Introduction

On-DemandRideHailing

1

Introduction

On-DemandRideHailing

2

FromStreetHailingtoOn-DemandRideHailing

Streethailing On-demandridehailing

•  lack of information sharing with commuters

•  fast, flexible, convenient

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Introduction

IsOn-DemandRideHailingMoreEfficient?

•  “The Shanghai city government bans the use of taxi-booking

apps by cab drivers during rush hours.” —Rose Yu. The Wall Street Journal. 2014. •  “People waiting on Manhattans Fifth Avenue in the middle of rush

hour, don’t need an app to tell cabs to come to the area.” - Joseph Steinberg. Forbes. 2012. •  New York City Taxi and Limousine Commission (T&LC) maintain a

certain number of taxis dedicated to street hailing through Street Hail Livery (SHL).

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Research Question

ResearchQuesBons

1

2

3

v.s.

•  Which matching mechanism is more efficient in terms of passengers' average waiting time? -  Build models to study the street-hailing and on-demand ride hailing

systems. -  Identify the advantage and disadvantage of the two matching

mechanisms -  How to approximate of the two mechanisms using M/M/k queueing

systems?

•  How to address the inefficiency of on-demand ride hailing mechanism?

Street hailing On-demand ride hailing

5

Research Question

RelatedLiterature

Sharing economy Benjaafar et al.(2015) Fraiberger and Sundararajan (2015) Jiang and Tian (2015)

Vehicle routing Spivey and Powell (2004) Meyer and Wolfe (1961) McLeod (1972) Bailey and Clark (1992)

Matching Allon et al. (2012) Cullen and Farronato (2014) Anderson et al. (2015) Hu and Zhou (2016)

On-demand platform staffing and pricing

Gurvich et al. (2015) Taylor (2016) Cachon et al. (2015) Fraiberger et al. (2015) Riquelme et al. (2015) Tang (2016)

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Model

ModelSetup:TransportaBonSystemonaCircularRoad

A circular road with perimeter R.

•  Passengers arrive according to a Poisson process with rate λ •  The location of each arrival is uniformly distributed •  The duration of each trip follows an exponential distribution

with mean 1/µ•  Taxis have a constant speed of one

k taxis

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MatchingMechanismsforStreetHailingandOn-DemandRideHailing

Street hailing On-demand ride hailing

Matched to nearest available taxi No matching until a taxi is passing by a passenger.

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One Direction No-Call/Call Systems

OneDirecBonNo-CallSystem (StreetHailing)

Utilization Utilization

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The average waiting time of the one direction no-call system is increasing in the utilization λ/(kμ)

Longer waiting time with higher road length R

Shorter waiting time with more taxis in the system

One Direction No-Call/Call Systems

OneDirecBonCallSystem (On-demandRideHailing

Utilization Utilization

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The average waiting time of the one direction call system is not always monotone in the utilization λ/(kμ)

The non-monotonicity is more significant with higher road length R.

Shorter waiting time with more taxis in the system

DecomposePassengers’WaiBngTime

Arrival Dispatch Pick-up Drop-off

Enroute On-trip Response

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DecomposePassengers’WaiBngTime

Arrival Dispatch Pick-up Drop-off

Enroute On-trip Response

A passenger’s waiting time consists of two parts:

-  Response time: Time before a ride request is responded. -  Enroute time: Time a taxi spent to approach a passenger.

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OneDirecBonCallSystem:Non-monotonicity

•  Enroute time is non-monotone in utilization, and it peaks at medium utilization level.

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ecom

posi

tion

Waiting Time = Response Time + Enroute time

Utilization

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WhenUBlizaBonisLow

Enroute time becomes smaller when a lot of taxis are idle

Medium utilization Low utilization

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WhenUBlizaBonisHigh

Enroute time becomes smaller when a lot of passengers are waiting

Medium utilization High utilization

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WhenUBlizaBonisMedium

•  Enroute time is the highest when the system is balanced. •  Taxis spend too much time in picking up passengers •  Passengers have to wait for longer time •  The inefficiency is most significant when R is large

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Utilization

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ComparisonofOneDirecBonCall/No-CallSystems

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R = 50, k = 20

call system

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R = 200, k = 20

call system

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One direction no-call system leads to smaller average waiting time compared to the call system

TwoDirecBonNo-Call/ CallSystems

No-CallSystem CallSystem

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Aver

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The average waiting time is increasing in the utilization

The average waiting time is not always monotone in the utilization

ComparisonofTwoDirecBonCall/No-CallSystems

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R = 50, k = 20

call system

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no−call system

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R = 200, k = 20

call system

The no-call system is more efficient when the utilization is in the middle range.

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Utilization

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The two direction call system is not always more efficient than the two direction no-call system

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TwoDimensionalGridNetwork

m

n

Number of horizontal roads

Number of vertical roads

TwoDimensionalGridNetwork

The disadvantage of street hailing is more significant with the increase of the road complexity

Increase the number of roads

m = n = 5 m = n = 10 m = n = 15

Utilization Utilization Utilization

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k = 500

TwoDimensionalGridNetwork

The disadvantage of on-demand ride hailing is more significant with the increase of number of taxis k

Increase number of taxis

k = 100 k = 300

Utilization Utilization Utilization

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ApproximaBon:M/M/kQueuewithStateDependentServiceRate

•  State: Number of passengers n in the system •  Arrival Rate: •  Expected Extended Service time:

•  State Dependent Service Rate：

�n = �

µn =

(n

1/µ+EET , if n k,k

1/µ+EET , if n > k.

