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[orcid=0000-0002-1912-1115]

[1]

1] organization=Faculty of Mathematics and Computer Science, Jagiellonian
University, addressline=Profesora Stanisława Łojasiewicza 6, city=Krakow,
postcode=30-348, country=Poland 2] organization=Doctoral School of Exact and
Natural Sciences, Jagiellonian University, addressline=Profesora Stanisława
Łojasiewicza 11, city=Krakow, postcode=30-348, country=Poland

[orcid=0000-0002-9767-8883] URL]https://rafalkucharskipk.github.io/

[cor1]Corresponding author

# Spatiotemporal variability of ride-pooling potential – half a year New York
City experiment

Olha Shulika<EMAIL_ADDRESS>[  Michal Bujak
<EMAIL_ADDRESS>[  Farnoud Ghasemi
<EMAIL_ADDRESS>Rafal Kucharski<EMAIL_ADDRESS>
###### Abstract

Ride-pooling systems, despite being an appealing urban mobility mode, still
struggle to gain momentum. While we know the significance of critical mass in
reaching system sustainability, less is known about the spatiotemporal
patterns of system performance. Here, we use 1.5 million NYC taxi trips
(sampled over a six-month period) and experiment to understand how well they
could be served with pooled services. We use a utility-driven ride-pooling
algorithm and observe the pooling potential with six performance indicators:
mileage reductions, travellers’ utility gains, share of pooled rides,
occupancy, detours, and potential fleet reduction. We report distributions and
temporal profiles of about 35 thousand experiments covering weekdays,
weekends, evenings, mornings, and nights. We report complex spatial patterns,
with gains concentrated in the core of the network and costs concentrated on
the peripheries. The greatest potential shifts from the North in the morning
to the Central and South in the afternoon. Offering pooled rides at the fare
$32\%$ lower than private ride-hailing seems to be sufficient to attract
pooling yet dynamically adjusting it to the demand level and spatial pattern
may be efficient. The patterns observed in NYC were replicated on smaller
datasets in Chicago and Washington, DC, the occupancy grows with the demand
with similar trends.

###### keywords:

ride-pooling mobility as a service ride-splitting spatiotemporal demand
patterns ride-sharing

##  1 Introduction

Ride-pooling (also called shared ride-hailing or ride-splitting) is a service
in which passengers with similar origins or destinations are pooled to the
same vehicle to travel together. The total mileage is then reduced and the
travel costs can be now shared by the co-travellers (Santi et al., 2014;
Alonso-Mora et al., 2017). Ride-pooling hardly reached the critical mass in
the pre-pandemic period and almost completely stopped during the pandemic
(Foljanty, 2022), nonetheless it remains a promising emerging mobility mode
with the significant potential to contribute towards sustainability
transitions. Effective pooling can complement public transport (Cats et al.,
2022), and when demand levels exceed the so-called critical mass, this becomes
efficient for all parties: for travellers who pay less, for drivers who can
earn more, for the service provider (mobility platform) that can reduce the
total mileage and better utilise its fleet, and for the city that can reduce
traffic congestion and externalities (Shaheen et al., 2016).

High demand levels are substantial in reaching the full potential of pooling
services, but can be insufficient. The actual performance depends also on
operating area, supply concentration, topology etc. (Fielbaum et al., 2023;
Liu et al., 2023; Manik and Molkenthin, 2020). As a result, identifying the
efficiency and attractiveness of ride-pooling for various parties involved is
more nuanced and calls for a detailed analysis. While the general trends of
shareability have been widely reported, so far, the detailed spatiotemporal
analysis was missing. To illustrate the significance of more detailed
analysis, let’s analyse the following glimpse of our results in blueFig.
1black left. The average occupancy non-linearly increases with the demand
level in NYC and the logarithmic elbow curve well explains the general trend,
yet the variability among individual experiments (dots) remains huge, e.g. the
occupancy for demand levels of 300 trips per hour vary from 1.2 to 1.6.

In this study we aim to explain this residual variability and explore the
potential of ride-pooling on the big dataset. To provide more thorough
understanding of ride-pooling potential in dense urban areas, we synthesize
the results of 9 000 half-hour ride-pooling experiments in which the sample of
1.5 million actual trip requests from New York are pooled into attractive
shared rides (blueFig. 1black right). We provide detailed results that go
beyond the classical notion of a critical mass. We observe how shareability
changes for various days of the week and hours of the day, and report the
temporal and spatial distributions of six various ride-pooling performance
indicators. The results can help understand the actual potential of ride-
pooling and its limitations. The results can help policymakers and
transportation network companies develop policies for the development of
sustainable, attractive and commercially successful ride-pooling services.

Figure 1: The problem statement (left) and an overview of the methodology
(right) applied in this study to understand the potential of ride-pooling.

###  1.1 Literature review

Ride-pooling is the most effective with high demand (Santi et al., 2014;
Alonso-Mora et al., 2017; Tachet et al., 2017). While in public transport, the
demand density is a key to reach efficiency, it also varies greatly with
spatial and temporal distributions (Fielbaum et al., 2016). Here, we want to
see if this is also true for ride-pooling services.

Santi et al. (2014) propose a quantification system to measure the spatial and
temporal compatibility of individual trips based on a shareability network of
New York City with a high population and taxi traffic density in a relatively
geographically small area. Tachet et al. (2017) generalise it and observe
similar trends also for: San Francisco, Singapore, and Vienna; further
extended by Ke et al. (2021) to Chengdu and Haikou. Notably, the demand for
pooled services is elastic and correlates, e.g. with: the availability of
alternative public transport (Cats et al., 2022), sociodemographic
characteristics of population (Abouelela et al., 2022; Compostella et al., ),
urban structure of the city (Li et al., 2019), etc. Zwick and Axhausen (2022)
analyse the big pre-pandemic demand dataset of the ride-pooling service MOIA
in Hamburg and Hanover from May 2019 to February 2020 and propose regression
models predicting ride-pooling demand capturing the impact of the density of
workplaces, gastronomy and culture. Hou et al. (2020) analyse the impact of
trip, time, and location on the willingness-to-share for Chicago based on TNC
data set (for Via, UberPool and LyftShare services). Using multivariate linear
regression, the authors reveal the significance of income level and airport
trips on travellers’ willingness to share a trip. Du et al. (2022) analyse
Chicago ride-hailing data from March 2019 and identify how the spatial
patterns of socioeconomic and built environment influence ridesplitting
performance during morning and evening peak hours on weekdays and weekends.
The authors find an increased demand for pooled trips during weekday morning
and evening peak hours, which differs from the findings of an earlier study by
Li et al. (2019), who study the spatial and temporal characteristics of solo
and pooled rides based on DiDi Chuxing data from November 2016. Li et al.
(2019) analyse the correlation of pooled rides distribution with the built
environment and temporal parameters, they find that ride-pooling demand is
higher during non-work hours, for longer distances in the direction from the
central part of the city. Compostella et al.  found, based on 5,136 trips
conducted by 1,991 travellers in California between November 2018 and November
2019, that individuals’ mobility profile is the primary determinant in
choosing a pooled trip along Transportation Network Companies (TNC) services
usage and population density. Liu et al. (2023); Fielbaum et al. (2023); Lehe
et al. (2021) on the NYC data set analyse ride-pooling scale effects, cost-
saving opportunities and cost-increasing factors.

