1 Introduction
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Formulation of the scheduling and allocating problem in the 2-hop vehicular network;
-
Design of a optimal link scheduling and resources allocation scheme for vehicular networks with considerably lower computational complexity; and
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Performance comparison against the maximum sum rate (MSR) and BG-based schemes of [14].
2 System model and problem formulation
2.1 System model
Symbol | Description |
---|---|
N
| The total number of vehicles in the scenarios |
N
B
| The number of vehicles that directly communicate with eNB |
N
V
| The number of vehicles that cooperatively communicate with eNB |
K
B
| The number of radio resources available for direct communication |
K
V
| The number of radio resources available for cooperative communication |
P
B
| Transmit power over per bandwidth |
P
T
| Total transmit power of eNB |
P
i,j
| Transmit power for V2V link between vehicles i and j
|
\({\tilde P_{T}}\)
| Total transmit power of each vehicle |
N
0
| Unilateral power spectral density of AWGN |
W
| System bandwidth |
N
C
| The number of cells |
β
| Path loss attenuation factor |
A
| Binary matrix that represents the resource allocation between CVs |
B
| Binary matrix that represents the resource allocation between SVs |
η
B,i
| Achievable data rate of the ith CV |
η
i,j
| Achievable data rate of the link between vehicle i and j
|
n
i
| Radio resource allocated for the ith CV |
n
i,j
| Radio resource allocated for link between vehicle i and j
|
-
The vehicles and evolved NodeB (eNB) broadcast signaling to indicate the existing of themselves via control channel periodically;
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The vehicles which receive the signaling to estimate the V2V and V2I link quality and update the CSI;
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Then, the vehicles upload the CSI to the scheduling center;
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Based on CSI, the scheduling center schedules links, allocates radio resources and broadcasts the scheduling results via control channel.
2.1.1 2.1.1 Direct communications
2.1.2 2.1.2 Cooperative communication
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Each SV can be assisted by only one CV at any time;
-
One CV can forward data to more than one SV;
-
The DF relaying is applied at CV.
2.2 Problem formulation
3 Multidimensional-multi-choice knapsack problem-based scheduling scheme
3.1 MD-MCKP problem
Subset | Profit | First weight | Second weight |
---|---|---|---|
First subset | (2,3,4,5) | (1,2,3,4) | (0,0,0,0) |
Second subset | (3,4,5,6) | (1,2,3,4) | (0,0,0,0) |
Third subset | (5,6,7,7) | (1,2,3,4) | (0,0,0,0) |
Fourth subset | (2,3,4,5,3,4,5,6,5,6,7,7) | (1,2,3,4,1,2,3,4,1,2,3,4) | (1,2,3,4,1,2,3,4,1,2,3,4) |
Fifth subset | (2,3,4,5,3,4,5,6,5,6,7,7) | (1,2,3,4,1,2,3,4,1,2,3,4) | (2,3,4,5,2,3,4,5,2,3,4,5) |
3.2 2D-MCKP-based scheduling scheme
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Construct the group of 2D-MCKP.For VE j, group G j of selections is constructed. If vehicle j is CV,$$ {G_{j}} = \left\{ {{g_{p}} = {\eta_{B,j}}\left(p \right)\left| {1 \le p \le {K_{B}}} \right.} \right\}, $$(27)otherwise,$$ \begin{array}{l} {G_{j}} = \left\{ {{g_{(i - 1){K_{B}}{K_{V}} + (q - 1){K_{B}} + p}} = {{\tilde \eta }_{B,i,j}}\left({p,q} \right)} \right\},\;\\ \quad \quad for\;1 \le p \le {K_{B}},1 \le q \le {K_{V}},{\mathrm{1}} \le i \le {N_{B}} \end{array}. $$(28)where the set G j contains K B or K B ×K V ×N B elements, each of which represents the data rate corresponding to VE j, i.e., η B,j (p) and \({{{\tilde \eta }_{B,i,j}}\left ({p,q} \right)}\) are both defined in Section 2.Based on 2D-MCKP, we consider all the selections of S V j as a group and refer the K B and K V as the packet volumes. The mapping C 1(∙) and C 2(∙) is to obtain the first and second index of the solution. For CV i, the first dimension cost is p and the second dimension cost is 0, i.e., C 1(g m )= mod (m,K B ), C 2(g m )=0. However, for SV j, the first dimension cost is p and the second dimension cost is q, i.e., \({C_{1}}\left ({{g_{m}}} \right) = \bmod \left ({m,{K_{B}}} \right),\;{C_{2}}\left ({{g_{m}}} \right) = \left \lceil {\frac {{\bmod \left ({m,{K_{B}}{K_{V}}} \right)}}{{{K_{B}}}}} \right \rceil \). The 2D-MCKP aims to achieve the maximum utility of all VEs, i.e.,$$ \max \sum\limits_{i = 1;{g_{m,i}} \in {G_{i}}}^{{N_{B}} + {N_{V}}} {f\left({{g_{m,i}}} \right)}, $$(29)subjected to$$ \begin{aligned} {\sum\limits_{i = 1}^{{N_{B}}{\mathrm{+ }}{N_{V}}} {{C_{1}}\left({{g_{m,i}}} \right)} \le {K_{B}},}\\ {\sum\limits_{i = 1}^{{N_{B}}{\mathrm{+ }}{N_{V}}} {{C_{2}}\left({{g_{m,i}}} \right)} \le {K_{V}}.} \end{aligned} $$(30)Then the problem of resource management is converted to 2D-MCKP.
