Fig 1.
(A) The road system is composed of two single-lane roads of length L, crossing at an intersection. The square intersection area of side s is shaded. Vehicles, each of length ℓ, enter the system at the beginning of the North road if they belong to the N flow, or at the beginning of the East road if they belong to the E flow. To model a worst-case situation, vehicles approaching the intersection from different flows are assumed to have a conflicting trajectory: e.g., going straight. A vehicle’s intersection access time is defined as the time at which the head of the vehicle enters the intersection area. (B) Safety requirements dictate that two vehicles consecutively accessing the intersection and belonging to the same flow must be separated by tailgate distance dtail. (C) If the two consecutive vehicles belong to different flows, they must be separated by vehicle stopping distance dstop, which is larger than dtail for practical values of the system parameters. The tailgate and vehicle stopping distance are formally defined in S1 Supporting Information.
Fig 2.
Illustration of the BATCH formation strategy.
The value of the time interval used to reshuffle vehicle requests equals the first vehicle delay Δ = (ti − αti). Vehicles 2, 3 and 4 are reshuffled. Vehicles in the same flow are represented with circles of same color. Since Vehicle 1 and Vehicle 3 belong to the same flow, Vehicle 3 is given access to the intersection before Vehicle 2. The process is then repeated using Vehicle 5 as reference for Δ. To ensure design goal ii), BATCH imposes also an upper bound N on the total number of vehicles in a batch. When the number of requests in a batch is 1, BATCH is equivalent to FAIR.
Fig 3.
Slot-based intersection control doubles capacity.
The capacity of three control strategies is compared: FAIR, the slot-based strategy with first-come-first-serve service policy; BATCH, the slot-based strategy with adaptive vehicle platooning; and FIXED, the traffic light strategy with fixed cycle duration. The service rate of BATCH is twice that of FIXED, and converges to the optimal capacity as the value N of the maximal number of platooned vehicles increases. Optimal capacity is estimated assuming a single road without intersections, as dictated only by safety considerations. The service rate of FAIR is only marginally larger than that of FIXED.
Table 1.
Average delays vary dramatically with the control strategy.
Expectation and variance of delay for the different strategies and for varying vehicle arrival rates: FIXED, FAIR, and BATCH. FIXED statistics are computed according to [23]. Slot based control strategies dramatically reduce average delay with respect to traffic light control. Delay variance is reduced to a greater extent, indicating that slot based control strategies can lead to more predictable travel times.