Such variability of the demand calls for the detailed analysis of ride-pooling
efficiency, we argue and demonstrate that for the same demand levels in the
same area the ride-pooling efficiency can vary dramatically (blueFig. 1black
left). We present an overview of previous approaches to ride-pooling potential
evaluations in Table 1. Since large-scale ride-pooling has barely been seen in
practise, most of studies rely on simulations. In the seminal work of Santi et
al. (2014), the pooling potential is measured with the two indicators: number
of trips that can be successfully shared (shareability) and travel time
savings. While this shows general patterns, the perspective of travellers and
their utility, as well as service operator benefits, is missing. Other
measures include occupancy (Alonso-Mora et al., 2017; Simonetto et al., 2019).
Young et al. (2020) measure the shareability potential for big dataset of
ride-hailing trips in Toronto with: number of successfully matched trips
(matching propensity) and travel detour time. With the results showing that,
first, high-demand areas have a greater likelihood of successful ride-sharing
and, secondly, longer wait times before the driver arrives can actually
increase the chances of matching shared trips. Finally, shared trips
experience only a minor variance in travel detour time. Using the total cost
minimization approach that considers the interests of both users and
operators, Militão and Tirachini (2021) explore the potential for ride-pooling
under different scenarios for vehicle automation. Du et al. (2022) perform
temporal-spatial analysis for Chicago and report the share of pooled trips.
Kucharski and Cats (2020) follows utility-based demand-centric approach and
measure the shareability potential using occupancy (the ratio of total
passenger-hours travelled to vehicle -hours travelled with passengers),
vehicle-hour reduction, passenger hours increase and travelers’ utility gains
for Amsterdam experiments with up to 4 000 travellers per hour. Here, we use
this set of indicators as the one providing the complete picture, and apply it
for the big dataset. Soza-Parra et al. (2022) follow a similar direction and
use the Exact Matching of Attractive Shared Rides (_ExMAS_) algorithm to
explore the impact of spatial travel demand patterns on ride pooling
performance for different number of attraction centres, density of
destinations around each centre, and trip length distribution, using Amsterdam
as an example with a fixed level of synthetic demand.

Table 1: Review of previous ride-pooling potential evaluation studies. Work | KPIs | Temporal patterns | Spatial patterns | Dataset
---|---|---|---|---
Santi et al. (2014) | Number of shared trips, Travel time savings | + | - | 150 million trips: NYC (Manhattan), 6 months of 2011
Tachet et al. (2017) | Number of shared trips | + | - | Over 156 million taxi trips: New York City (in 2011), San Francisco (in 2009), Singapore, and Vienna
Alonso-Mora et al. (2017) | Travel delay, Occupancy | + | - | About 3 million trips: NYC (Manhattan), 05.05.2013-11.05.2013
Simonetto et al. (2019) | Travel delay, Occupancy | + | + | About 3 million trips: NYC (Manhattan), 05.05.2013-11.05.2013
Li et al. (2019) | Travel delay, Travel detour | + | - | 6.1 million ridesourcing orders, Chengdu (China), 01.11.2016-30.11.2016
Young et al. (2020) | Matching propensity (the number of successfully matched trips), Travel detour | + | + | 12 million records of ride-hailing trips: Toronto (Canada), 07.09.2016-31.03.2017
Militão and Tirachini (2021) | Vehicle size, Fleet size | + | - | 8.7 million trips for one day in 2011: Munich (Germany)
Kucharski and Cats (2020) | Total vehicle hours, Total passenger hours, Travellers’ utility gains, Occupancy | + | - | 241 000 trips per working day in Amsterdam (Netherlands)
Soza-Parra et al. (2022) | Total vehicle hours, Total passenger cost, Share of pooled trips, Occupancy | + | + | 1 000 trip requests are generated during a one-hour period, Amsterdam (Netherlands)
Our research | Total vehicle hours, Total passenger hours, Share of pooling, Travellers utility gains, Occupancy, Fleet size | + | + | 1.5 million trips, New York City (Manhattan), 6 months of 2016

###  1.2 Methodological approach and contributions

To reveal the actual potential of ride-pooling, we need a detailed
understanding of its performance. Previous studies either relied on synthetic
demand data (Soza-Parra et al., 2022), short time periods (Simonetto et al.,
2019), reported only few measures (Du et al., 2022; Tachet et al., 2017;
Militão and Tirachini, 2021), adopted the service-operator’s perspective
(Alonso-Mora et al., 2017), or their results were just an illustration of the
algorithm and not analysed in detail (Kucharski and Cats, 2020).

Here, we explicitly focus on the analysis of the spatial and temporal patterns
of the potential ride-pooling service performance. We use the big dataset of
ride-hailing trips and apply the utility driven ride-pooling algorithm to
report a set of six indicators measuring the potential of ride-pooling
potential: for different parties involved (travellers, drivers, operators and
policymakers) during varying time periods (weekends, weekdays, peak hours and
nights) and across the different parts of Manhattan. In particular, we:

  * •

use the big dataset (1.5 million trips) of the actual ride-hailing travel
demand spanning over six months,

  * •

apply the demand-driven ride-pooling algorithm to make sure that the pooling
alternative remains attractive for travellers,

  * •

report the comprehensive set of six performance indicators,

  * •

run detailed temporal and spatial analysis of the results,

  * •

visualize spatial distributions of ride-pooling performance,

  * •

experiment with varying the discount offered,

  * •

to understand how general are our findings, we compare NYC results with
Chicago and Washington and observe a similar pattern.

##  2 Methods and data

The methodology applied to obtain spatial and temporal insights on the
potential performance of ride-pooling is illustrated with blueFig. 1black
right. We first collect a big dataset of trip requests with detailed spatial
and temporal references. Then, to understand the potential of ride-pooling, we
run the utility-based ride-pooling algorithm ExMAS to match travellers to
shared rides. We divide the six months of data into about 9 000 batches of
half-hour for each of which we run the ride-pooling algorithm. ExMAS first
identifies all the feasible and attractive pooling combinations and then
matches travellers into attractive shared rides. Since pooled rides identified
with ExMAS are strictly attractive for travellers, in the matching we may
focus on the system (and operators’) perspective and minimise the total
vehicle mileage.

