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Leich, G.; Bischoff, J. (2018): Should autonomous shared taxis replace buses? A simulation study. In:
mobil.TUM 2018 : Urban Mobility - Shaping the Future Together.
Gregor Leich, Joschka Bischoff
Should autonomous shared taxis replace
buses? A simulation study
Accepted manuscript (Postprint) Conference paper |

submitted to mobil.TUM 2018 ”Urb an Mobility - Shaping the F utur e T o gether” - International Scientific Confer enc e
on Mobility and T r ansp ort , conference pro ceedings to b e published in T r ansp ortation R ese ar ch Pr o c e dia
Should autonomous sha red taxis replace buses?
A simulation study
Gregor Leic h * , 1 , Josc hk a Bischoff 1
1 T ec hnisc he Univ ersit¨ at Berlin
Departmen t of T ransp ortation System Planning and T elematics
Salzufer 17–19; 10587 Berlin; German y
* Corresp onding author (e-mail: leic [email protected] erlin.de; tel.: +49-30-314-28666)
Octob er 1, 2018
The in tro duction of shared autonomous v ehicles (SA V) will lik ely reduce op eration cost p er v ehicle and
migh t thereb y allo w to enhance con v entional public transit systems with n umerous small SA Vs offering
flexible ridesharing-lik e feeder services. These demand-resp onsiv e services could replace con v en tional bus
lines limited b y their fixed routes and their fixed sc hedules. This sim ulation study explores the p oten tial
of replacing con v en tional bus lines with shared autonomous v ehicles in a suburban area of Berlin. Sev eral
scenarios with differen t fleet sizes and v ehicle sizes are sim ulated using the m ulti agent transport simulation
MA TSim. The sim ulation suggests for all ev aluated scenarios higher op erating costs and only slight tra v el
time sa vings in comparison to con v en tional buses. Do or-to-do or service allo ws for significan t reductions
in a v erage w alk time, but causes n umerous detours which consume a high share of the time gained. A
fleet of 150 SA Vs with 4 seats eac h seemed appropriate for the simulated area with appro ximately 24 000
inhabitan ts.
1 Intro duction
T ransp ortation net work companies lik e Ub er ha v e app eared on the roads only a few years ago and y et are already
dev eloping in to increasingly imp ortan t comp etitors to con v entional public transport such as buses. Sc haller (2017)
analyzed the example of New Y ork Cit y where buses and even sub w a ys started to lo ose more and more passengers
whereas ride services (ride-hailing, con v entional taxis and similar) more than compensate for this and are growing
faster than all other mo des included in the statistic. In a surv ey by Clewlo w and Mishra (2017) ride-hailing users
rep ort a decrease in their public transit use with a 6 % reduction for bus services and a 3 % reduction for ligh t rail
services. Ho wev er, they also rep ort a 3 % increase in hea vy rail usage. Apparen tly ridesharing services comp ete with
con v en tional public transit, but can also complement it. Some transit authorities, e.g. SEPT A (2016), partnered with
Ub er to offer discoun ts for last mile rides from and to their train stations. The Canadian cit y of Innisfil made headlines
(see Smith (2017)) with the more radical decision to partner with Ub er rather than in tro ducing a con v en tional bus
system at all.
Ride-hailing apps and ridesharing allo w for a more flexible service than con v en tional bus lines, b ecause they can
react to the actual demand instead of op erating on fixed routes and fixed sc hedules. So they can p oten tially offer
a more attractiv e service for the customer b y departing closer to where and when the passenger w an ts. Th us, they
can eliminate op erating costs for sc heduled services whic h ev en tually run empty , b ecause no passenger chose to tak e
these services. F urthermore, they allo w for do or-to-do or service whic h is more attractiv e and remo v es the w alk time
to access the next bus stop. According to the surv ey by Clewlo w and Mishra (2017), ha ving less than enough transit
stops is the second most imp ortan t reason for substituting ride-hailing for public transit.
1

In order to realize the full p oten tial of ridesharing-lik e services as part of a public transit system, ridesharing-lik e
services will lik ely need to use man y small v ehicles instead of a few large con v en tional buses, b ecause the more v ehicles
there are, the more frequen t the service they offer can b e. A large barrier to the use of more v ehicles seem to b e
driv er-related costs whic h according to F rank et al. (2008) amoun t to ab out 40 % of the sum of all op erating and
in v estmen t costs for a con v en tional bus in German y . The in tro duction of shared autonomous v ehicles (SA Vs) in the
future will lik ely remo v e all driv er-related costs and thus could allo w to replace eac h large con ven tional bus with man y
smaller v ehicles whic h could offer a more frequen t service without the tremendous increase in driver-related costs this
w ould cause to da y . F urthermore, prices for ride-hailing services are lik ely to fall making them an ev en more attractiv e
comp etitor for passengers.
