Improving Unmanned Aerial Vehicle Traffic Flow at a Crossroads
by Splitting Demand into Parallel Streams
W. Bonnella,∗ , R.E. Wilsonba Department of Aerospace Engineering, University of Bristol, UK

wb17716@bristol.ac.uk
b Department of Engineering Mathematics, University of Bristol, UK

re.wilson@bristol.ac.uk∗ Corresponding author

Extended abstract submitted for presentation at the 11th Triennial Symposium onTransportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

January 12, 2022
Keywords: Unmanned aerial vehicles, autonomy, distributed control, emergent dynamics

1

INTRODUCTIONGoods delivery is one of a number of emerging applications for unmanned aerial vehicles (UAVs),see (Shakhatreh et al., 2019) for a review. While predictions of future demand are highly uncertain, some authors predict dramatic growth in the sector, e.g., Oosedo et al. (2021) forecast that32,887 deliveries a day in Sendai (Japan) will be targeted for UAV delivery. Current proposals
for unmanned traffic management (UTM) to facilitate such operations, e.g., (European Union
Aviation Safety Agency, 2020, Federal Aviation Administration, 2020), are based on a centralizedapproach where flight plans are deconflicted prior to take off. In our opinion, this centralized
approach is likely to become both computationally infeasible for such large numbers of UAVs,
and potentially vulnerable to brittle failures.
An alternative approach (Sedov & Polishchuk, 2018) is to adopt decentralized methods for
traffic management where UAVs instead autonomously resolve future conflicts as they arise byimplementing a sense and avoid (S&A) scheme. In (Bonnell & Wilson, 2021) we developed asimple pairwise S&A scheme using velocity obstacle (VO) methods (Fiorini & Shiller, 1998) inwhich UAVs modify their velocities to ensure a safe separation S is maintained. Inspired bycurrent rules of the air (ICAO, 2005), UAVs will, by default, turn to the right to avoid eachother. Furthermore, an optimal velocity model (Bando et al., 1995) is employed to modify each
UAV’s velocity such that in the absence of S&A maneuvers, it steers towards a given destination.
Inspired by UAV delivery applications, we also developed a simple scenario to test our decentralized S&A scheme where UAVs fly between fixed points, e.g., warehouses, and thus naturally
form streams of traffic in the airspace, which we model as a 2D plane to reflect current flightceilings (120 m in UK and EU) and the desire to maximize vertical separation with pedestrians
or property. An example is shown in Figure 1(a), where two uni-directional streams of trafficintersect at a point to form a sort of ‘crossroads’ at which UAVs will need to avoid each other. We
have shown how the performance of such a system deteriorates as the demand at the crossroads
increases and this paper will therefore explore a higher level design solution, inspired by (Maoet al., 2000), where a traffic stream is split in to two streams and the demand shared between
them, see Figure 1(b). Thus the total number of crossroads is increased, but the contention ateach is decreased.
TRISTAN XI Symposium

Original abstract submittal

W. Bonnell and R.E. Wilson
t5(a)

(b)
t2

y/m

t1y/m

2

λ1
t3

λ1

t4

λ2x/m

λ22

∆L

λ22x/mFigure 1 – (a) Two streams of autonomous UAV traffic, described by take off rates λ1 and λ2
from the origin ports, form a crossroads and use a S&A method to resolve future conflicts. (b)The vertical traffic stream (as viewed on the page) in (a) has been split in to two parallel streams,∆L apart, that equally share the demand of the single stream. Thus the number of crossings has
increased but the contention at each is reduced.

2EXPERIMENTAL SETUP

We employ a simple conceptual model of UAV traffic between fixed points in which we assume
that all UAVs are of the same multi-rotor type, with a common desired cruising speed vCS that
represents some regulatory speed limit. In order to simplify the complexity of the distributed
control we restrict the horizon of S&A maneuvers to those in which the time-to-conflict (i.e.,
the time remaining until two UAVs breach the safe separation distance based on their current
displacements and velocities) is less than the natural time scale τ := 2vCS /amax , where amax isthe maximum achievable acceleration. Note τ is the time it takes for a UAV travelling at thecruising speed to reverse its direction.
For this paper, the base case is the simplest possible crossroads setup, used to produce thesimulation snapshot in Figure 1(a), in which UAVs fly between four ‘ports’ at positions (±L/2, 0)
and (0, ±L/2) which form two sets of origin-destination pairs. UAVs are generated at the origin
ports at (−L/2, 0) and (0, −L/2), with initial velocities vCS (1, 0) and vCS (0, 1), according toindependent Poisson processes. There are thus two traffic streams, a ‘horizontal’ stream (asviewed on the page) and a ‘vertical’ stream (as viewed on the page) with Poisson rates λ1 andλ2 respectively. When a UAV is generated, it is added to a queue for take-off, which is served
deterministically to maintain a minimum spatial separation Stakeoff := 3S/2 that ensures UAVs
do not come into conflict in the early stages of their flight. UAVs are removed from the simulation
when they enter a ‘landing zone’ disk of radius RLZ ≪ L centred upon their destination. We
therefore measure the performance of a given setup by comparing the flight time between takeoffand entering the landing zone, to the time (L − RLZ )/vCS that each UAV would have taken in
the absence of interactions with any other UAVs.
In Figure 1(b) the vertical stream has been split in two. In our simulations, this is achievedby replacing one of the origin-destination pairs with new ports at positions (±∆L/2, ±L/2)
to produce two parallel streams of traffic distance ∆L apart. The demand at the new origin
ports is set to λ2 /2, to ensure that the total demand is the same as the base case. Later wewill also consider setups in which the horizontal stream of traffic is split instead. Due to theright-handedness of the default S&A maneuvers, the system performance is different in this case.
TRISTAN XI Symposium