Notably, we assume that travellers are rational decision makers and opt only
for pooled rides more attractive than private ride-hailing (solo-rides). We
obtain the detailed results from which we assess the system performance with a
variety of indicators. Performance is observed at the batch level (system-wide
performance for all trips requested in 30-minute batch), as well as at the
individual level (where performance for individual travellers can be used for
spatial analysis). The results (input data, ExMAS scripts, and reproducible
results) are stored at the public repository (Shulika et al. (2022)).

###  2.1 Dataset

We analyse ride-pooling potential with over 1.5 million solo taxi trips
recorded in Manhattan (NYC) in the first half of 2016. We used sample of NYC
Taxi and ride-hailing trip requests from Manhattan (Schneider, 2015, 2019).
Each record ($q_{i}$) contains information on its origin ($o_{i}$),
destination ($d_{i}$) and request time ($t_{i}$); the exact route was not
reported. Our baseline is a scenario where all travellers use solo ride-
hailing. Then, we assess how much of the ride-hailing can be substituted with
ride-pooling such that all travellers have at least the same satisfaction with
the service (utility formulas) and the overall vehicle millage is reduced.
Travellers who cannot be attractively matched into pooled rides are served
with solo rides. We used a 5% sample of the total demand (ca. 60 million trips
per year) as a reasonable reference point for the plausible potential market
share of ride-pooling. In the pre-pandemic peaks around $15\%$ of the taxi
demand was opting for a pooled services, yet only half was actually pooled (in
Toronto, Young et al. (2020)), and the post-pandemic the ride-pooling
operations are practically ceased. As we report below, the demand levels and
density at 5% market share allowed to observe a variety of ride-pooling
regimes (from hypocritical to hypercritical). The temporal profiles of the
demand (reported in blueFig. 2black) as well as spatial patterns (blueFig.
3black) follow the observed general trends reported, e.g., in Schneider
(2019).

Figure 2: Temporal profiles of the demand dataset. We used 1.5 million trips
recorded over 6 months of 2016 in Manhattan. The top figures present the
average demand levels (trips per hour in Manhattan, which has an area of
60$km^{2}$) and their variability (standard deviation error bars) within-day
(top left) and within-week (top right). The bottom row shows the average
demand levels throughout the week and their standard deviation. Demand is
distributed fairly uniformly on all days of the week, with a peak on weekend
nights. Tuesdays to Thursdays are very similar, while Friday and Saturday are
more pronounced at night, and Sunday has a substantially different profile.
Demand typically reaches a flat plateau from 8 to 16 and peaks in the
evenings. Weekends are much more variable in the demand. Figure 3: Spatial
distribution of the trip origins, concentrated in the core and south parts and
lower on the peripheries, with a decreasing trend from the central part of the
network (Midtown) towards the north (Upper Manhattan).

###  2.2 Solving ride-pooling problems with ExMAS

We divide the dataset into about 9 000 half-hour batches, for which we apply
the ExMAS ride-pooling algorithm. ExMAS is an open-source Python algorithm
that solves the offline ride-pooling problem for rational travellers
(Kucharski and Cats, 2020). For a given demand set of trips with their origin,
destination, and departure time, ExMAS first identifies all the feasible
(attractive) door-to-door pooled rides (groups of travellers that want to
travel together) and optimally assigns each traveller to a vehicle with the
objective of minimising total mileage. ExMAS is utility-based and assumes that
pooling is selected only if it is attractive, i.e., rational travellers opt
for pooled options for which the utility of pooling exceeds the utility of
travelling solo. Utility is composed of travel time (weighted with value of
time) and cost (per-kilometer fare multiplied with the distance). The fare is
discounted if the ride is pooled, which shall at least compensate the detour
(longer travel time), delay (waiting for co-travellers) and discomfort
(penalty multiplier for sharing). To assess whether a pooled ride candidate
$r_{k}$ is attractive to the traveller $i$, we compare its perceived utility
$U$ with the utility of a private ride by applying the following formulas:

$\displaystyle U^{ns}_{i}=\beta_{c}\lambda l_{i}+\beta_{t}t_{i}$ (1)
$\displaystyle U^{s}_{i,r_{k}}=\beta_{c}(1-\lambda_{s})\lambda
l_{i}+\beta_{t}\beta_{s}(\hat{t}_{i}+\beta_{d}\hat{t}^{p}_{i})+\varepsilon,$

where $U^{s}_{i,r_{k}}$, $U^{ns}_{i}$ denote, respectively, the utility of
shared ride (for $i$-the traveller, ride $r_{k}$) and the utility of non-
shared ride (for $i$-th traveller). $\lambda$ stands for the per- fare, while
$\lambda_{s}$ denotes a discount for sharing a ride. $\beta^{c}$, $\beta^{t}$,
$\beta^{s}$ $\beta^{d}$ are the exogenous behavioural parameters: cost
sensitivity, value of time, willingness-to-share and delay sensitivity,
respectively. $t_{i}$ and $\hat{t}_{i}$ stand for the travel time of non-
shared and shared rides, respectively, $\hat{t}^{p}_{i}$ is a pick-up delay
associated with pooling and $\varepsilon$ is a random term (for the sake of
simplicity, assumed here to be constant and null, which yields a deterministic
model). Thanks to such constraints, the algorithm identifies all the pooled
rides of any degree for which the costs of pooling (detour, delay and
discomfort) are at least compensated with reduced fare. ExMAS assumes that the
ride is attractive if the utility of pooling is greater than the utility of
travelling alone for all the travellers sharing a ride.

The final solution to the ride-pooling problem is found by solving the so-
called matching problem. In the matching problem, ExMAS selects the subset of
feasible rides that yield minimal total mileage, under the constraint that
each traveller is uniquely assigned to a ride. Notably, the rides in the
solution may be pooled or solo (private ride-hailing, when no attractive
matches are found). ExMAS is exact and explores all feasible rides of any
degree (number of travellers), its results are consistent with discrete-choice
theory; however, it assumes the demand is known in advance (offline), and the
vehicle fleet is not explicitly modelled (demand-oriented). Thanks to such an
approach, we can reveal the ride-pooling potential of historical trip records.