Ho w ev er, using man y small v ehicles instead of a few large buses could increase road congestion. F urthermore, taxi
lik e services could
So should transit authorities replace con v en tional bus lines with ride-hailing services op erated b y future autonomous
shared taxis in some areas? How w ould tra v el times and op eration costs change? These questions are to b e examined
in a case study for a lo w-densit y suburban area in Berlin using the m ulti agen t transp ort simulation MA TSim. 1
2 Simulation mo del
The aim of the study is to compare a base case scenario with con v en tional bus lines to sev eral scenarios in whic h
these bus lines w ere replaced b y autonomous shared taxis of v arying fleet sizes and capacities p er v ehicle. The m ulti
agen t transp ort sim ulation MA TSim (Horni et al. (2016)) w as chosen because it is capable of simulating large-scale
scenarios at sufficien tly high computing sp eeds and pro vides soft w are mo dules for shared taxis and in termo dal trips.
MA TSim consists of a common base and sev eral optional extensions whic h are called “con tributions”. Three of these
extensions w ere used in the study: The A V-Con tribution (A V for “autonomous v ehicles”) w as emplo y ed to calculate
in termo dal routes com bining con v en tional public transit and SA Vs as a feeder service. In order to sim ulate ride-hailing
and ridesharing with SA Vs the DR T- and D VRP-Con tributions w ere used (DR T for “demand-resp onsiv e transp ort”
and D VRP for “dynamic v ehicle routing problem”).
MA TSim is based on the sim ulation of agents and their daily plans whic h consist of activities lik e home or w ork
and trips b et w een their activit y lo cations. Before eac h sim ulated da y , some agents try to impro v e their plans, e.g.
b y selecting a differen t route or mo difying activit y start and end times. The resulting plans are then sim ulated and
scored based on their p erformance b efore the next iteration starts and plans are mo dified and sim ulated again. Several
transp ort mo des w ere included in the sim ulation. Ho w ev er, the underlying input data w as not calibrated for mo de
c hoice, so mo de c hoice w as fixed and shared taxis were handled as a part of the public transport system. Therefore,
only agen ts who had already b een using public transp ort b efore could use shared taxis (as w ell as normal buses and
trains) and mo de shift effects w ere neglected. F urthermore, the same fare system applies to shared taxis and public
transit and there is no comp etition with p oten tial other ride-hailing op erators.
2.1 Intermo dal router
The A V-Con tribution comes with an intermodal router, whic h allows to com bine a public transit route with other
mo des to access the first transit stop and egress from the last transit stop. It is not a full in termo dal router, as it do es
not consider trips with other mo des b et w een t w o public transit rides, such as a bus-bik e-train trip. Access and egress
mo des are selected b y b eeline distance b et w een activit y lo cation and transit stop. F or this study the so-called “flexible
st yle” for access/egress mo de c hoice w as selected. F or beeline distances of less than 300 m the router alwa ys assumes
the mo de “transit w alk”. T aking in to accoun t the w ait time for a shared taxi, it seems unlik ely that using a taxi has
significan t adv an tages for the passenger whic h could justify the additional exp ense for the shared taxi op erator and
p ossible detours for other passengers of that shared taxi. F or b eeline distances b et ween 300 m and 1 000 m the router
selects b y random either mo de “drt” (shared taxi) or “transit w alk”. So, multiple rout ing requests for the same trip
can result in routes with differen t access and egress mo des. Thereb y , the router implements mode choice for access
and egress legs. F or b eeline distances greater than 1 000 m the router alw a ys assigns the mo de “drt”, b ecause it is
unlik ely that passengers w ould accept suc h a long w alk, if a faster and more comfortable alternative is a v ailable.
In order to restrict the op eration area of shared taxis, the in termo dal router w as mo dified to assign the mo de “drt”
only to access and egress legs whose origin and destination are lo cated inside the designated op eration area (see
1 This pap er is based on the master’s thesis b y Leic h (2017).
2

figure 1), so no agen t has a route whic h asks for shared taxis outside the op eration area. If no plausible transit route
could b e found, the router returns a direct “transit w alk” resp ectiv ely “drt” leg from trip origin to trip destination.
As the router calculates tra v el time and cost of access and egress legs based on b eeline distances only , some bus stops
inaccessible due to riv ers and lak es had to b e excluded man ually as access and egress stops for activit y lo cations inside
the study area (see bus line 136 in figure 2).
