Virtual Platoon Coordination

• Virtual Platoon is a systems abstraction where coordination is achieved through additional layers like routing, timing, and communication rather than just close-gap control.
• It employs methodologies such as clustering, linear optimization, and dynamic programming to form heterogeneous groups that optimize route overlap, travel time, and cost-sharing.
• Recent advances integrate learning-based algorithms and software-defined control to enhance platoon stability, merging efficiency, and vehicular cloud resource pooling.

Searching arXiv for recent and directly relevant papers on virtual platoons and closely related platoon abstractions. Virtual platoon denotes a platoon whose coherence is created by an additional coordination layer—routing, timing, communication hierarchy, learning policy, or resource virtualization—rather than by short-gap longitudinal control alone. In the literature, the term is used explicitly for same-day urban delivery, where heterogeneous autonomous electric vehicles from different logistic service providers are grouped into constrained, preference-aware platoons over a road network (Sebe et al., 2019). Closely related constructions include Virtual Leaders for long truck convoys (Won, 2019), schedule-induced platoons at intersections (Timmerman et al., 2019), and software-defined platoon environments used for federated and deep reinforcement learning (Boin et al., 2022, Lei et al., 2022). This suggests that virtual platoon is best understood as a systems abstraction: a coordinated unit whose membership, spacing, route, and sometimes even computational role are mediated by information and optimization.

1. Terminology and conceptual scope

The baseline meaning of a platoon remains the standard automated-driving notion of vehicles traveling together in close proximity, “like a train,” under coordinated control (Yadavalli et al., 2022). In the urban-logistics formulation of PFaRA, a platoon is a set of vehicles that travel together as one coordinated unit, sharing the same speed and a common route for as long as possible, while possibly differing in destination, speed capabilities, battery or autonomy limits, delivery time windows, and cost preferences, and even belonging to different self-interested logistic service providers (Sebe et al., 2019). The platoon is therefore heterogeneous by construction, and viability depends on jointly satisfying speed, time, route-length, and cost constraints.

Other papers virtualize different parts of the platooning stack. In reservation-based intersection management, the platoon is the unit of negotiation: only the leader communicates with the intersection manager, and the scheduler reasons over platoons rather than individual vehicles (Bashiri et al., 2018). In long-truck DSRC platooning, leadership itself is virtualized by inserting intermediate Virtual Leaders that locally extend the original leader’s communication and control coverage (Won, 2019). In multi-platoon car-following, several platoons can behave as a larger communicatively coupled aggregate, so that each platoon leader serves as an interface node in a higher-level control network (Hui et al., 2024). In hybrid CAV platoons, the term is not used explicitly, but the architecture behaves as a virtual formation because different vehicles obey different spacing laws while remaining dynamically linked through sensing and V2V communication (Zheng et al., 2021).

A recurring misconception is that “virtual” means “merely simulated.” The literature does include purely software platoon environments, but many virtual-platoon constructions are intended for physical deployment. The term more often marks an abstraction layer—leader representation, schedule-based grouping, information-topology design, or cloud-style resource pooling—than a distinction between real and simulated vehicles.

2. Formation through routing, timing, and network optimization

In urban logistics, PFaRA formulates virtual platoon formation as a two-stage grouping-and-routing problem on a directed graph $G=(V,E)$ (Sebe et al., 2019). The first stage is speed clustering: vehicles in a platoon must travel at the same speed, so the algorithm repeatedly chooses the maximum of the minimum acceptable speeds and groups vehicles whose maximum speed is at least that threshold. The second stage is a linear optimisation step that finds the longest common route while enforcing per-vehicle route-length, travel-time, and cost budgets. Edge traffic density is used as the cost weight, and platooning incentives are implemented by splitting the edge price across participants,

$$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$

On the Berlin Tiergarten network, one provider’s total costs were reported as 198761 when vehicles drove alone, 121897.97 under a simple overlap baseline, and 102558.95 under PFaRA; with 25 vehicles the runtime was under two seconds, and for groups of 5–10 vehicles it was roughly in the 0.5–0.75 second range (Sebe et al., 2019). The resulting platoons are explicitly described as a group-specific best or Pareto-style compromise rather than a purely user-optimal outcome.

A second timing-based mechanism appears in large-scale multi-fleet trucking, where trucks with fixed routes independently schedule waiting times at hubs so that departures align on shared road segments (Bai et al., 2023). After discretizing both waiting decisions and arrival states, the authors show that dynamic programming solves the problem exactly without loss of optimality, because an optimal decision is either to wait zero or to wait exactly until a predicted partner departure. On a Swedish network with 5,000 trucks and 855 fleets, predictive multi-fleet platooning achieved around 15 times higher monetary profit than single-fleet platooning and increased CO$_2$ emission reductions from 0.4% to 5.5%; over 98% of decision instances took less than 10 seconds (Bai et al., 2023).