The ExMAS is parameterized with traveller behaviour: value-of-time
($\beta_{t}$, which we assume to be 11,6 $\$/h$); penalty for sharing (
$\beta_{s}$, travel time multiplier due to discomfort of pooling, which we
assume to be 1.3 based on the results of Alonso-González et al. (2020). In the
baseline scenario, we use the discount $\lambda$ of $32\%$ and then experiment
with lower discounts of $20\%$, $24\%$, and $28\%$. We assume a trip fare
$\beta_{c}$ of 1,38 $\$/km$ (according to Uber (2022)) and constant and
network-wide flat speed of 21.6 $km/h$ (a very rough estimate for of highly
variable actual network speeds in Manhattan, which, for sake of clarity, we
did not incorporate in this longitudinal study). We use the standard waiting
time multiplier of 2, per analogy with the public transport studies Yap et al.
(2020), and each pick-up drop-off operation takes 15s.

###  2.3 Ride-pooling Performance Indicators

We measure ride-pooling performance with the following set of indicators
computed from the solution of ride-pooling problem for each of 9 000 batches
in our case study:

  * •

Vehicle hours reduction ($\triangle{T}_{v}$) - measure benefits for service
operator. It indicates the relative reduction of vehicle hours due to the
pooling. Here, we calculate it as a relative difference between total vehicle
hours (with travellers only) in the solo-ride scenario (when pooling is not
available) and in our pooled scenario.

  * •

Travellers utility gains ($\triangle{U}_{p}$) - measure benefits for
travellers. It indicates the relative increase in travellers (dis)utility due
to pooling, i.e. how well the discounted fare compensates the discomforts of
pooling (detour and delay). Computed as the total utility gains for all the
travellers being part of the ride-pooling problem solution, as expressed with
eq.LABEL:eq:utility_original_exmas.

  * •

Share of pooling (${S}$) - indicates a portion of travellers that managed to
be successfully pooled into shared-rides, i.e. share of travellers which, in
the final ride-pooling problem solution, have been assigned to the pooled
rides.

  * •

Occupancy (${O}$) - measures the pooling effectiveness. It indicates a ratio
of the total passenger hours in the solo ride-hailing scenario to the total
vehicle hours in the pooled scenario. It equals 1 in the solo scenario and
reaches 1.6 in the most effective experiments.

  * •

Passenger hours increase ($\triangle{T}_{p}$) - measures perceived costs for
travellers. It indicates an increase in the total travel time of all
travellers relative to the solo-rides scenario.

  * •

Potential fleet reduction ($\Delta F$) - roughly approximates the potential
reductions in fleet size. Since vehicles are not treated explicitly in ExMAS,
we approximate it using the maximum number of rides being undertaken at a
given time. In the solo-rides scenario, this equals to the maximal number of
simultaneous trips, while in the pooled scenario, this is reduced as some
trips are pooled in the same vehicle. Measuring how pooling reduces the number
of simultaneous rides offers a rough approximation, yet for exact fleet
estimation this shall be refined with explicit fleet methods (like Alonso-Mora
et al. (2017)).

To understand the impact of pooling to the above measures, we (following Soza-
Parra et al. (2022)) compare vehicle hours, travellers utility, passenger
hours, and fleet size when the ride-pooling service is available (subscripted
$S$) and is not applied (subscripted $P$) as follows:

$\begin{array}[]{ll}\Delta
T_{v}=\frac{\mathrm{T}_{v}^{S}-\mathrm{T}_{v}^{P}}{\mathrm{T}_{v}^{P}};\quad\Delta
U_{p}=\frac{\mathrm{U}_{p}^{S}-\mathrm{U}_{p}^{P}}{\mathrm{U}_{p}^{P}};\\\
\quad\Delta
T_{p}=\frac{\mathrm{T}_{p}^{S}-\mathrm{T}_{p}^{P}}{\mathrm{T}_{p}^{P}};\quad\Delta
F=\frac{\mathrm{F}^{S}-\mathrm{F}^{P}}{\mathrm{F}^{P}}\end{array}$ (2)

##  3 Results

We start by confirming the notion of critical mass and its significance for
ride-pooling performance in blueFig. 4black. On one hand we observe strong
trends against all six indicators, on the other the huge residual variability
calls for more detailed analysis. Then we illustrate distributions of six KPIs
in blueFig. 5black each following similar, yet subtly different profiles. In
blueFig. 6black we report the within-day variability of the results. Most of
KPIs have similar within-day profile and variability, except travellers
utility gains which remains flat during the day while others peak in the
evenings. blueFig. 7black illustrates the spatial concentration of pooled
rides, with half of the rides concentrated in only 14% of spatial hexagons.
Spatial patterns of three selected indicators are presented in blueFig. 8black
with nuanced pictures. For a richer picture, we select one indicator and show
its spatial distributions in eight different time periods in blueFig. 9black.
In blueFig. 10black we experiment to see how the price (discount) affects
pooling performance. We conclude with smaller experiments in Chicago and DC
(blueFig. 11black).

###  3.1 Critical mass

black blueFig. 4black reveals the strong, non-linear trend of demand against
all indicators. Each dot represents the result of respective KPI for a given
demand in an experiment. The logarithmic curve (thick lines) fits the
intuitive notion of critical mass well and fits the results of our
experiments. We observe intensive growth at initial phase of low demand values
and gradual stabilisation as the demand goes beyond the levels of 200 trips
per hour. Stabilisation in all performance indicators indicates reaching the
critical mass, at which the service becomes effective for all participants:
for the platform, travellers and drivers. Notably, at high demand levels
trends in all KPIs remain positive.

The results remain highly variable, and the logarithmic trend against the
demand levels fails to describe a residual variability. For the same demand
level of 400 trip requests per hour, the vehicle hours reduction varies from
10% to over 30%; travellers gain between 2% and 6% of their perceived utility;
35% to 70% of trips are pooled; the occupancy varies from 1.2 to 1.6,
passenger travel times may increase either by 4% or by over 10%, and potential
reduction in fleet size varies from 10% to 40%.

Figure 4: Six key performance indicators of ride-pooling plotted against the
demand levels. Each dot represents the result of a single experiment
(30-minute demand batch), thick dots denote average per demand level, and a
thick lines denote a logarithmic trend fit. Each performance indicator follows
a similar trend: it starts low, grows fast, and stabilises with a flat, yet
still increasing trend for high demand levels.

###  3.2 Performance distributions

We follow with the distribution of each indicator in blueFig. 5black, each
data point is a single batch experiment. Observations with null values show
experiments in which none of the trips was successfully pooled (there were no
batches with zero requests). While all the distributions are similar, there
are differences. The distribution of utility gains has the smallest variance,
while vehicle hours reductions and potential fleet reduction are most
variable. Share of pooling has the longest left tail, while occupancy right
tail. The share of pooling, passenger hours increase, and utility gains
indicate the same (left-skewed) asymmetry with different magnitudes. Occupancy
is symmetrically distributed, similarly to passenger hours increase, and
potential fleet reduction, as well as travellers utility gains, which is also
the most narrow of obtained distributions. The null values are obtained in ca.
200 batches, however, in 220 cases passenger hours did not increase at all
(with over 400 batches with null fleet reductions on our proxy).