F urthermore, giv en a certain set of departure time, trip origin and trip destination the router alwa ys returned the
same route. This turned out to b e a ma jor issue, b ecause the router estimates access leg tra vel times based on the
b eeline distance and a fixed mo de sp eed. Ho w ev er, shared taxi legs hav e v arying w ait and in-v ehicle tra v el times,
so man y agen ts missed connecting trains they planned to tak e. This issue is aggrev ated by the fact that the study
area has t w o hea vy rail lines to the cit y center. Figure 2 sho ws that line S25 (sho wn in green) has b etter accessible
stations than line U6 (sho wn in blue), so the router mostly returned routes using line S25. Nev ertheless, line U6 offers
a far more frequen t service whereas missing a S25 train causes a 20 min w ait. This lead to increased public transit
w ait times despite less public transit legs in the first preliminary sim ulation runs. In order to address this issue, the
router w as altered to c ho ose b y random at eac h routing request whether to include or exclude all three concerned S25
stations in the study area during routing. Thus, o v er the course of several iterations with sev eral routing requests the
agen t will test routes with and without using the three S25 stations.
2.2 Simulation of sha red taxis
The shared taxis are sim ulated using the DR T-Con tribution in tro duced in Bisc hoff et al. (2017). F or the v ehicle routing
and assignmen t the DR T-Con tribution uses the DVRP-Con tribution presented in Maciejewski (2016) as bac k end.
Shared taxis offer do or-to-do or service. Agen ts request their shared taxi ride after finishing the last activity before the
trip, i.e. without pre-b o oking (Bisc hoff et al. (2017)). Ride requests are only serv ed if a shared taxi can serve them
within certain time constrain ts. These consist of a maxim um w ait time to departure at the requested journey origin
and a maxim um total tra v el time (the sum of w ait and tra v el time) (Bisc hoff et al. (2017)). Both time constrain ts
m ust b e satisfied for the requested ride and for all ride requests already assigned to the shared taxi (Bisc hoff et al.
(2017)). That means additional trav el time caused b y detours to serve the new ride request ma y not violate the time
constrain ts of ride requests already sc heduled. The requested ride is assigned to the v ehicle whic h can serve it with
the least additional op eration time needed to serv e the requested ride (Bisc hoff et al. (2017)).
Otherwise, if no taxi can serv e the ride without exceeding the ab ov e men tioned constrain ts, the ride request is rejected
(Bisc hoff et al. (2017)). In the current implemen tation, the corresp onding agent will nev ertheless w ait for the shared
taxi to arriv e. Since no taxi w as sc heduled to serv e the customer, he will w ait un til the iteration ends. That means he
is not able to con tin ue his daily plan and will not execute an y activit y or trip scheduled after the shared taxi ride. This
p oses some issues for analysis, b ecause no tra v el time can b e calculated for the age n t and different agen ts are affected
in differen t scenarios. Therefore, all trips whic h w ere not completed in all scenarios (ab out 8.6 % of all completed
trips) w ere excluded from analysis of en tire trip tra v el times in section 4.2. Th us, it can b e a v oided that e.g. v ery
long trips with high shared taxi tra v el times increase a v erage trip tra v el times of scenarios with sufficient v ehicle fleets
whereas the rejection of these ride requests in other scenarios decreases the a v erage trip tra v el times in these other
scenarios. Eac h trip excluded from analysis w as completed in at least one SA V scenario. T aking in to accoun t only
these completed measuremen ts, there seems to b e no significant difference betw een excluded and included trips, i.e.
the a v erage trip tra v el time is v ery similar and the difference in a verage trip tra v el time b et ween SA V scenarios and
the base case is similar to the difference calculated for included trips. So the exclusion of that data from analysis do es
not seem to ha v e a significan t influence on the results, but allo ws to compare the very same trips for all scenarios.
When the sim ulation w as run, there w as no option to use the DR T-Con tribution without rejections. Agen ts could
try to a v oid ride request rejections to some exten t, e.g. b y c ho osing a differen t departure time. How ev er, rejections
can b e erratic for agen ts, i.e. the v ery same daily plan migh t w ork fine in one iteration, but migh t b e ab orted due
to a rejection in another iteration. Which request is rejected depends on which requests w ere issued b efore, so small
alterations in other agen ts’ plans migh t decide whether there is a SA V av ailable or not. Instead of rejecting requests
they could b e assigned to SA Vs despite long exp ected w ait times. How ev er, a long wait time w ould render a daily
plan v ery unattractiv e just lik e a rejection in the curren t implemen tation would do. F urthermore, the o ccurence of
long w ait times migh t b e just as erratic as rejections. This issue requires further researc h.
