Adoption of dynamic ridesharing system under influence of information on social network

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Transportation Research Procedia 37 (2019) 401–408 www.elsevier.com/locate/procedia st 21 EURO Group onon Transportation Meeting, EWGT 2018, 17th 17-19 – 19th September 21st EUROWorking Working Group Transportation Meeting, EWGT 2018, September2018, 2018, 21st EURO Working Group on Transportation Meeting, EWGT 2018, 17-19 September 2018, Braunschweig, Germany Braunschweig, Germany Braunschweig, Germany

Adoption of dynamic ridesharing system under influence of Adoption of dynamic ridesharing system under influence of information on social network information on social network Phathinan Thaithatkulaa*, Toru Seobb, Takahiko Kusakabeaa, Yasuo Asakurabb Phathinan Thaithatkul *, Toru Seo , Takahiko Kusakabe , Yasuo Asakura

The Center for Spatial Information Science, the University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8568, Japan b The Center Spatial Information Science, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8568, Japan School offor Environment and Society, Tokyothe Institute of Technology, 2-12-1 Ookayama, Mekuro-ku, Tokyo 152-8552, Japan b School of Environment and Society, Tokyo Institute of Technology, 2-12-1 Ookayama, Mekuro-ku, Tokyo 152-8552, Japan

a a

Abstract Abstract In an era of highly developed information and communication technologies, social networks play an important role in all aspects In era of highly developed information and communication technologies, socialwhich networks an important role in allcan aspects of an businesses, including transportation. The use of dynamic ridesharing systems, are play systems in which travelers find of businesses, including transportation. usetime, of dynamic ridesharing systems, which areinformation systems in propagated which travelers can find partner(s) to share their upcoming rides The in real is also expected to be affected by the by friends on partner(s) to shareIntheir rides in realhow time, is also expectedintoboth be affected by the information propagated by friends on social networks. this upcoming study, we investigate such information online and offline social networks affects travelers’ social networks. In this study, we investigate such information both online offline social networks travelers’ decisions pertaining to ridesharing over days.how Because travelers caninchoose whichand information to obtain, weaffects also investigate decisions pertaining to ridesharing overfrom days. Because travelers can choose to obtain, we also investigatea whether the information collected only nearby friends (in physical space) which affectsinformation their decisions. To do this, we formulate whether thebehavior-based information collected only from nearby friends (in physical space) affectsfrom theirthe decisions. To experiments, do this, we formulate day-to-day model of a dynamic ridesharing system. Results obtained numerical which area day-to-day model of athat dynamic ridesharing system. Resultsonobtained from the the numerical experiments, whichhas, are based on thebehavior-based formulated model, show with the information propagation social networks, more friends that a traveler based on theisformulated show who that with the information propagation the greater the numbermodel, of travelers use dynamic ridesharing systems.on social networks, the more friends that a traveler has, the greater is the number of travelers who use dynamic ridesharing systems. © 2019 The Authors. Published by Elsevier Ltd. © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The under Authors. Published by Elsevier B.V. Peer-review responsibility of the scientific of the 21stof EURO Group on Transportation Meeting. st Selection and peer-review under responsibility of thecommittee scientific committee the 21Working EURO Working Group on Transportation Meeting, Peer-review the scientific committee of the 21st EURO Working Group on Transportation Meeting. EWGT 2018,under 17th –responsibility 19th Septemberof2018, Braunschweig, Germany. Keywords: Dynamic ridesharing system; day-to-day behavior adjustment; social network; information propagation Keywords: Dynamic ridesharing system; day-to-day behavior adjustment; social network; information propagation

1. Introduction 1. Introduction A dynamic ridesharing system (DRS) is a system in which travelers can find a partner(s) with whom to share their A dynamic ridesharing (DRS) is studies a systemhave in which travelers find aaspartner(s) with whom (SO) to share their upcoming personal trip in system real time. Many developed DRScan models social optimization models. upcoming personal trip in real time. Many studies have developed DRS models as social optimization (SO) models. The SO solution is generally assigned for travelers to achieve the maximum social benefits, such as to minimize the The SO solution is generally assigned achieve the maximum benefits, suchthe as SO to minimize the total vehicle miles traveled (Agatz et for al., travelers 2012). Intopractice, travelers may social not always follow assignment. total vehicle miles traveled (Agatz et al., 2012). In practice, travelers may not always follow the SO assignment. Rather, they will maximize the individual (expected) utility. Travelers may change their behavior (e.g., travel mode) Rather, they will maximize the individual (expected) utility. Travelers may change their behavior (e.g., travel mode) * Corresponding author. * Corresponding E-mail address:author. [email protected] E-mail address: [email protected] 2352-1465 © 2018 The Authors. Published by Elsevier B.V. 2352-1465 2018responsibility The Authors. of Published by Elsevier B.V.of the 21st EURO Working Group on Transportation Meeting. Peer-review©under the scientific committee Peer-review under responsibility of the scientific committee of the 21st EURO Working Group on Transportation Meeting. 2352-1465  2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 21st EURO Working Group on Transportation Meeting, EWGT 2018, 17th – 19th September 2018, Braunschweig, Germany. 10.1016/j.trpro.2018.12.209