Figure 5: Distribution of observed key indicators of ride-pooling. Each data-
point is the result of one ride-pooling experiments on a 30-minute batch. A
significant share of null observations (where sharing was not induced at all)
was reported for all six indicators. The remainder of the distribution follows
various shapes: symmetrical (like occupancy), left-skewed with fat left tail
(like share of pooling and passenger hour increase) or narrow (like utility
gains).

###  3.3 Within-day performance

Within day mean and standard deviation of indicators is shown in blueFig.
6black. A fairly large variability in the values of the analysed indicators
suggests the presence of other factors, apart from temporal, that affect the
ride pooling performance. While the profiles of average values are similar
throughout the day, the variability of utility gains is the greatest, in
contrast to the smallest variability of its distribution. Notably,
distributions are different from the demand pattern (blueFig. 2black), utility
gains do not increase in the evening and remains reasonably flat throughout
the day, while the increase in the evenings’ occupancy and vehicle hours
reductions is significant.

Figure 6: Within-day ride-pooling performance. Averages of six indicators
observed throughout the day (thick lines) and their standard deviations. Four
indicators have remarkably similar profiles with low performance and high
variability at night, a flat plateau during the day, and a peak of performance
in the evening. Only travellers utility gains follow a slightly different
pattern, with less significant increase in the evening (despite high occupancy
and vehicle hours reductions).

###  3.4 Pooling concentration

In blueFig. 7black, to understand how the pooling is distributed across
Manhattan, we show the concentration of pooled trips in the space (hexagons).
Pooled trips origins are highly concentrated, with 50% of them covering only
14% of spatial hexagons. For this and further spatial analyses, we divided the
area into 532 hexagons (using the Uber’s H3 library Brodsky (2018)), each of
532 hexagons has an edge length of 200m and area of over $105~{}000m^{2}$.

Figure 7: Concentration of pooled trips origins in the space. The top $13.8\%$
of hexes account for half of all pooled rides, with $5\%$ of hexes containing
$25\%$ of the rides and $27.2\%$ covering $75\%$. It indicates an unevenly
distributed demand for ride-pooling and the presence of territorial centres
where ride-pooling is the most attractive.

###  3.5 Spatial patterns of pooling performance

We plot the spatial distributions for three indicators: travellers utility
gains, share of pooling and increase in passenger hours in blueFig. 8black. We
used the requests’ origins as a spatial reference and aggregated mean values
over spatial hexagons. Since occupancy and vehicle hours reduction is
calculated not for requests (single trips) but for rides (of presumably
multiple passengers with multiple origins), mapping them spatially is
ambiguous and we refrained from plotting it.

Spatial distributions allowed us to reveal interesting patterns. We expected
the maps to simply resemble the demand distribution (blueFig. 2black) as the
demand density is the main driver of pooling performance. Surprisingly, the
patterns are more nuanced. Utility gains (blueFig. 8blacka) are concentrated
in the central part of Manhattan, spanning to its southern tip. The share of
pooled rides has a smaller concentration area, confined to the central part,
yet with another hotspot in the southern part of Manhattan (blueFig. 8blackb).
The pattern of detours is substantially different, peaking in the south, with
few smaller peripheral areas with higher detours (blueFig. 8blackc). Despite
the clear patterns and big dataset, several outliers appear, typically in the
upper Manhattan (North).

Figure 8: Spatial patterns of potential ride-pooling performance at trip
origins. Travellers utility gains (a) are pronounced in the central part of
the network, but the greatest share of pooling (b) is observed also in the
southern part (Wall Street), here, however, the increase in passenger hours is
the greatest (c).

We complement the above with spatiotemporal analysis. We report in blueFig.
9black how the spatial patterns of share of pooled rides varies within the
weekday (top) and weekends (bottom) in the: morning, afternoon, evening and
night.

Weekday mornings and afternoons are somehow complementary, as the morning
origins often become afternoon destinations. The evening pattern, with bigger
shares of pooled rides in general, is more uniformly distributed, both in
weekdays and weekends. While weekend afternoon has the similar pattern to
weekday, weekend mornings are different, more uniform. A more uniform pattern
may explain high pooling performance in the evenings.

Figure 9: Spatial patterns of the resulting share of pooled rides for the
ride-pooling problems of the working days (top) and weekends (bottom) for four
periods of the day (columns). In the afternoons, evenings, and nights of the
weekend, half of the trips can be attractively shared, while in the evening
the highest concentration is uniformly spanned over Manhattan. During the day
there is a concentration in the central and the southern parts, and at night
in the part of Manhattan between the central and southern parts.

###  3.6 Controlling performance with a discount

We leverage on our utility-based approach and test travellers’ sensitivity to
the pooling incentives. We see how the four various discounts offered for
ride-pooling (relative to the ride-hailing fare) attract travellers. While
previous results were computed for the 32% discount, now we experiment with
values of 20%, 24% and 28% discounts. This affects the system performance, as
we demonstrate in blueFig. 10black. Notably, the demand levels in those
experiments remain intact, and the discount only affects how many travellers
are satisfied and opt for pooling (as expressed with eq.
LABEL:eq:utility_original_exmas).

With 32% discount for 200 out of 9 000 batches there was null potential to
pool. This increases to over 700 batches when the service provider offers 20%
discount (blueFig. 10black right). The average occupancy decreases when
decreasing the discount; it shifts from 1.35 to 1.1 with the 20% discount.
Notably, for the service to be profitable, the discounts (which are perceived
by the platform as costs) need to be compensated with benefits (which can be
indirectly proxied with occupancy). This means that offering too low discounts
will not induce enough benefits, while offering too high discounts will reduce
the costs beyond the obtained benefits. We argue that offering 20% discount in
the above experimental setting is insufficient to induce sustainable pooling,
while 32% discount attracts the travellers to pool, yet the vehicle hours are
reduced by only 13.7%.

Figure 10: Controlling the ride-pooling performance with the ride-pooling
discount (relative to ride-hailing). The average occupancy (central ride-
pooling efficiency indicator) increases with the discounts offered, both
within the day (left) and in general (right). The within-day profiles have the
same shape, yet magnified. The share of solo rides (bars at occupancy of 1 in
the right panel) substantially decreases with increasing discount, and the
occupancy shifts to the right.