The maxim um p ermissible shared taxi w ait and tra v el time sum t r
max is calculated based on the tra v el time for a
direct ride t r
dir ect (without w ait and detours) and t w o parameters α and β (Bisc hoff et al. (2017)):
t r
max = α ∗ t r
dir ect + β (1)
3

The selection of the time constrain t parameters α , β and maxim um w ait time t w ait
max has a significan t influence on the
a v erage tra v el times and the share of rejected ride requests as test runs in Bisc hoff et al. (2017) sho w. Based on their
results sev eral com binations w ere tested for the data set of this study . Since the same set of time constrain t parameters
w as to b e used for all scenarios, all test runs w ere conducted for a fleet of 200 shared taxis with 4 seats p er v ehicle. α
v alues other than 1.5 w ere not tested, b ecause these lead to higher tra v el times in Bisc hoff et al. (2017) and b ecause
of the high computation time necessary for more test runs.
T able 1: Selection of time constrain t parameters α , β and t w ait
max .
α β t wait
max t wait t r d dir ect d detour d T d U ρ
[mm:ss] [mm:ss] [mm:ss] [mm:ss] [km] [km] [km] [km]
1.5 10:00 10:00 06:18 17:34 4.87 1.21 49 715 105 170 0.05
1.5 10:00 12:00 07:26 18:28 4.94 1.08 54 809 109 795 0.01
1.5 12:00 12:00 07:48 19:30 4.95 1.36 53 090 114 739 0.01
1.5 15:00 15:00 10:02 22:21 4.94 1.56 52 808 118 462 0.01
T able 1 depicts a significan t increase in a verage total tra v el times t r (sum of w ait and in v ehicle tra vel time) and
a v erage w ait times t w ait with increasing β and t wait
max v alues, although demand and v ehicle fleet w ere equal in all test
runs. How ev er, the share of rejected ride requests ρ is m uc h larger in the upp ermost test run than in all other test runs,
that means less requests w ere actually serv ed enabling p oten tially b etter service qualit y for the remaining requests.
This migh t explain the lo w er a v erage direct distance b et w een request origin and destination d dir ect and the lo w er
distance driv en d T . More generous time constrain ts β and t w ait
max also lead as exp ected to more bundling of rides whic h
can b e seen in the decreasing total distance driv en d T despite increasing rev en ue distance d U (total length of all rides
serv ed). The rise in rev en ue distance despite stable demand is partly caused b y rising detour distances d detour . Detour
distances w ere calculated as the difference b et w een the length of a theoretical direct trip from origin to destination of
a ride request and the distance the agen t really sp en t tra v elling in the SA V, whic h migh t b e longer, b ecause the SA V
serv ed other agen ts on the w a y . The first parameter set β = 10 and t w ait
max = 10 sho ws a higher detour distance than
β = 10 and t w ait
max = 12, although t r
max is equal for b oth. One p ossible explanation is that giv en a certain p ermissible
time budget t r
max the stricter w ait time criterion of the former parameter set will allo w for higher in-v ehicle tra v el
times. These can b e used to allo w for longer detours to bundle more ride requests.
A high rejection rate ρ could put at risk the acceptance of the new shared taxis as a replacemen t of con v en tional bus
lines. Therefore no β and t w ait
max lo w er than 10 min w ere tested. Instead the highlighted parameter set w as selected for all
follo wing sim ulation runs since it deliv ers the lo w est tra vel times at an acceptable rejection rate. A p ossible explanation
wh y tigh ter time constrain ts could not b e used is the lac k of a relo cation strategy . The shared taxi op eration area
is to o large to reac h ev ery p ossible pic k-up lo cation from ev ery p ossible v ehicle lo cation in 10 min or less. A t the
b eginning all SA Vs were distributed ev enly ov er the op eration area, but with a largely mono directional demand in
the morning rush hour it could happ en that all empt y SA Vs accum ulate at the train stations in the southeast of the
op eration area whereas all v ehicles in other areas are to o busy to accept new ride requests. Consequently , the fleet
w ould b e unable to serv e ride requests in the north w est in time.
3 Study a rea
The sim ulation is based on a real-w orld data set for Berlin in use at T ransp ort System Planning and T ransport
T elematics departmen t of TU Berlin. It includes a 100 % sample of a syn thetic p opulation of Berlin and Branden burg,
a road and rail net w ork and a public transit sc hedule.
The study area sho wn in figure 1 is situated in the b orough of Berlin-Reinic k endorf and consists of Heiligensee and
Konradsh¨ ohe districts and some mostly forest areas of T egel district excluding the cen ter of T egel. It contains mostly
lo w densit y residen tial areas. Figure 2 depicts the public transit lines in the study area. There are four bus lines
op erating in the study area (124, 133, 222 and 324) with headw a ys of 10-30 min during rush hour and 20-30 min
during the rest of the da y . Most agen ts use these buses as a feeder system to reac h T egel station where the hea vy rail
lines S25 and U6 connect to other parts of Berlin. In the base case the public transit sc hedule remained unc hanged.