A third line of work makes formation explicitly traffic-state dependent. In Flow-Aware platoon organization, connected automated vehicles are allowed to change lanes to create longer platoons only when local flow is low and local speed is high (Woo et al., 2021). The paper shows that naïve platoon organization can reduce capacity because additional lane changes disrupt the surrounding stream; on a realistic Sacramento freeway corridor, the Flow-Aware strategy preserved discharge flow while still increasing platoon length, with flow-neutral platoon-length gains of roughly 8–20% over baseline depending on penetration (Woo et al., 2021).

3. Communication-mediated virtual platoons

L-Platooning virtualizes the leader function to overcome the limited DSRC range of long-body trailer convoys (Won, 2019). The motivating result is that “only less than 10 trailer trucks can form a platoon reliably due to the limited range,” and in a 30-truck convoy packet delivery rate begins dropping sharply around the 11th vehicle. Instead of multi-hop relaying, which can incur up to $100*n$ ms latency, the protocol elects one or more Virtual Leaders using the Virtual Leader Quality Index,

$$VLQI_i=\gamma \times CON_i^{Leader} + (1-\gamma)\times CON_i^{Follow},$$

with $CON_i^{Leader}=PRR_i^L$. The leader announces the chosen vehicle through selectedVLID, downstream followers switch through newVLID, and re-election uses oldVLID and newVLID. In Veins + SUMO + Plexe, a 30-truck convoy selected 3 virtual leaders, maintained the desired 20 m gap with mean error 6 cm and max error 22 cm, and completed join and leave maneuvers with average delays of 38 s and 35.7 s, respectively (Won, 2019).

Inter-platoon communication can also virtualize a larger aggregate out of several smaller platoons. In a multi-platoon car-following model, the no-connection linear stability condition for identical platoon size $N$ is

$a>\frac{2NV'(h)}{(N-1)^2+1},$

whereas two-way inter-platoon communication with backward sensitivity $p$ and delay $t_d$ yields

$$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$0

The paper concludes that stability increases with platoon size and connection availabilities and decreases exponentially with large delay (Hui et al., 2024). This makes virtual platooning sensitive to V2V latency: communication improves stability, but only while delays remain small.

The coupling between control and wireless delay is formalized directly in joint communication-control design for autonomous vehicular platoons (Zeng et al., 2018). There, plant stability and string stability impose upper bounds on allowable V2V delay, and wireless reliability is defined as the probability that end-to-end delay meets the control-layer budget. With controller gains $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$1 and $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$2, the paper reports maximum allowable delays of about 13.9 ms for plant stability and 0.5 s for string stability; joint control optimization improves reliability by up to about 15% (Zeng et al., 2018). A related control-theoretic variant replaces communication augmentation with wave absorption at the platoon ends: the wave-absorbing vehicular platoon controller suppresses reflections that would otherwise create oscillatory transients, reducing settling-time growth from quadratic to approximately linear in platoon length for large platoons (Martinec et al., 2013).

4. Learning-based and software-defined platoons

A distinct usage of virtual platoon appears in learning environments where the platoon is a controllable software object. RLPG addresses dynamic intra-platoon gap adaptation for highway on-ramp merging by casting the problem as an MDP solved with DDPG (Yadavalli et al., 2022). The RSU observes mainline density, ramp density, average speeds, platoon length, and each member’s gap, then outputs continuous gap actions in the range $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$3. This turns a compact platoon into a flexible virtual platoon that can temporarily widen merge opportunities. In SUMO with Simpla, Keras/TensorFlow, and TraCI, RLPG improved average speed by 31.8% for platoon size 20 and 66.3% for platoon size 30 relative to a base case with no gap-adjustment mechanism; computation delay was within 10 ms in over 90% of cases, with average delay 4.5 ms (Yadavalli et al., 2022).

AVDDPG uses a custom AV platooning environment to study federated reinforcement learning for platoon control (Boin et al., 2022). Each vehicle runs a DDPG actor-critic agent, and a federated server aggregates either gradients or weights across agents. The paper distinguishes Inter-FRL, where vehicles at the same position index in different platoons share parameters, from Intra-FRL, where followers learn directionally from vehicles ahead in the same platoon. Intra-FRL with weight aggregation (Intra-FRLWA) performed best. For platoon sizes of 3, 4, and 5 vehicles, reported average system rewards were $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$4, $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$5, and $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$6 for Intra-FRLWA, compared with $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$7, $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$8, and $$p(i,j)_v=\frac{d(i,j)}{NP_{(i,j)}}, \qquad NP_{(i,j)}=\sum_v x(i,j)_v.$$9 without FRL (Boin et al., 2022).

Deep reinforcement learning aided platoon control relying on V2X information addresses a further virtualization problem: which upstream information should be transmitted so that the state is “just sufficient” (Lei et al., 2022). The paper models platoon control as a finite-horizon SSDP under different information topologies—PF, PLF, TPF, and TPLF—and uses conditional KL divergence of transition models to quantify the value of candidate information. The theoretical result is that predecessor information can improve the optimal policy, follower information does not, and in practice the second-predecessor topology gives a strong performance-overhead compromise because its state augmentation is informative without incurring the largest dimensionality penalty (Lei et al., 2022).

