity of node i

v AB

Magnitude of the relative velocity between nodes A and B

HI i

HI of node i

TI i

TI of node i

HImin

Minimum threshold of HI

HImax

Maximum threshold of HI

T in

Moment B moves into the transmission range of A

T out

Moment B moves out of the transmission range of A

(T, x)

State of B when A broadcasts the k th hello packet

(T j , x Bj )

State of B when it generates the j th hello packet and is moving in the range of A

D

Time between the entrance of B to the transmission area of A until the next hello of A is issued

S

Time between the entrance of B to the transmission area of A until the next hello of B is issued

r

Ratio between number of new neighbors and current total number of neighbors of A during a HI

r th

Threshold of r

N new

Number of new neighbors of A during the investigative HI

N cur

Current total number of neighbors of A during the investigative HI

p new

Probability of a random node that can be a new neighbor of reference node (A) during HI A

p 0

Probability of v HI A > 2R

P1'(P1)

Probability of a random node that can be a (new) neighbor of A since the node is outside of A at T

P2'(P2)

Probability of a random node that can be a (new) neighbor of A since the node is inside of A at T

p cur

Probability of a random node that can be neighbor of the reference node A at the time of T + HI A

FS-D()

cdf of S – D

n

Allowed hello loss