In all scenarios with shared taxis bus lines 124, 133 and 222 are shortened to terminate outside the study area and
bus line 324 is susp ended.
Starting from the giv en data set, all agen ts with activities inside the study area and all agen ts who pass through
the study area b y car w ere extracted for this study . All in all, 50 000 agen ts (a 100 % sample) w ere included in
4

Figure 1: lo cation of the study area (blue) in Berlin.
the sim ulation of whic h only ab out one half has activities inside the study area. All others are car driv ers who were
included to pro vide realistic road congestion lev els while passing through the study area.
In order to allo w access and egress to t w o ma jor hea vy rail stations in T egel the router uses a shared taxi op eration
area sligh tly larger than the study area used to cut out the syn thetic p opulation. The router op eration area was later
simplified to reduce computation time.
4 Results
The analysis of sim ulation results is divided in to an isolated examination of the shared taxi legs only and an analysis
of tra v el times for the en tire trip including all public transit and w alk legs.
4.1 Sha red taxi p erfo rmance
Scenarios with 1, 4, 8, 12 and 20 seats p er taxi v ehicle were run. Despite the concen tration of transp ort demand
at one ma jor h ub (T egel), more than 8 seats were rarely used. F urthermore, table 2 sho ws that scenarios with less
than 120 v ehicles had rejection rates ρ higher than 5 % no matter ho w man y seats p er v ehicle w ere offered. Av erage
total tra v el time on shared taxis (including w ait) w as roughly equal for all scenarios. Neither priv ate taxi op eration
in scenario D2D 400 Cap1 (1 seat p er v ehicle only) nor an o v ersupply of v ehicles in scenario D2D 1000 Cap4 lead to
an imp ortan t reduction in total tra v el time (including w ait). Analysis then fo cused on the follo wing scenarios: 120
taxis with 8 seats (D2D 120 Cap8), 150 taxis with 8 seats (D2D 150 Cap8), 150 taxis with 4 seats (D2D 150 Cap4)
and 200 taxis with 4 seats (D2D 200 Cap4). These fleet dimensions allo w to k eep the share of rejected ride requests
at or b elo w 5 %.
Due to the shared taxi implemen tation in the DR T-Con tribution, tra v el times differ only sligh tly b et w een scenarios
with differen t taxi fleet sizes. Larger taxi fleets reduce the n um b er of rejected ride requests as more rides can b e serv ed
main taining the time constrain ts. How ev er, larger fleets ha v e little influence on w ait and tra v el times, b ecause the
optimization algorithm tends to sc hedule high w ait times (see 95%-p ercen til of wait times t wait
p 95 only sligh tly b elo w
the maxim um admissible 12 min) and high total tra v el times t r (sum of w ait and in-v ehicle tra v el) while trying to
minimize the time SA Vs are in op eration. So, whenev er p ossible the algorithm will rather bundle ride requests together
in order to sa v e v ehicle op eration time than pro vide higher service qualit y . This is illustrated b y figure 3 whic h shows
5

a b
Figure 2: (a) public transit lines in the base case; (b) public transit lines in all other scenarios; (bac kground map
c
 Op enStreetMap con tributors).
T able 2: Sim ulation results for the shared taxi legs. Scenarios selected for further analysis are highligh ted.
Scenario n um b er of seats rides t wait
av g t wait
p 95 t r
av g d direct d detour d T d U ρ
taxis p er v eh. serv ed [mm:ss] [mm:ss] [mm:ss] [km] [km] [km] [km]
D2D 50 Cap20 50 20 10 109 06:59 11:43 18:10 5.18 1.21 26 724 64 623 0.35
D2D 75 Cap12 75 12 13 563 06:53 11:41 17:58 5.08 1.16 35 648 84 590 0.19
D2D 100 Cap12 100 12 15 920 06:42 11:42 17:55 4.99 1.17 41 344 98 129 0.09
D2D 100 Cap8 100 8 15 807 06:53 11:43 17:56 4.99 1.13 41 292 96 843 0.10
D2D 120 Cap8 120 8 17 151 06:50 11:40 18:05 4.96 1.18 44 684 105 268 0.05
D2D 150 Cap8 150 8 18 024 06:47 11:40 18:13 4.97 1.19 46 454 111 023 0.02
D2D 150 Cap4 150 4 17 238 07:32 11:44 18:15 4.92 1.07 51 646 103 254 0.05
D2D 200 Cap4 200 4 18 258 07:26 11:44 18:28 4.94 1.08 54 809 109 795 0.01
D2D 400 Cap1 400 1 17 214 08:42 12:08 17:40 4.94 0.00 117 546 85 115 0.05
D2D 1000 Cap4 1 000 4 18 668 05:55 11:28 17:42 4.95 1.35 49 015 117 533 0.00
a significan t share of SA Vs o c cupied b y more than one passenger ev en in off-p eak hours, e.g. at midday . Consequently
the n um b er of v ehicles in op eration is reduced to just b et w een one third and one half of the total fleet a v ailable at
midda y . In scenario D2D 1000 Cap4 with 1 000 v ehicles a v ailable no more than 250 are ev er in op eration at the same
time due to the taxi assignmen t algorithm. The high degree of trip bundling b ecomes clear lo oking at the high share
of p o oled trips, i.e. trips with at least one more passenger sharing the vehicle for at least a par t of the route, which is
e.g. 96 % of all trips o v er the da y in scenario D2D 200 Cap4.