5. Intersectional, aerial, robotic, and computational extensions

At intersections, virtual platooning is primarily a scheduling abstraction. PAIM treats platoons as the objects to be reserved through the conflict zone, with the leader of each platoon negotiating with a centralized intersection manager (Bashiri et al., 2018). The reservation-based policy permits simultaneous crossing of non-conflicting turning movements, and the scheduler can optimize either Platoon-based Variance Minimization or Platoon-based Delay Minimization. Against a fixed-time 4-phase traffic light, the reported averages were: delay 43.26 s for traffic light, 6.56 s for PVM, and 22.71 s for PDM; capacity 1388 veh/h, 1617 veh/h, and 1426 veh/h; and delay standard deviation 31.44 s, 6.37 s, and 30.48 s (Bashiri et al., 2018).

A more recent unsignalised intersection model forms platoons by combining a polling-system scheduler with a speed-profiling algorithm that generates closed-form trajectories in a control region upstream of the intersection (Joshi et al., 2023). Vehicles receive safe crossing times and then decelerate and accelerate so as to arrive exactly at those times and re-enter the intersection at $_2$0. The resulting formation is virtual in the sense that vehicles are centrally compressed into headway-separated convoys just before the conflict point, rather than maintaining a rigid highway platoon continuously (Joshi et al., 2023).

The concept also extends beyond road control. In “platoon-assisted vehicular cloud,” the platoon becomes a platoon cloud: a logically unified compute and storage pool formed by vehicles traveling together and coordinated through V2V networking, with MEC-assisted roadside units providing a second layer of infrastructure (Nasimi et al., 2020). Three scenarios are discussed: collaborative task offloading within a platoon, offloading from external vehicles to a platoon cloud, and MEC offloading to platoons. The third case is explicitly described as unsuitable for highly delay-sensitive applications such as virtual reality and augmented reality because the offloading path is multi-hop (Nasimi et al., 2020).

Aerial and robotic literature generalizes the same idea. Safe platooning of UAVs via reachability defines a platoon as a single-file formation on an air highway, restricts maneuvers through a hybrid-mode abstraction, and guarantees safety for one safety breach within a single altitude range, with multiple altitude ranges handling multiple simultaneous breaches (Chen et al., 2015). Spontaneous-ordering platoon control for multirobot path navigation adds a path parameter as a virtual coordinate, making neighbor relations and ordering occur in parameter space rather than pure Euclidean space; the paper proves global convergence to a spontaneous-ordering platoon and validates it in 2D USV experiments and 3D simulations (Hu et al., 2023).

6. Benefits, trade-offs, and open problems

Across these formulations, the main benefits are operational rather than merely geometric. Virtual platoons can improve aggregate logistics utility and cost sharing in heterogeneous urban delivery (Sebe et al., 2019), increase truck-platooning profit and CO$_2$1 reduction in fragmented multi-fleet networks (Bai et al., 2023), preserve traffic flow during highway merging by adaptive gap opening (Yadavalli et al., 2022), reduce delay and variance at intersections (Bashiri et al., 2018), and expose platoons as distributed computing resources in vehicular cloud architectures (Nasimi et al., 2020). The concept is therefore valuable precisely when the relevant coordination variable is not just distance, but route overlap, meeting time, communication coverage, merge opportunity, reservation slot, or resource availability.

The trade-offs are equally consistent. PFaRA sacrifices some individual optimality to obtain better group-level feasibility and cost sharing (Sebe et al., 2019). Flow-aware lane changes show that longer platoons do not automatically imply higher capacity, because lateral maneuvers can destroy the very throughput gains platooning seeks to create (Woo et al., 2021). Communication-enhanced platoons gain stability only while delays remain sufficiently small (Hui et al., 2024), and vehicular-cloud offloading can fail delay-sensitive requirements when multi-hop paths become long (Nasimi et al., 2020). The literature also records several unresolved modeling gaps: physical vehicle size and spatial occupancy are ignored in the current PFaRA model, which the authors suggest addressing with time-headway models (Sebe et al., 2019); bargaining or negotiation mechanisms among self-interested providers remain future work in cross-provider logistics (Sebe et al., 2019); and spontaneous-ordering multirobot platoons degrade under sufficiently large disturbances, indicating a bounded robustness margin (Hu et al., 2023).

A final misconception is that virtual platoon names a single architecture. The evidence points instead to a family of architectures that share one principle: the platoon is treated as an information-defined collective. Sometimes the collective is physically present but hierarchically controlled, as with Virtual Leaders; sometimes it is schedule-induced, as at intersections; sometimes it is learned in software before deployment; sometimes it is a cloud resource pool rather than a traffic primitive. The unifying feature is not a particular controller, but the elevation of platooning from local car-following to system-level coordination.