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Solution of 2D-MCKP.The solution of 2D-MCKP is described in detail in Algorithm 1.
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Optimization of N V .Based on the above discussion, we can calculate the total utility of all VEs, which is determined by parameter N V in a certain optimization problem. With a relatively large N V , more SVs in poor conditions may be assisted by the CVs, and consequently increase the total utility. However, an overly large N V will limit the data rates of the V2V links, resulting in the reduction of the total utility. Furthermore, a too small N V is unable to make full use of the V2V resources, leading to waste of radio resources. In other words, the total utility is an unimodal function of N V . The optimal N V can be obtained through binary search.
4 Performance evaluation
4.1 Simulation configuration
Parameter | Value |
---|---|
Cell radius | 500 m |
VE number | 10 to 100 |
Traffic model | Microscopic model in [26] |
Max drive speed | 126 km/h (35 m/s) |
Acceleration | 2.6 m/s
2
|
Deceleration | −4.5 m/s
2
|
Length of time slot | 1 ms |
Link scheduling interval | 1 s |
LTE configuration (V2I link) | |
Carrier frequency | 2 GHz |
Bandwidth | 40 MHz |
Transmit power of eNB | 52 dBm for 40 MHz |
Configuration of V2V link | |
Carrier frequency | 5.9 GHz |
Bandwidth | 5 MHz |
VE transmit power | 20 dBm for 5 MHz |
Utility function for elastic service | |
a
| 50 |
b
| 1 |
R
max
| 6000 |
Path loss model | |
V2I link |
\(\begin {array}{l} P\left (d \right){\mathrm {= }}l{\mathrm {+ }}37.6{\log _{10}}\left ({\frac {d}{{1000}}} \right){\mathrm {,}} \\[-2pt] l{\mathrm {= }}128.1{\mathrm {- }}2GHz \\[-2pt] \end {array}\)
|
V2V link |
\(P\left (d \right){\mathrm {= \textit {P}}}\left ({{d_{0}}} \right){\mathrm {+ }}10\gamma {\log _{10}}\left ({\frac {d}{{{d_{0}}}}} \right){\mathrm {+ }}{X_{\sigma } }\)
|
4.2 Results and analysis
Number of VEs | Scheduling scheme | 5 % CDF | Average data rate | ||
---|---|---|---|---|---|
Data rate (kbps) | Gain (%) | Data rate (kbps) | Gain (%) | ||
20 | MSR scheme | 407 | 100 | 4386 | 100 |
BG-Based scheme | 1120 | 275.18 | 4350 | 99.18 | |
2D-MCKP-based scheme | 1748 | 429.48 | 4552 | 103.79 | |
30 | MSR scheme | 348 | 100 | 3014 | 100 |
BG-Based scheme | 996 | 286.21 | 2990 | 99.20 | |
2D-MCKP-based scheme | 1563 | 449.14 | 3110 | 103.19 | |
40 | MSR scheme | 296 | 100 | 2336 | 100 |
BG-Based scheme | 862 | 291.22 | 2320 | 99.32 | |
2D-MCKP-based scheme | 1266 | 427.70 | 2430 | 104.02 |