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W. Bonnell and R.E. Wilson
200(b)

λ1 split
λ2 splitT̄1 (λ1 , λ2 )T̄1 (λ1 /2, λ2 )2T̄1 (λ1 , λ2 /2)
0.4

0.6

0.8

1

λ1 split
λ2 splitT̄2 (λ1 , λ2 )2T̄2 (λ1 /2, λ2 )T̄2 (λ1 , λ2 /2)00.20.40.6
0.8
1λ/λmaxλ/λmaxFigure 2 – Bootstrapped estimates (inter-quartile range) of mean time delay experienced by UAVsin the (a) horizontal and (b) vertical streams. We also show the base case delay (black lines) andthe predicted mean delay when the horizontal stream (red dashed line) or the vertical stream (bluedashed line) is split, which can be compared to the estimated mean delays of the same color. In(a) we see that there is a larger than expected reduction in the mean delay when the horizontal
stream is split but all split traffic scenarios improve upon the base case when demand is high.

30.2

20

T̄2 / sT̄1 / s(a)3RESULTS

For both the base case and split stream setups, we sweep through generation rates λ1 = λ2 , fromsmall values where UAV√ interactions are rare and delays are small, up to a theoretical maximum
rate λmax := vCS /(2 2S) that the crossroads could sustain, without interaction between theUAVs, if the traffic streams were evenly spaced and perfectly phased with each other. Eachsimulation is run until 1,000 UAVs have taken off from each origin port, corresponding typicallyto 4, 000–40, 000 s of simulated time, of which the first 200 s of departures are discarded assimulation ‘run-up’ (where delays are anomalously short). The flight times of the remaining UAVs
are bootstrapped to estimate a confidence interval for the mean delays T̄1 and T̄2 experienced byindividuals in the horizontal and vertical streams respectively.
From Figure 2, splitting the vertical stream provides a marked reduction in delays, while
splitting either stream provides some benefits to both streams. A key modelling idea is toexplain the total delays that result in terms of the delays incurred at each individual crossing. For
example, when the vertical stream is split, two crossroads result, which might each be modelledby the demand combination (λ1 , λ2 /2) from the base case setup. The two vertical streams
experience just one of these crossroads each, whereas the unsplit horizontal stream experiences
both crossroads, so its delay should be double the (λ1 , λ2 /2) base case. Figure 2 shows that thisapproach to modelling delay is accurate for almost all of the setups tested, with the exception of
the delay T̄1 incurred by the horizontal stream when it is split, which is less than that predicted,
when demand is sufficiently high. In fact, close inspection of the data (not shown here) reveals
that the two ‘branches’ of the horizontal stream incur quite different delays.
The greater than expected reduction in T̄1 when the horizontal stream is split can be explainedby the default S&A rule where UAVs turn to the right. UAVs are thus displaced from theirlinear flight path and are dispersed laterally, see Figure3(a), and since the UAVs’ destinations
are distant from the first crossing, the traffic stream stays dispersed which in turn lowers theeffective contention at the second crossing. Note that the dispersion effect is still present whenthe vertical stream is split, see Figure 3(b), but its impact is small compared with the splitting
effect.

4DISCUSSION

In this paper we have shown that splitting UAV traffic into parallel streams can significantly
reduce the delays experienced at ‘crossroads’ where streams cross. Furthermore, analysis ofresulting UAV trajectories shows a variety of non-local effects where one crossroads is affected
TRISTAN XI Symposium

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W. Bonnell and R.E. Wilson(a)4

λ = λmax , λ1 is split(b)

λ = λmax , λ2 is split

λ1 /2y/my/m

λ1

λ1 /2

λ2

λ2 /2x/mx/m

λ2 /2Figure 3 – Time aggregated density plots for traffic in the (a) vertical stream when the horizontal
stream is split and (b) horizontal stream when the vertical stream is split. In both scenarios thetraffic in the un-plit stream is dispersed laterally so that the contention at the second crossroads
it encounters is reduced.
by another, in particular, each crossroads has the effect of spreading traffic laterally which candeliver further benefits at downstream crossroads.

5ACKNOWLEDGMENTS

This work is funded and delivered in partnership between the Thales Group and the Universityof Bristol, and with the support of the UK Engineering and Physical Sciences Research Council
Grant Award EP/R004757/1 entitled ‘Thales-Bristol Partnership in Hybrid Autonomous Systems
Engineering (T-B PHASE)’.

References
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Federal Aviation Administration. 2020. Unmanned Aircraft System (UAS) Traffic Management (UTM):
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International Journal of Robotics Research, 17.
ICAO. 2005. Annex 2 - Rules of the Air - Tenth Edition.
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Delivery Models in 2030 Japan. Journal of Robotics and Mechatronics, 33.
Sedov, L., & Polishchuk, V. 2018. Centralized and Distributed UTM in Layered Airspace. In: 8thInternational Conference on Research in Air Transportation.
Shakhatreh, H., et al. 2019. Unmanned Aerial Vehicles (UAVs): A Survey on Civil Applications and Key
Research Challenges. IEEE Access, 7.

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