As discussed in section 2.2, setting more restrictiv e time constrain ts reduces taxi w ait and tra vel times only sligh tly
while v astly increasing the n umber of rejected ride requests. So given the shared taxi assignmen t algorithm used, there
seems to b e no ob vious w a y to significan tly decrease the a v erage shared taxi w ait and tra vel times without putting
acceptance of shared taxis at risk b y rejecting man y ride requests.
4.2 T ravel times fo r entire trips
After analyzing the shared taxi legs only , in the follo wing the en tire trips b etw een trip origin and trip destination
shall b e examined for all trips concerned b y the substitution of SA Vs for conv en tional buses, that means all completed
6

a
0 20 40 60 80 100
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idle
empty ride
1 pax
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8 pax

b
0 50 100 150
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c
0 50 100 150
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d
0 50 100 150 200
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3 pax
4 pax

Figure 3: v ehicle o ccupancy: (a) D2D 120 Cap8; (b) D2D 150 Cap8; (c) D2D 150 Cap4; (d) D2D 200 Cap4.
public transp ort trips originating or ending inside the study area, including trips which do not include shared taxi
legs. Based on agen t id and the p osition of the trip in the agen t’s daily plan, all trips were assigned a unique iden tifier.
Since the activities, their lo cations and their order did not c hange during sim ulation, eac h of these unique trips has
the same origin, the same destination and a roughly similar departure time in all scenarios. So there is one execution
of the v ery same trip p er scenario, unless the agen t got stuc k e.g. b ecause his shared taxi request w as rejected. T ri ps
whic h w ere not completed in at least one of the scenarios to b e ev aluated w ere excluded from analysis as describ ed in
section 2.1.
18 761 trips completed in eac h scenario remained in the analysis. Dep ending on the shared taxi fleet scenario b et w een
15 602 and 15 749 of these trips (0 in the base case) include at least one shared taxi leg and b et w een 13 936 and
13 965 of these trips (16 301 in the base case) include at least one public transit leg. This means ab out one quarter
of all completed trips do es not include public transit, b ecause there was no suitable public transit service a v ailable,
e.g. b ecause the trip originates and ends inside the shared taxi op eration area where con v en tional public transit was
mostly remo v ed.
Figure 4 sho ws that in comparison to the base case without shared taxis the a v erage total trip tra v el time from origin
to destination is reduced from ab out 53 min b y less than 2 min. The a v erage w alk time decreases by 8 min and the
time sp en t w aiting for or tra v elling on buses or trains is reduced by 2 respectively 7 min, but shared taxi w ait times
of ab out 6 min and tra v el times of ab out 9 min partly mak e up for this. The shared taxi w ait times and tra vel times
do not equal the v alues giv en in table 2, b ecause the av erage illustrated in figure 4 includes trips without shared taxi
legs whic h lo w er the a v erage v alues. T otal time sp en t waiting for and tra v elling on public transit and shared taxis
increases in ev ery scenario in resp ect to the base case. This means the sligh t reduction in trip tra v el time is based only
on the decrease in w alk time and agen ts with trips originating or terminating righ t next to existing bus stops migh t
ev en exp erience higher a v erage trip tra v el times.
One basic assumption b efore sim ulations w ere started w as that shared taxis could allo w to reduce trip tra v el time
sp en t b et w een t w o activit y lo cations b ecause do or-to-do or op eration reduces walk distances and departure times can
b e c hosen more flexibly . How ev er, it seems that do or-to-do or op eration also causes longer detours for shared rides
7

120 taxis, 8 seats
150 taxis, 4 seats
150 taxis, 8 seats
200 taxis, 4 seats
base case
00:00
10:00
20:00
30:00
40:00
50:00 transit_walk
dr t in v ehicle
dr t wait
pt in vehicle
pt wait
total 52:01 total 51:59 total 51:39 total 51:46 total 53:28
04:24
14:56
05:40
09:12
17:47
04:17
14:56
06:15
08:51
17:38
04:17
14:55
05:35
09:19
17:31
04:13
14:54
06:08
09:04
17:25
06:12
21:52
25:23

Figure 4: Av erage trav el times for the en tire trips including w alk and public transit legs and their comp onents [mm:ss].
