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Capacity of Cooperative Vehicular Networks with Infrastructure Support: Multi-user Case
Jieqiong Chen, Guoqiang Mao, Changle Li, Weifa Liang, Degan Zhang
TL;DR
The paper addresses capacity in infrastructure-supported vehicular networks under interacting V2I, V2V, mobility, density, and cooperation factors. It proposes a cooperative dissemination strategy for VoIs and helpers, analyzes it with a finite-density analytical framework, and finds stronger capacity gains when few vehicles have download requests.
Problem
Existing approaches cannot satisfy diverse vehicular communication requirements, while prior capacity analyses often assume sufficiently large vehicle populations or densities.
Method
The paper combines V2I, V2V, vehicle mobility, and cooperation among vehicles and infrastructure, then derives a closed-form capacity expression for finite-density data dissemination.
Results
The cooperative strategy significantly improves capacity over the non-cooperative counterpart, especially when the proportion of VoIs is small.
Takeaways & Limitations
The results provide guidance for infrastructure spacing and cooperative communication design to maximize vehicular-network capacity.
Abstract
from arXiv · showhide
Capacity of vehicular networks with infrastructure support is both an interesting and challenging problem as the capacity is determined by the inter-play of multiple factors including vehicle-to-infrastructure (V2I) communications, vehicle-to-vehicle (V2V) communications, density and mobility of vehicles, and cooperation among vehicles and infrastructure. In this paper, we consider a typical delay-tolerant application scenario with a subset of vehicles, termed Vehicles of Interest (VoIs), having download requests. Each VoI downloads a distinct large-size file from the Internet and other vehicles without download requests assist the delivery of the files to the VoIs. A cooperative communication strategy is proposed that explores the combined use of V2I communications, V2V communications, mobility of vehicles and cooperation among vehicles and infrastructure to improve the capacity of vehicular networks. An analytical framework is developed to model the data dissemination process using this strategy, and a closed form expression of the achievable capacity is obtained, which reveals the relationship between the capacity and its major performance-impacting parameters such as inter-infrastructure distance, radio ranges of infrastructure and vehicles, sensing range of vehicles, transmission rates of V2I and V2V communications, vehicular density and proportion of VoIs. Numerical result shows that the proposed cooperative communication strategy significantly boosts the capacity of vehicular networks, especially when the proportion of VoIs is low. Our results provide guidance on the optimum deployment of vehicular network infrastructure and the design of cooperative communication strategy to maximize the capacity.
I. INTRODUCTION
The paper studies capacity in infrastructure-supported vehicular networks where V2I, V2V, vehicle mobility, density, and cooperation interact. It proposes a cooperative dissemination strategy and analytical framework for finite-density networks, showing improved capacity and guidance for infrastructure deployment.
- Motivation: Existing V2I-only and V2V-only approaches cannot meet all vehicular communication requirements because availability, reliability, density, and deployment constraints vary.V2V can become unreliable with many hops or sparse traffic, while V2I availability may be limited by deployment cost, especially in rural or early-deployment settings.
- Research gap: Prior capacity analyses largely assume sufficiently large vehicle populations or densities and therefore use asymptotic scaling laws.The paper targets capacity analysis with finite vehicular density.
- Approach: The proposed strategy combines V2I, V2V, vehicle mobility, and cooperation among vehicles and infrastructure for delay-tolerant delivery to Vehicles of Interest.VoIs request distinct large files, while helpers without download requests assist delivery.
- Approach: The paper develops an analytical framework and closed-form capacity expression linking performance to infrastructure spacing, communication ranges, sensing range, rates, density, and VoI proportion.The framework models data dissemination under the cooperative strategy.
- Results: Simulations and numerical analysis show that cooperation improves capacity over the non-cooperative counterpart, especially when the proportion of VoIs is small.The results also provide insight into infrastructure interval distance and cooperative-strategy design.