###  3.7 Validation in Chicago and Washington, DC

To see if the detailed NYC findings would generalise to other cities, we run
smaller experiments with the two cities for which similar datasets were
available: Chicago (from February 2023, 641 half-hour batches) and Washington
(from September 2019, 1468 batches). Despite the unique spatial setting of
Manhattan, with flattened and dense demand patterns, the occupancy (most
important KPI in our analysis) followed very similar growth patterns (blueFig.
11black), both in terms of shape, values and variability. This, coupled with
other studies suggesting generalisation of ride-pooling performance (Tachet et
al., 2017) can be used as an argument for some universality across different
topologies and land-use patterns.

Figure 11: blackGeneralisation of the occupancy results to two other cities:
Chicago (ca. 600 experiments) and Washington (ca. 1500 experiments). Despite
highly different urban structure, land-use and topology, occupancy for all
three cities follows both similar values (reaching average occupancies of 1.4)
and trends (starts low, grows fast, and stabilises with a flat, yet still
increasing trend for high demand levels).black

##  4 Conclusions

Revealing spatiotemporal patterns of the system performance allowed us to
better understand the potential of ride-pooling services. By experimenting
with the utility driven ride-pooling algorithm on the big set of actual ride-
hailing trips in New York, we obtain the rich picture of ride-pooling
potential by reporting six different performance indicators: vehicle-hour
reductions, travellers’ utility gains, share of pooling, occupancy, passenger
hours increase, and potential fleet reduction. They reveal the complex and
nuanced spatial and temporal patterns of potential pooling performance in the
first half of 2016 in Manhattan.

If offered with a 32% discount, around 695 000 out of 1.5 million trip
requests would be successfully pooled into attractive rides. This would reduce
vehicle hours by 25.2% and improve the passengers’ perceived utility by 4.1%.
The vehicle occupancy could reach up to 1.8 passenger hours per vehicle hour,
with the mean at 1.33. The fleet size could be reduced by 40% in the most
effective periods, with the mean reductions at 25% (blueFig. 4black). Only in
2.3% of the cases the pooling would fail to attract at least one traveller,
and in 45.3% of the analysed half-hour scenarios more than half would pool
(blueFig. 5black). The potential is greatest in the evenings; at 10PM the
vehicle hours could be saved by 25% on average and only by 10% at 5AM
(blueFig. 6black). The evenings, presumably due to their unique spatial
patterns, break out from the correlation with the demand: the demand decreases
from 6 to 11PM and the ride-pooling performance increases. The expected
occupancy reaches 1.45 at 10PM and drops to 1.35 during the day (8AM-4PM).

We argue that while demand level well represents the general patterns,
temporal and spatial components are crucial to better understand the ride-
pooling potential (blueFig. 4black). With a demand of up to 150 travellers per
hour, intensive growth is observed in all six indicators. After reaching the
critical mass, increasing demand improves the ride-pooling performance
(vehicle hours reduction) from the platform’s perspective, but its impact on
travellers utility is lower. Notably, unlike the classic works of Tachet et
al. (2017), all KPIs increase also at high demand levels. For all indicators
in the demand stabilisation stage the variability decreases and the single
observations are concentrated around mean. Interestingly, the expected
travellers utility gains and share of pooling remain almost stable in the
range of 250 to 450 travellers per hour (per 60$km^{2}$).

We reveal the distributions of indicators obtained over the half-year study
(blueFig. 5black) with similar, yet subtly different shapes. The average
occupancy in the six-month experiment was around 1.4, yet we observed values
ranging from occupancy of 1 (no pooling) up to 1.8. Suggesting the existence
of time periods where pooling is highly effective, as well as periods without
any potential to pool. The temporal profiles of six KPIs follow very similar,
yet subtly different trends, both in means and in variances (blueFig. 6black),
strongly correlating with the demand. The mean occupancy in the evenings is
above 1.45 and drops to 1.2 during the night (blueFig. 6black). Low demand
from midnight to early morning yields less efficient ride-sharing, two peak
hours during the day (7:00AM and 9:00PM) lead to high system performance.
Notably, while the average demand decreases from 6PM to 11PM (blueFig. 2black)
the performance over that period improves in all KPIs.

The shared rides are highly concentrated in space (blueFig. 7black), $75\%$ of
all pooled rides origins are in 27% of spatial hexagons into which we divided
Manhattan. Spatial patterns do not necessarily follow the demand density. More
nuanced patterns are revealed. Travellers’ gains are concentrated in the
central part of Manhattan (blueFig. 8blacka), the share of pooling is high
also at the southernmost tip (blueFig. 8blackb). Surprisingly, the detours are
greatest at the southern tip and are scattered around other parts of the city
(blueFig. 8blackc). The results in blueFig. 8black can be, to some extent,
explained with the demand distribution in blueFig. 3black. In high demand
areas travellers utility gains are high because of many travellers to
potentially share one’s ride. But, interestingly utility gain for travellers
is highest at southernmost tip, presumably because they are longer (in longer
trips passengers benefit from ride sharing more and better compensate the
detours and delays).

We show spatial patterns of share of rides that were actually pooled for
workdays and weekends in the morning, afternoon, evening and nighttime
intervals (blueFig. 9black). In the afternoons, evenings, and nights of the
weekend half of the trips can be attractively shared, while in the evening the
highest concentration occurs in almost the entire territory of Manhattan
except for the northern part. For the weekend mornings, in many cases less
than $40\%$ of trips are shared, in the weekday nights often times no trips
are pooled at all (blueFig. 9black). The difference in those patterns may
explain high pooling performance in the evenings, despite lower demand levels,
the demand distribution is more uniform in the evenings and rides are pooled
equally across the core of Manhattan.

Thanks to our utility-based approach, the travellers’ satisfaction is (to some
extent) controllable by the discount offered for pooling. By increasing
discount from $20\%$ to $32\%$ the number of cases when no pooling is
observed, drops over threefold and the average occupancy raises from 1.1 to
1.35 (blueFig. 10black). Our validation in Chicago and DC is promising, since
we observe very similar trends in the occupancy. In future, a more detailed
spatiotemporal analysis of those datasets shall determine if our findings are
general.

##  5 Discussion

Ride-pooling still has the potential to become an attractive alternative mode
of transport, presumably reducing car dependence and vehicle mileage in urban
areas. To realize this potential, we need to understand it in depth. Demand
density is not the only factor driving the ride-pooling potential. As we
demonstrate, for the same demand levels, the efficiency of pooling services
may vary significantly. Here, we tried to understand this residual variance
with the longitudinal experiment with big data in New York City.

The demand levels greater than 180 trip requests per hour in the area of
Manhattan ($60km^{2}$), i.e., 3 trip requests per hour per square kilometre,
allow reaching critical mass of ride-pooling in Manhattan, with ca. 20%
reductions in vehicle hours, travellers’ utility improved by 3.5% compared to
solo ride-hailing and over 40% of trips actually pooled into attractive rides
of average occupancy greater than 1.3 passenger hour per vehicle hour. When
demand doubles (to ca. 6$trips/h/km^{2}$) performance improves, but not
drastically (50% of pooled rides and occupancy of 1.4). However, this is far
not guaranteed, as 6$trips/h/km^{2}$ may yield 13 or 33% vehicle hour
reductions (blueFig. 4black).