“drt” and “pt” denote shared taxi resp ectiv ely public transit legs.
whic h con tribute to a noticeable increase in total in-v ehicle time sp en t tra v elling in public transit and shared taxis of
ab out 2 min.
Additionally , the decrease in public transit w ait time is lo w er than exp ected, probably b ecause the lac k of an y pre-
b o oking feature made departure times ev en more unpredictable, so connecting trains w ere often missed. The latter
problem is less visible, b ecause in resp ect to the base case a higher share of agen ts going to the cit y cen ter used the
more frequen t U6 hea vy rail line instead of the less frequen t S25, but actually the preference for the more frequent
rail line could also b e a result of less predictable arriv al times. Before the router w as altered to create more v ariabilit y
(see section 2.1) more agen ts c hose S25 compared to the base case and there w as a significan t increase in public transit
w ait time despite less public transit b oardings, although shared taxis allow for a more flexible departure time c hoice
than con v en tional bus lines. Whereas con v en tional bus lines with fixed sc hedules can b e planned to pro vide transfer to
a defined connecting train (and the connecting train migh t ev en w ait for the bus in some cases), the time constrain ts
for shared taxis allo w for a wide range of departure and arriv al times. F or a direct tra v el time of 10 min and the
parameters α = 1 . 5 and β = 10 min used for this study , the admissible arriv al time has a range of 15 min (see section
2.2) whic h almost equals the headw a y of line S25. So the agen t would ha v e to start 15 min prior to the departure time
necessary for a direct trip and will most lik ely often end up w aiting at the train station for some min utes or more.
The practical range migh t b e smaller in man y cases, how ev er the shared taxi sc heduling adds an additional la y er of
uncertain t y whic h con v en tional buses do not hav e.
5 Cost-b enefit evaluation
Cost calculations for autonomous v ehicles are sub ject to serious uncertainties as autonomous v ehicles ha ve not reac hed
series pro duction y et. Additionally , shared autonomous v ehicles replacing curren t wheelc hair accessible buses w ould
ha v e to cater for unaccompanied passengers with disabilities whereas to da y’s taxi v ehicles are mostly not suited for
wheelc hair users at all. Costs for future fuels or batteries and propulsion systems and future in terest rates remain in
doubt, to o.
Therefore, costs w ere calculated based on existing fossil-fuel-p o wered taxis and articulated buses omitting all driv er-
related costs. The n um b er of buses whic h could b e sa v ed by shortening bus lines as explained in section 3 w as
estimated at 10 articulated buses. A main tenance reserv e of 10 % w as added to the n um b er of buses resp ectively
SA Vs and the total distance driven w as split ev enly among all v ehicles. The calculations assume an in terest rate of
3 %, a life span of 5 y ears for SA V and 12 y ears for articulated buses, purc hasing prices of 28 211.75 e for a 8-seat
SA V, 18 845 e for a 4-seat SA V and 321 000 e for an articulated bus. Bus capital costs (for the vehicle purc hase)
and op eration costs w ere calculated according to F rank et al. (2008) whereas op eration cost for SA Vs is based on data
8

b y Autok ostenc hec k (2017). These op erating and capital costs w ere summed up to ann ual costs presen ted in table 3.
The detailed calculation can b e found in Leic h (2017).
T able 3: Costs and b enefits p er scenario. “∆costs” is the difference b et w een shared taxi costs and con v en tional bus
costs sa v ed. “ U scenar io -∆costs” is the b enefit-cost difference. t r
tr ip,day is the trip tra vel time per day and
∆ t r
tot,y ear is the difference in trip tra v el time p er y ear in comparison to the base case.
Scenario costs ∆costs t r
tr ip,day ∆ t r
tot,y ear requests U r U b U scenario U scenar io -∆costs
[ e /a] [ e /a] [h/day] [h/a] rejected [ e /a] [ e /a] [ e /a] [ e /a]
D2D 120 Cap8 2 645 698 507 169 16 268 -166 258 859 803 024 -302 875 500 149 -7 020
D2D 150 Cap8 2 980 258 841 729 16 153 -208 287 324 1 006 027 -114 239 891 788 50 059
D2D 150 Cap4 2 235 897 97 368 16 257 -170 017 825 821 182 -290 887 530 295 432 927
D2D 200 Cap4 2 621 056 482 527 16 192 -194 045 212 937 237 -74 749 862 488 379 961
base case 2 138 529 / 16 723 / / / / / /
Despite the lo w er degree of capacit y utilization, driv erless articulated buses on con v entional bus lines w ould still b e
c heap er to run than driv erless demand-resp onsiv e shared taxis. Replacing con v entional bus lines, cost increases b y
5 % for 150 shared taxis with 4 seats or 39 % for 150 shared taxis with 8 seats. Ho w ever, the curren t budget allows for
con v en tional buses and driv er-related costs, so the driv er-related costs sav ed b y automation w ould probably allo w to
co v er the additional exp ense for shared taxi op eration. Nev ertheless, it is not clear whether subsidies and fares would
remain on curren t lev els, if automation allo ws for similar service levels at reduced costs. There migh t b e p olitical
pressure to cut subsidies or to increase fares for the more comfortable do or-to-do or shared taxi service. The latter
could cause con tro v ersy as p o or p eople w ould b e left without any more affordable alternativ e.