- System model: The system model uses a bidirectional highway with regularly spaced infrastructure and directional vehicle densities and speeds, with traffic represented by homogeneous Poisson processes.Infrastructure points are separated by equal distance d, and vehicles in each direction have densities ρ1 and ρ2 and speeds v1 and v2.
B. Wireless Communication Model
The model combines one-hop V2I and V2V communication under simplified channel and access assumptions. Its cooperative strategy divides roadway operation into cycles and combines infrastructure delivery, helper forwarding, vehicle mobility, and cooperation to define achievable VoI capacity.
- Wireless communication model: The model assumes single-antenna vehicles, unicast transmission, and at most one simultaneous recipient per infrastructure point or vehicle.Single antennas prevent vehicles from transmitting and receiving simultaneously.
- Wireless communication model: Vehicles use separate V2I and V2V channels, with fixed radio ranges and no mutual interference between the two communication modes.V2I and V2V links use distinct channels; V2V access follows CSMA with sensing range R_c.
- Cooperative communication strategy: Infrastructure prioritizes VoIs, while helpers receive infrastructure data only when no VoI is within coverage and forward it to VoIs over one-hop V2V links.Transmitters may select receivers in either direction within transmission range.
- Cooperative communication strategy: Requested files are split across infrastructure points and helpers, allowing different nodes to store pieces needed by different VoIs.A central server is assumed to know the dissemination process and ensure helpers receive data required by encountered VoIs.
- Capacity analysis: The capacity η measures the long-term data received by all VoIs, including data obtained directly from infrastructure and indirectly from helpers.The analysis separates the V2I and V2V contributions before combining them.
- Capacity analysis: A cycle consists of one infrastructure-covered V2I Area and the adjacent uncovered V2V Area, and its capacity combines direct and helper-delivered data.Renewal theory makes the long-term capacity from each cycle identical, enabling capacity calculation over longer highway segments.
A. Capacity achieved by VoIs from V2I communications
The V2I analysis estimates how often at least one VoI occupies an infrastructure point’s coverage and converts that occupancy into long-term direct-delivery capacity. Under the Poisson vehicle model, the occupancy probability is 1 − e^(−pρ2rI).
- V2I capacity analysis: q1(i) equals 1 when at least one VoI is within infrastructure point I1’s coverage during slot i, and 0 otherwise.Time is divided into sufficiently small slots so vehicles can be treated as stationary within each slot.
- V2I capacity analysis: 1 − e^(−pρ2rI) is the expected fraction of time that at least one VoI lies within I1’s coverage.This follows from ergodicity, stationarity, and the Poisson distribution of vehicles.
- V2I capacity analysis: The one-cycle V2I capacity is obtained by combining the expected coverage occupancy with the preceding direct-transmission expression.The resulting expression gives the long-term capacity achieved by VoIs through V2I communications.
B. Capacity achieved by VoIs from V2V communications
The V2V capacity analysis models helper-to-VoI delivery as constrained by both infrastructure-fed data and simultaneous V2V transmissions. It derives an optimal scheduling rule and uses transmitter-spacing distributions to obtain the capacity expression.
- V2V delivery is limited by both the data helpers receive through V2I and the data helpers can transmit to VoIs through V2V.The two rates act as the incoming rate and processing speed of an equivalent queue.
- Theorem 1 gives the capacity achieved by VoIs through V2V communications during one cycle.
- The helper V2I communication probability is determined by the condition that infrastructure coverage contains no VoI but at least one helper.This probability is calculated using the Poisson distributions of VoIs and helpers.
- The optimal schedule selects active helper-VoI pairs from left to right, spacing successive transmitters by at least Rc and choosing distinct VoI receivers.The process starts with the first eligible helper and repeatedly selects the nearest feasible helper until the V2V area ends.
- Under the optimal schedule, the first transmitter spacing differs from later spacings, while later transmitter distances are identically and independently distributed.Renewal theory is then used to calculate the expected number of simultaneously active helper-VoI pairs.