Pooling is most promising in the core and less in peripheries, at peripheries,
even when pooling is attractive its costs are higher as it yields longer
detours there. The greatest potential area shifts from the North in the
morning to the Central and South in the afternoon. Weekend mornings have low
and uniformly distributed pooling potential, which concentrates in the South
of Manhattan on weekend nights. Pooling in the evening is most efficient,
presumably is due to uniformly distributed share of pooling (blueFig. 9black),
unlike higher, yet more concentrated demand in the afternoons.

The 32% flat discount seems to be sufficient to attract pooling from ride-
hailing. We argue that it is a good balance: lower discounts make pooling less
attractive and thus less used, while greater discounts would induce longer
detours, which could not be compensated for the platform. Whether such
services need to, or should be, publicly subsidized remains opened. Here, we
show that the 32% fare reduction is compensated with only 25% reductions in
vehicle hours, which may deem unprofitable for the commercial operator. This
is inline with observation of policies of the greatest ride-hailing platforms,
who seem to lose enthusiasm to offer pooling in the post-pandemic era.

Ride-pooling is not colinear in its performance indicators. As depicted in
blueFig. 8black, the maximum mileage reduction is not necessarily associated
with the maximised travellers utility or the share ratio. It implies that
policymakers and researches should be clear about their objectives. In
particular, advocating ride-pooling benefits by maximising the sharing ratio
only seems to be an inadequate approach.

The practical implications of this analysis shed light on the future strategy
of introducing pooled services. Specifically, the proposed post-pandemic Uber
pooled services (Tsay, 2023) with a 5% to 20% discount seems to be not
attractive enough to become successful. However, pooling services may benefit
when tailored to the demand conditions. Our results would suggest offering
pooled rides: in weekday afternoons from South and Central Manhattan, in the
evenings without spatial limitation, and in the mornings from Northern
Manhattan. Pooling shall not be offered at night, as it is neither efficient
for the platform, nor attractive for travellers. The discounts may be time and
space varying, e.g. 28% discount in the evening and 32% during the day yields
the same occupancy levels. The discount may be lower in the core of the
network, where disutilities of pooling (detours) are lowest and benefits
highest.

Policymakers can exploit the revealed spatiotemporal patterns of pooling
performance, e.g. by forcing ride-hailing companies to offer ride-pooling in
the periods and areas when it is attractive for the city (vehicle hour
reductions). Or subsidise the pooling in the less attractive periods and areas
to improve the accessibility. This shall be controlled with the total mileage,
which shall not increase after introducing ride-pooling services. In the event
of the new pandemic, we may now understand when and where the ride-pooling
services may be proposed as the intermediate transport mode between private
cars and mass transit. With occupancy being a proxy for virus spreading, one
can decide which spatiotemporal patterns of NYC trips may be served with ride-
pooling, to balance between system’s performance and virus-spreading.

Despite its merits, this study has certain limitations. First, it uses the
revealed demand of taxi users, which may have substantially different spatial
and temporal structure than the general demand. Second, the behavioural
assumptions used in this study can be extended to cover heterogeneity of ride-
pooling aptitudes, as revealed, e.g., in Alonso-González et al. (2020), where
the population varies from enthusiasts to pooling-averse. The ExMAS algorithm
is limited to door-to-door ride-hailing, the attractiveness is evaluated
against solo ride-hailing only, the demand is known in advance and fleet is
not explicit. We argue that our approach with implicit fleet operations is not
a limitation. In general, the fleet needed to operate the pooled rides shall
not be greater than for solo ride-hailing. Thus, on average, the waiting times
for pooled rides, with the same fleet of vehicles, shall be lower than for
ride-haling. Finally, in this study we used network-wide and constant speed,
which is obviously wrong for the congested cities and may affect both the
results from the congested periods (AM peak) where due to slower trips,
detours are longer and pooling would become less attractive, and, inversely,
for uncongested periods (nights), where faster trips may make the longer
detours more acceptable.

In future, this methodology may be applied to more cities, like Chicago and DC
for which we ran small validations, with elastic demand and real network
speeds. This would allow drawing more generally applicable conclusions and
presumably reveal universal patterns of shareability.

##  6  Credit authorship contribution statement

Olha Shulika: Investigation, Writing - Original Draft. Michal Bujak:
Investigation. Farnoud Ghasemi: Visualization. Rafal Kucharski: Supervision,
Conceptualization, Writing - Reviewing and Editing.

##  7 Declaration of Competing Interest

On behalf of all authors, the corresponding author states that there is no
conflict of interest.

##  8 Acknowledgements

This research was funded by the National Science Centre in Poland program OPUS
19 (Grant Number
2020/37/B/HS4/01847).

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1038 Research

# Interactive Probing of Multivariate Time Series Prediction Models: A Case of
Freight Rate Analysis

Xu Haonan
Singapore Management University  e-mail<EMAIL_ADDRESS>Li
Haotian
Hong Kong University of Science and Technology
Singapore Management University e-mail<EMAIL_ADDRESS>Wang Yong
Singapore Management University e-mail<EMAIL_ADDRESS>
###### Abstract

We present an interactive probing tool to create, modify and analyze what-if
scenarios for multivariate time series models. The solution is applied to
freight trading, where analysts can carry out sensitivity analysis on freight
rates by changing demand and supply-related econometric variables and
observing their resultant effects on freight indexes. We utilize various
visualization techniques to enable intuitive scenario creation, alteration,
and comprehension of time series inputs and model predictions. Our tool proved
to be useful to the industry practitioners, demonstrated by a case study where
freight traders are given hypothetical market scenarios and successfully
generated quantitative freight index projection with confidence.

###### keywords:

What-if Analysis, Multivariate Time Series Prediction, Human-centered
Computing, Freight Rate Analysis

Introduction

What-if analysis is crucial for decision-making under uncertainty. It answers
the question of ”What would happen to the model’s prediction if input variable
changes?” [5] While cross-sectional data sets are gaining functional support
for user-defined variable perturbations, what-if capabilities for multivariate
time series analysis tools are lagging behind.

We identity freight rate prediction as an exemplar task that requires what-if
support: freight rates’ extremely high volatility and tight co-integration
factors mean that any slight perturbation to demand or supply factors bring
about large changes to freight rate. This challenges freight analysts to keep
an active eye out on market events and make informed and precise gauges about
future freight rates using the ”what-if” paradigm.

