Effect of adaptive cruise control systems on traffic flow

The flow of traffic composed of vehicles that are equipped with adaptive cruise control (ACC) is studied using simulations. The ACC vehicles are modeled by a linear dynamical equation that has string stability. In platoons of all ACC vehicles, perturbations due to changes in the lead vehicle’s velocity do not cause jams. Simulations of merging flows near an onramp show that if the total incoming rate does not exceed the capacity of the single outgoing lane, free flow is maintained. With larger incoming flows, a state closely related to the synchronized flow phase found in manually driven vehicular traffic has been observed. This state, however, should not be considered congested because the flow is maximal for the density. Traffic composed of random sequences of ACC vehicles and manual vehicles has also been studied. At high speeds $\left(\sim 30\mathrm{m}∕\mathrm{s}\right)$ jamming occurs for concentrations of ACC vehicles of $10\%$ or less. At $20\%$ no jams are formed. The formation of jams is sensitive to the sequence of vehicles (ACC or manual). At lower speeds $\left(\sim 15\mathrm{m}∕\mathrm{s}\right)$, no critical concentration for complete jam suppression is found. Rather, the average velocity in the pseudojam region increases with increasing ACC concentration. Mixing $50\%$ ACC vehicles randomly with manually driven vehicles on the primary lane in onramp simulations shows only modestly reduced travel times and larger flow rates.

Figure 1

Velocity of ACC vehicles vs position at various times (200, 300, 400, $500\mathrm{s}$) responding to a perturbation due to the lead vehicle that was stopped for $2\mathrm{s}$ before accelerating to $20\mathrm{m}∕\mathrm{s}$.

Figure 2

A comparison of the velocity of ACC vehicles (upper trace) and manually driven vehicles (lower trace) at $500\mathrm{s}$ as a function of position. In response to the lower velocity $\left(12\mathrm{m}∕\mathrm{s}\right)$ of the lead vehicle, manual vehicles initially at the critical density ($0.04\text{vehicles}∕\mathrm{m}$ for velocity $15.34\mathrm{m}∕\mathrm{s}$) form a jam of nearly $2\text{km}$ length, whereas the ACC vehicles make a smooth transition. The manual vehicles are described by the modified optimal velocity model (ModOV).

Figure 3

Velocities of ACC vehicles as a function of time at the beginning of the merge region (“entry”) in both lanes and just beyond the downstream end of the merge region (“exit”). The length of the merge region is $500\mathrm{m}$. The total incoming flow is at capacity for the initial headway and velocity ($42\mathrm{m}$ and $35\mathrm{m}∕\mathrm{s}$, the maximum allowed velocity) with $80\%$ in lane 1 and the remaining $20\%$ in lane 2, the onramp. Parameter values: $\tau ={\tau }_1=0.5\mathrm{s}$ and $h_d=1.0\mathrm{s}$.

Figure 4

Flow rate at the entry and exit of the merge region. The lowest trace is the flow on the onramp. Parameters and initial conditions are the same as in Fig. 3.

Figure 5

Velocities of ACC vehicles as a function of time for larger incoming flow ($30\%$ of capacity) on the onramp with lane 1 flow at $80\%$ capacity.

Figure 6

Flow rates for individual lanes as a function of time for incoming flow that is $30\%$ of capacity on the onramp and at $80\%$ capacity in lane 1. Parameters are the same as in Fig. 5.

Figure 7

Velocities of ACC vehicles as a function of time for large incoming flow rates, approximately $80\%$ of capacity in each lane at the initial velocity of $29.77\mathrm{m}∕\mathrm{s}$. Here $h_d=1.1085\mathrm{s}$ and a speed limit of $29.77\mathrm{m}∕\mathrm{s}$ was imposed.

Figure 8

Flow rate $q$ in each lane vs density $\rho$ and ideal rate for ${\nu }_{max}=29.77\mathrm{m}∕\mathrm{s}$ and $h_d=1.1085\mathrm{s}$. The incoming flow rates in each lane are approximately $80\%$ of the capacity of a single lane.

Figure 9

Velocity vs position of vehicles at $t=500\mathrm{s}$. With no ACC vehicles and with $10\%$ ACC randomly mixed in with manual vehicles, a jam is formed due to encountering a slower moving lead vehicle (traveling at $25\mathrm{m}∕\mathrm{s}$). In this example, if $20\%$ of the vehicles were ACC, no jam was formed. Initially all vehicles in the platoon were traveling at $29.77\mathrm{m}∕\mathrm{s}$ with a headway of $40\mathrm{m}$. The parameters were $\tau ={\tau }_1=0.5\mathrm{s}$, $h_d=1.1085\mathrm{s}$, and $t_d=0.75\mathrm{s}$ (manual-driven vehicles only).

Figure 10

Velocity vs position at $t=500\mathrm{s}$ for two sequences of manual and ACC vehicles (approximately $13\%$ concentration) for the initial conditions and parameters of Fig. 9. The change of a single manual vehicle (the $188\text{th}$) to ACC suppressed the formation of a jam (square symbols).

Figure 11

Velocity vs position at $t=500\mathrm{s}$ for initial conditions $h=25\mathrm{m}$ with $\nu =15.34\mathrm{m}∕\mathrm{s}$ and 0, 10, and $50\%$ ACC vehicles encountering a lead vehicle traveling at $13\mathrm{m}∕\mathrm{s}$. The headway time for the ACC vehicles was $h_d=1.1735\mathrm{s}$.

Figure 12

Velocity vs position at $t=300\mathrm{s}$ for ACC vehicle concentration in lane 1 of $p=0.1$, 0.2, and $1∕3$. Parameters were the same as in Fig. 11.

Figure 13

Velocity vs time for vehicles in lane 1 passing the upstream end of the merge region. The squares correspond to all manual vehicles and the solid line is for $50\%$ of the vehicles in lane 1 randomly taken to be ACC. Vehicles in lane 2 (the onramp) were all manual. The headway time was $h_d=1.1085\mathrm{s}$. The delay for manually driven vehicles was $t_d=0.75\mathrm{s}$. The initial conditions were $h=40\mathrm{m}$ with $\nu =29.77\mathrm{m}∕\mathrm{s}$, $p_1=0.8$ and $p_2=0.2$.

Figure 14

Velocity vs position at $t=500\mathrm{s}$ for the initial conditions and parameters of Fig. 13.