F or the cost-b enefit ev aluation, tra v el time reductions w ere considered as b enefits U r . Rejected ride requests were tak en
in to accoun t as a 12 min tra v el time increase (maximu m p ermissible wait time w as 12 min) stated as (negativ e) b enefit
U b in table 3. F rom the resulting b enefit p er scenario U scenar io the increase in costs (∆costs) is substracted to obtain
b enefit-cost differences. Only the tw o scenarios with 150 resp ectively 200 taxis with 4 seats eac h had a significan tly
p ositiv e b enefit-cost difference of 432 927 e /a resp ectiv ely 379 961 e /a. Benefit-cost differences are somewhat difficult
to in terpret, b ecause it is not clear what a go o d or bad b enefit-cost difference w ould b e for the pro ject and ho w m uc h
b enefit is obtained p er eac h e sp en t. Ho w ev er, a classical b enefit-cost ratio cannot b e calculated, b ecause there is no
real in v estmen t here. An approximation to something lik e a b enefit-cost ratio is to divide the b enefit from trav el time
sa vings b y the ann ual costs giv en ab o v e, ev en though op eration costs are usually subsumed as (negative) benefit. This
giv es a ratio of 5.5 for 150 4-seat SA Vs and 1.8 for 200 4-seat SA Vs and ab out 1 for the other t w o scenarios.
T able 4: Benefit-cost differences for v arying SA V costs.
Scenario b enefit-cost difference [ e /a] for a v ariation of SA V costs by
-30 % -20 % -10 % -5 % +/- 0 % +5 % +10 % +20 % +30 %
D2D 120 Cap8 786689 522120 257550 125265 -7020 -139305 -271590 -536160 -800729
D2D 150 Cap8 944136 646111 348085 199072 50059 -98954 -247967 -545993 -844018
D2D 150 Cap4 1103696 880106 656517 544722 432927 321132 209337 -14252 -237842
D2D 200 Cap4 1166277 904172 642067 511014 379961 248908 117855 -144250 -406356
The most doubtful asp ect in the cost-b enefit ev aluation seem to b e SA V costs. T able 4 sho ws the influence of v arying
SA V costs on b enefit-cost differences. F or sligh t v ariations in SA V costs there is no ma jor change, ho w ev er at a 20 %
or more increase in SA V costs all scenarios seem disadv an tageous. Suc h a high misestimation cannot b e excluded giv en
the uncertain ties men tioned ab o v e.
6 Conclusion
All in all, the sim ulation suggests that the substitution of con v en tional bus lines with shared taxis could ha ve some
b enefits for the passengers at a reasonable cost for the op erators. Ho w ever, the adv an tages seem to b e smaller than
exp ected. An enhanced shared taxi routing algorithm might impro v e the case for shared taxis, but some issues would
probably remain. Do or-to-do or op eration app ears to reduce w alk distances, but would lik ely increase detours to serv e
other passengers. It seems that shared taxis tend to ha v e unpredictable departure and trav el times if routes are altered
to add another passenger while others are already on the taxi. F urthermore, shared taxis could remain more exp ensive
to op erate, esp ecially if the taxi routing algorithm w ould b e altered to pro vide lo wer w ait times b y bundling less
rides.
9

Nev ertheless, should priv ate ridesharing op erators en ter the mark et as comp etitors of public transp ort, decreasing
passenger n um b ers could mak e con v entional bus lines less profitable, creating a vicious circle of reducing costs by
reducing services and falling passenger v olumes. So on the long run the case for shared taxis could impro v e and public
transp ort authorities migh t ha v e no other c hoice than to partner with ridesharing companies or op erate shared taxis
themselv es.
F uture studies could in v estigate mo de choice effects as w ell as com binations of con v en tional bus and shared taxi
services, e.g. k eeping conv en tional bus lines during the da y and replacing them with shared taxis only during the night
or only on ligh tly used lines suc h as line 324 in the study area.
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