Literature on what-if tools for time series models is rare, two closest pieces
related to the field include TimeFork[1], an interface to explore the inter-
correlations between different time series variables. Google’s What if tool[5]
only allows editing and comparing cross-sectional data. To the best of our
knowledge, there is no existing tool that enables users to easily manipulate
time series input and understand the output of models in a comprehensive
manner.

We introduce a visual analytic solution to simulate market scenarios for
freight rate prediction by probing the industry’s commonly used multivariate
time series models such as ARIMAX, multiple linear regression,VECM [3] and
LSTM[4]. The system is created with four design goals in mind: intuitive
manipulation of time series market data through line chart dragging; useful
sensitivity analysis by generating scenario comparison views. Variable
comprehension and model comparison that enable users to better understand the
inner mechanism of models and spatial data aggregation for supply-side
analysis. We’ve also conducted a case study with freight traders, the study
shows that our solution can reliably assist users in anticipating and
preparing for hypothetical market scenarios.

##  1 Visual Design

Our solution contains 6 views. Fig. 1a is the what-if input view which allows
scenario adjustments. Fig. 1b is the coefficient impact view which facilitates
indicator comprehension. Fig. 1c is the model comparison view that shows model
performances for model selection and ranking. Fig. 1d is the spatial data view
that supports aggregating spatial data. Fig. 1e is the prediction and what-if
view. Fig. 1f is the what-if histories view which logs scenarios outputs.

Figure 1: The what-if solution interface

The what-if input view satisfies the first design goal, allowing users to
flexibly create and update market scenarios. The historical line chart shows
the general trend and seasonality of the variable data, it supports zooming
through scrolling and displaying Bollinger Bands. The near term and the what-
if data chart share the same time scale. The former magnifies the past 4
weeks’ data. The latter applies a forward-fill strategy with the default
forward window set to 1 to minimize the accumulation of error. Users can drag
the green what-if data point vertically and the system updates the what-if
value by inverse scaling the pixel shifts and variable values ranges. After
dragging the data point(s) to the desired value(s), the user submits the data.
The server computes the scenario output from time series models and the system
displays the updated output in Fig. 1e and detailed comparison with the
original prediction in Fig. 1f.

The variable impact factor view consists of vertically aligned area charts
shaped in normal distribution. By showing their value range on the same chart,
users get a grasp of the magnitude in which each variable affects the target
time series variable. Thanks to the reduced height, the view also serves as an
efficient variable localization window. Multiple regression-based and ARIMAX
models have scalar variable coefficients for exogenous variables, we integrate
them directly into the view. On the other hand, VECM models have vector
coefficients and LSTM models hold model parameters in neurons and gates, we
reached a design choice to not include them.

The spatial data aggregation view is a map displaying the raw spatial data and
aggregated demand/supply-based information. Individual vessel information is
represented by colored droplets. The tip of the droplets indicates the
vessel’s heading and the color reflects cargo status. More specifically, A red
droplet highlights an empty(ballast) vessel whereas blue indicates the vessel
is loaded with cargoes. Such information help traders identify potential
vessels for chartering. Meanwhile, a unique vessel identifier number(IMO) is
shown on hover when the user is interested in chartering the ship. In this
way, users can make informed guesses about economic drivers with temporal
features.

The what-if history view is a table, each row displays every run’s what-if
difference with the original predictions. It offers the user a complete
history of scenario outputs. The X-Axis is positioned at the middle of the
Y-Axis(Difference), its sign highlights the general trend of the freight index
before and after applying the market scenario. The user can also inspect
individual models’ difference curves, by checking the curve’s relative
position around y=0, the user could have a grasp on the detailed trajectory of
freight movement. This could prove useful in identifying hedging, speculation,
and arbitrage opportunities.

##  2 Evaluation

We carried out a case study with three freight traders to assess the
solution’s usefulness. The process explored the effect of a torrential flood
around a Brazil iron ore mine. The goal was to anticipate the resultant
freight rate movement and uncover business opportunities for chartering. Each
participant was tasked to perform the same set of actions on the interface as
freight trader Alice.

Prediction on original data and model preference: Freight trader Alice
observes that Minas Gerais, a state in Brazil with steady iron ore
exports(freight demands), is experiencing an unusually heavy rainy season. She
recalls the devastating Brumadinho dam disaster and its negative impacts on
route C3’s(from Brazil to China) freight rate[2]. Anticipating the possibility
of another sharp drop in iron ore production in the region, she initiates a
what-if analysis process to simulate the worst-case scenario. She first
selects route C3 from Fig. 1a and waits for the pre-trained models’
predictions based on the current week’s market information Fig. 1e. She
notices model VECM and LSTM enjoy significantly lower errors margins by
looking at the model comparison view Fig. 1c. Anticipating the infrastructural
damage and long-term consequences of the flood, she selects LSTM and VECM to
be the primary models for the what-if scenario.

What-if probing: She starts looking for variables to change: Brazil loading
and iron ore price. As the model has a fair amount of variables, she opted to
look for it in the coefficient view as it encapsulates variables in a compact
size. She clicked on ”Brazil Loadings” in Fig. 2a, the input view
automatically slides to the target row as shown in Fig. 2b. Then, looking at
the past month’s steady trends, she dragged down the production for 2000 mt as
shown in Fig. 2c and clicks the ”Submit Scenario” button.

Figure 2: (a) User finds ”loading” in the coefficient view and clicks. (b) The
click event triggers what if window to scroll to loading’s input section. (c)
User changes the scenario value through dragging.

Anticipating scenario output and mitigate risks: The what-if dotted lines in
Fig. 3b go lower than the original prediction as anticipated. Meanwhile, she
notices in the what-if history view that the middle line for the x-axis is
nearly y=-2 in Fig. 3b. Now she has a clear outlook on what would happen
should the rain continues. She starts looking for the ballast(empty) vessels
approaching Brazil in the map view and taking down the IMOs of the vessels as
shown in Fig. 4. She knows should the worst happen, some unfortunate ship
owners will leave empty-handed from Brazil and be forced to charter out the
vessels at a much lower price, that’s when she’ll strike for a bargain.

Figure 3: (a) Loading variable’s new value. (b) The average difference between
original prediction and updated scenarios is around -2. Figure 4: User locates
empty vessels approaching Brazilian ports and identify potential chartering
targets

##  3 Conclusion and future work

We presented a what-if tool for manipulating and anticipating market scenarios
for freight rate prediction. We evaluated the solution with industry
practitioners. The user study reflects that the solution enables users to
accurately capture freight index changes and respond to market events
proactively. In the future, we plan to improve the accuracy of the machine-
filled what-if data through learning statistical patterns of variables. We
also aim to improve the applicability of the tool by incorporating seasonal
parameters.

## References

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