1

µ+ Expected Enroute Time (EET)

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On-demand ride hailing Street hailing

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Utilization

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Utilization

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Utilization

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Utilization

One-Direction

Two-Direction

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DisadvantageofOn-demand/StreetHailingSystems

Ondemandridehailing(call)•  The match may not be

efficient enough since

-  the taxi may encounter other incoming passengers before reaching the matched passenger

-  the passenger may be more close to a taxi that becomes available after the matching.

Streethailing(no-call)•  A taxi near a passenger

could be driving in the opposite direction.

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Utilization 25

DisadvantageofOn-demand/StreetHailingSystems

Ondemandridehailing(call)•  The match may not be

efficient enough since

-  the taxi may encounter other incoming passengers before reaching the matched passenger

-  the passenger may be more close to a taxi that becomes available after the matching.

Streethailing(no-call)•  A taxi near a passenger

could be driving in the opposite direction.

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Utilization How to alleviate disadvantages of both systems?

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HowtoAlleviateDisadvantagesofBothSystems?

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call system

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R = 200, k = 20call systemc c

Match if the nearest taxi is within within the distance C

Do not match if the nearest taxi is out of the distance C

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Response Cap If the nearest passenger-vehicle has a distance no larger than a fixed cap C, then match them; otherwise, do not match them.

HowtoAlleviateDisadvantagesofBothSystems?

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call system

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R = 200, k = 20call systemc c

Match if the nearest taxi is within within the distance C

Do not match if the nearest taxi is out of the distance C

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Response Cap If the nearest passenger-vehicle has a distance no larger than a fixed cap C, then match them; otherwise, do not match them.

HowtoAlleviateDisadvantagesofBothSystems?

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45

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R = 50, k = 20

call system

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call system

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Utilization

An on-demand ride hailing system with a response cap could outperform both street hailing and on-demand ride hailing without a cap.

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Two Direction Systems

HeurisBcCap

•  The probability that it takes longer than x for a taxi to encounter a passenger is

•  The expected distance to drive before encountering a later

arrived passenger:

•  Heuristic Cap:

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Utilization0

50%

100%

150%

200%

Extra

ave

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w

aitin

g tim

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no−call system call system

heuristic distance cap

min{R/2,

r⇡R

2�}

Z 1

0exp(

��x

2

2R

)dx =

r⇡R

2�

P (N = 0) = exp(��x

2

2R)

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Two Direction Systems

Performance Difference Compared to the Optimal Capped System

0

50%

100%

150%

200%

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time

%

no−call system

Utilization

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time

%

Extra

ave

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time

%

Utilization Utilization

R=100, k=10 R=100, k=20

R=100, k=30

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Summary •  On demand ride hailing may result in higher waiting time than street

hailing. It is more likely to happen when –  the road is long, –  the utilization level is in the middle range. –  many taxis in the system. –  roads are not very complex.

•  Enroute time is high when the system is balanced. –  Passengers’ average waiting time in on-demand ride hailing can be

non-monotone in system utilization –  Taxis spend too much time in picking up passengers –  A driver may miss the chance to serve another incoming passenger

who is in a shorter distance in the call system

•  A proper distance cap can reduce passengers’ average waiting time.

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Thankyou!

33

M/M/kQueueingApproximaBon

•  StreetHailing:One/Two-direcBon

µn =

(n

1/µ+R/(k�n+2) , if n k,k

1/µ+R/(n�k+1) , if n > k.

•  On-demand Ride Hailing -- One-direction -- Two-direction

µn =

(n

1/µ+R/2/(k�n+2) , if n k,k

1/µ+R/2/(n�k+1) , if n > k.

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µn

=

8<

:

n

1/µ+

RR

0 (R�x

R

)k�n+1exp

⇣� (n�1)µx

2

2R

⌘dx

, n k,

k

1/µ+

RR

0 (R�x

R

)n�k

exp

⇣��x

22R

⌘dx

. n > k.

One/TwoDirecBonApproximaBon

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OneDirecBonApproximaBonOn-demandRideHailing

StreetHailing

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Utilization

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Utilization

µn

=

8<

:

n

1/µ+

RR

0 (R�x

R

)k�n+1exp

⇣� (n�1)µx

2

2R

⌘dx

, n k,

k

1/µ+

RR

0 (R�x

R

)n�k

exp

⇣��x

22R

⌘dx

, n > k.

µn =

(n

1/µ+R/(k�n+2) , if n k,k

1/µ+R/(n�k+1) , if n > k.

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TwoDirecBonApproximaBonOn-demandRideHailing

StreetHailing

Aver

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Tim

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Utilization

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age

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ting

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Utilization

µn

=

8<

:

n

1/µ+

RR

0 (R�x

R

)k�n+1exp

⇣� (n�1)µx

2

2R

⌘dx

, n k,

k

1/µ+

RR

0 (R�x

R

)n�k

exp

⇣��x

22R

⌘dx

, n > k.

µn =

(n

1/µ+R/2/(k�n+2) , if n k,k

1/µ+R/2/(n�k+1) , if n > k.

37