Page 63 - ITU Journal Future and evolving technologies Volume 3 (2022), Issue 2 – Towards vehicular networks in the 6G era

ITU Journal on Future and Evolving Technologies, Volume 3 (2022), Issue 2

age up to peak
drop down
( ) = ( ) + Δ ( ) (1) S r steady

S g
where ( ) denotes the average transmission cost, and

Δ ( ) denotes average AoI.

time
In the model of transmission cost, the cost is the energy t 1 t 2 t 3 t 4 t 5 t 6 t 6'
consumed by the V2V communications. As shown in Fig. t 1' t 2' t 5'
t 3'
5, the cost of each hop can be modeled as the reduction of t 4'
AoI. For the road with length of , the delay of carrying Fig. 6 – Age of information with traf ic hole problem
″
by the vehicle is − = , and the delay of V2V commu‑

′
nication is − ≈ 0 which is too short to be neglected. As shown in Fig. 6, the irst update is generated at and is
1
′
Thus, the cost of each hop is calculated as follows: received at in a steady stage, where its delay is equal to
1
′
− . According to our discretization model, the number
1
1
of the update in steady stage is = ⌊
″
′
= ⋅ ( − ) ≈ ( ) 2 (2) ⌋.
ℎ
In the up‑to‑peak stage of each cycle, the traf ic light
changes to red, and the irst vehicle that carries an up‑
During the time of the green light, there will be cars date will stop at the intersection. The update delivery de‑

carrying updates passing by the traf ic light without stop‑ lay will increase so as to the age of information. Thus, the
ping. As can be seen from the previous assumptions, the delay of the update carried by the irst vehicle waiting for
distance between a vehicle and the vehicles in front of the traf ic light (denoted by ) is calculated as follows:
and behind it is greater than the communication radius.
Therefore, an update will pass from the source to a vehi‑ = 1 + + − (5)
2
cle by 1 hop, and from the vehicle to the destination by 1
hop. Since the number of updates driving through during In the drop‑down stage of each cycle, while the traf ic light
a green light is , the number of hops at a green light in is still red, the vehicles behind that carry new updates

a cycle is 2 . During the time of the red light, there are will catch up with the irst vehicle waiting at the traf ic

vehicles with updates queuing at the intersection, and light. Thus, they forward the new updates to the irst ve‑

− 1 vehicles will transmit an update to the irst vehicle hicle, and all these updates will send to the destination
at once. According to our discretization decentralization
before the red light through V2V. Similarly, it takes 2 hops
for a vehicle after receiving an update from the sensor and model, the amount of the updates in drop‑down stage of
ℎ

transmitting it from the vehicle to the RSU. Therefore, in each cycle is = ⌊ ⌋−1, and the update of them has
one cycle, the number of hops at red light is 2 + −1. the delivery delay as follows:

1 −

2
From the above explanation, the number of hops during = + ( − ⋅ ) + , ∈ [1, ] (6)

each green light is ℎ = 2 , and the number of hops dur‑

ing each red light is ℎ = 3 − 1. Thus the number of Therefore, to calculate the sum AoI, we divide the sum AoI

in each cycle into two areas: and as shown in Fig. 6,

hops in each cycle is ℎ = ℎ + ℎ . Thus, the average trans‑ which denote the sum AoI of the updates meet red light

mission cost of each cycle is calculated as follows:
and green light, respectively. The sum AoI of is calcu‑

2 + 3 lated as follows:
( ) = ( − 1) ⋅ ℎ (3) = 1 [( + ) − 2 ]

2

4.3 AoI in each cycle 2 1 2 + −
2
1
= ⋅ + ⋅ ( + ) (7)

2
The AoI in each cycle of traf ic light includes three stages:
up‑to‑peak, drop‑down and steady stages, as shown in The sum AoI of is calculated as follows:

Fig. 6. In the steady stage of each cycle, the traf ic light is 1 1
2
green and the vehicle carrying this update is moving with‑ = ⋅ [ ( + ) − 2 ]

2
2
out stopping. The update from the source is delivered by 1 + −
the vehicles via V2V communications. For simplicity, we = ⋅ ( + 1 2 ) (8)

2
assume that the distance between two moving vehicles is
larger than their transmission range, i.e. ⋅ > . Thus, Thus, the sum AoI of each cycle is calculated as follows:
the delivery delay of each update in the steady stage de‑ Δ = +
noted by is calculated by: 1 1 + −

2
= ( + )+ + 1 2 ⋅ (9)
+ − 2 2
1
2
= (4)

© International Telecommunication Union, 2022 51