- The transmitter-distance density for later active pairs is characterized under vehicular densities ρ1 and ρ2, VoI proportion p, radio range r0, and sensing range Rc.
- The resulting V2V capacity expression is given in equation (20).
C. Achievable capacity
The achievable-capacity analysis combines the capacity contributions from V2I and V2V communications over one infrastructure cycle, then extends the result to a long highway segment.
- The total capacity is obtained by combining the V2I and V2V capacities achieved during one cycle.The cycle-based result is then used to calculate capacity over a highway segment of length L.
1) Total Achievable Capacity:
The total capacity combines direct infrastructure delivery with cooperative helper delivery and has several notable boundary behaviors. It is independent of vehicle velocity under the stated stationary spatial-distribution conditions.
- The total highway capacity combines V2I and V2V contributions from each cycle.The resulting expression depends on the cycle geometry and the communication parameters represented in the capacity formula.
- Achievable capacity is independent of vehicle velocity when vehicle arrivals follow a Poisson process and the spatial distribution remains stationary and ergodic.The analysis therefore also applies to time-varying speed models that preserve a time-invariant spatial distribution.
- When p = 1, the cycle capacity equals the direct V2I capacity wI(1 −e^−ρ2rI).In this case, every vehicle has a download request and cooperative V2V communication provides no helper population.
- When p exceeds a certain threshold, cooperative V2V communication provides little capacity gain because all new data originates outside the vehicular network.V2V mainly extends effective coverage and balances data when infrastructure coverage lacks a VoI.
2) Capacity achieved by eastbound and westbound VoIs :
The paper separates capacity by travel direction and finds that each direction’s capacity scales with the corresponding directional vehicle density.
- Eastbound and westbound VoI capacities are proportional to the densities of eastbound and westbound vehicles, respectively.
- Higher density in a direction increases the opportunity for VoIs traveling that way to communicate with infrastructure and receive indirect V2V delivery.VoIs traveling in the same direction are statistically indistinguishable in the analysis.
V. SIMULATION AND DISCUSSION
Simulations validate the analytical framework and show how cooperation, VoI proportion, infrastructure spacing, and multi-hop choices shape vehicular-network capacity.
- Validation: Analytical and simulation results match closely for active helper-VoI pairs and directional capacity under the tested settings.The match is exact for Rc ≥ 2r0 and very close for directional capacity.
- Effect of VoI proportion: Capacity rises sharply with VoI proportion below pth=0.08, then approaches ηmax = wI(1 −e−ρ2rI) with little further increase.Below the threshold, capacity is limited by V2V retrieval; above it, VoIs retrieve almost all infrastructure-delivered data.
- Cooperation: Cooperative communication improves capacity even at small p, while its benefit decreases as more vehicles become VoIs and fewer helpers remain.Without cooperation, ηmax is reached only when p = 1 under the compared setting.
- Multi-hop communication: Multi-hop communication has little capacity impact; its marginal gain occurs through multi-hop V2I communication only when p < pth=0.006.Multi-hop V2V communication balances information among helpers but does not increase the network’s net available data.
- Infrastructure deployment: Increasing inter-infrastructure distance can improve one-cycle capacity at low density but decreases total achievable capacity.At high density, one-cycle capacities converge because most VoIs receive data directly from infrastructure.
- Infrastructure deployment: Infrastructure spacing should account for vehicular density; in high-density areas, cooperation can reduce the required number of infrastructure points.The deployment implication follows from the relationship between spacing, density, and total capacity.
VI. CONCLUSIONS
The paper analyzes finite-density vehicular-network capacity using cooperative V2I and V2V dissemination with mobility and infrastructure cooperation. It derives a closed-form capacity expression and finds larger gains when few vehicles have download requests.
- Conclusion: The study analyzes vehicular-network capacity under a cooperative strategy combining V2I, V2V, vehicle mobility, and vehicle-infrastructure cooperation.The setting assumes finite traffic density.
- Conclusion: A closed-form expression of the achievable capacity is obtained.The expression supports analysis of the cooperative dissemination strategy.
- Conclusion: Capacity improvement is more pronounced when the proportion of vehicles with download requests is low.The results also provide insight into infrastructure deployment and cooperative-strategy design.
APPENDIX A: PROOF OF THEOREM 2
The proof establishes that χopt maximizes simultaneous active helper-VoI pairs by recursively comparing transmitter locations under the proposed and an arbitrary scheduling scheme.
- Setup: The proof compares transmitter locations Xk under χopt with locations Yk under an arbitrary scheme, using Fig. 9 to illustrate their ordering.The target invariant is Xk ≤ Yk for every k.
- Induction: The base case holds because χopt selects the leftmost eligible helper as the first transmitter, giving X1 ≤ Y1.Eligibility requires at least one VoI within the helper’s coverage.
- Induction: For the induction step, both cases Xn+1 ≤ Yn and Xn+1 > Yn imply Xn+1 ≤ Yn+1.The argument handles whether the next optimal transmitter lies before or after the arbitrary scheme’s current transmitter.
- Conclusion: Therefore, χopt places every indexed transmitter no farther right than the corresponding arbitrary-scheme transmitter.The recursive ordering establishes the schedule comparison for all k.
APPENDIX B: PROOF OF THEOREM 3
The proof derives the distribution of consecutive-transmitter distances by modeling helper spacings, the selected helper index, and truncated coverage intervals under χopt.
- Distance model: Consecutive helper spacings are modeled as i.i.d. exponential variables because helpers follow a Poisson process with density (1−p)ρ.The proof uses these spacings to construct transmitter-distance distributions.
- Selected helper: The next transmitter is the mk-th helper after the current transmitter, where mk depends on VoI coverage conditions but is independent of helper spacings.The proof first derives Pr(mk = m) before calculating Lk.
- Selected helper: When m=1, the first eligible helper is selected; the eligibility condition differs according to whether Rc ≥2r0 or Rc <2r0.For Rc < 2r0, the current pair’s VoI may lie within the next helper’s coverage.
- Selection probability: For m ≥2, earlier helpers lack a distinct covered VoI while the m-th helper has at least one, yielding the selection probability structure.The coverage calculation uses truncated gaps hk,i = min{lk,i, 2r0}.
- Selection probability: Moment-generating functions of the truncated gaps and their sums are used to calculate Pr(mk = m).The proof applies the total probability theorem and the MGF definitions for Hk,m and hk,m−1.
- Distance distribution: Combining the selection probabilities with helper-spacing distributions yields the cdf and pdf of Lk.The resulting cdf is denoted FLk(x), and the derived pdf completes the theorem proof.
APPENDIX C: PROOF OF THEOREM 5
The proof decomposes eastbound and westbound capacity into V2V and V2I contributions, then shows each direction’s received data and resulting capacity scale with its traffic density.
- The capacity calculation separately analyzes V2V and V2I communications within one cycle area for eastbound and westbound VoIs.
- V2V communications: Under χopt, the travel directions of VoIs and helpers across randomly selected pairs are independent, enabling directional probabilities PVe and PVw.These probabilities satisfy PVe + PVw = 1.
- V2V communications: The scheduling geometry determines whether the helper selects the left-most eastbound or westbound VoI according to their relative locations Xe and Xw.The receiver travels east when the eastbound candidate satisfies Xe ≤ Xw.
- The V2V data received by each direction, and hence directional V2V capacity, is proportional to that direction’s traffic density.
- V2I communications: For V2I communication, the receiver-direction probabilities are PIe = ρ1/(ρ1+ρ2) and PIw = ρ2/(ρ1+ρ2), with expected directional data defined over one cycle area.The proof applies the same directional-probability method used for V2V communication.