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Phathinan Thaithatkul et al. / Transportation Research Procedia 37 (2019) 401–408 Phathinan Thaithatkul et al. / Transportation Research Procedia 00 (2018) 000–000

over days based on what they have experienced or perceived from different sources of information. Some studies have developed a day-to-day behavior-based model of DRS to track the changes in travelers’ behavioral patterns. Djavadian and Chow (2016) modeled a flexible transport service (involving ridesharing) to evaluate their vehicle operational policies when travelers can change travel mode and departure time choice decisions over days. Thaithatkul et al. (in press) developed a model specifically for DRS to investigate the evolution of DRS in terms of its adoption when travelers can change their travel mode and ridesharing partner choices. In their model, every traveler makes decisions based on information about the DRS performance provided by the system and personal experience. Social networking plays an important role in ridesharing transport, where most ridesharing trips are formed, e.g., between friends (Amey, 2011). Some studies have proposed the incorporation of the matching algorithm with the social network in order to increase the successful matching rate (Cici et al., 2014; Wang et al., 2017). In addition, information propagation on social networks was investigated to determine its influence on individuals’ behavior (Ngai et al., 2015), such as their purchase behavior (Pookulangara and Koesler, 2011), activity-travel behavior (Carrasco et al., 2008), and ridesharing behavior. Because travelers may obtain different types of information depending on an individual’s social network, their behaviors are also expected to be different. It is difficult to predict a traveler’s behavior with respect to the use of DRS without understanding the effects of information propagation on social networks. However, such effects have not yet been investigated in the DRS context. In this study, we focus on the long-term adoption level of DRS, where information of DRS can be propagated and perceived by travelers through individual social networks. A social network is defined as a set of individuals connected by social relationships (including offline and online social networks) in which information can be spread via some means of communication, such as face-to-face interaction for offline social networks, and information and communications technology (ICT) for online social networks (Kempe et al., 2003). Our first objective is to investigate the effects of information sharing on social networks with respect to the evolution of DRS adoption. The second objective is to investigate whether the information collected only from spatially close friends in the physical space— friends who have similar origins and destinations (OD)—has a different influence on a traveler’s decision in terms of ridesharing, compared with information obtained from any friend. To do this, the model proposed by Thaithatkul et al. (in press) is extended in Section 2 by enabling users to collect information from their friends in social networks instead of being informed about the same information by the system. Based on the formulated model, numerical experiments are presented in Section 3 to achieve the objectives. In addition, for practitioners, the formulated model can also be used to predict the long-term DRS adoption as well as for evaluations, considering operational policy. 2. Model development 2.1. Framework The framework is the same as that proposed by Thaithatkul et al. (in press); that is, a behavior-based DRS is a service that gathers potential users and facilitates the matching process in real time before a trip (i.e., the user’s behavior is not controlled, and en-route matching is not considered). Users are travelers who consider ridesharing by using DRS to find a partner in real time for their upcoming trip. A user’s decision process within each day is: choose to use DRS to find a partner (mode choice), then choose a partner. The actual matching is then a spontaneous result of the user’s decision regarding the choice of partner. The waiting choice, which is when a desired partner has not yet been found, is also considered by a repeating mode choice. In other words, the user may stop using DRS to find a ridesharing partner at any time, and instead opt to travel by other travel mode. 2.2. Key assumptions (a) For-hire vehicles with two passenger seats are used as a means of transport (e.g., shared autonomous vehicle). (b) The travel demand is assumed to be homogeneous during a certain period of time (e.g., peak hours)—the same travelers appear in the transport system every day—where users intermittently and randomly appear in the transport system in some sequence.



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(c) A user is rational and makes decisions (travel mode and partner choices) by maximizing the individual expectationof-utility, which is a utility that a user expects to receive at a given time of the day. The expectation-of-utility is used because the user has incomplete information about other users’ arrival times (owing to their random arrival). (d) The utility is evaluated using monetary-based factors that are affected by ridesharing, and is dependent on the partner’s OD and arrival time: cost of in-vehicle travel time, travel fare, and penalty for excessive travel time. (e) The penalty for excessive travel time is a cost that is incurred when a user travels longer than her/his acceptable travel time, which monotonically increases with excessive travel time. (f) The individual expectation-of-utility can be updated using the day-to-day behavior adjustment process. Specifically, it is updated by new information that can be obtained from two sources: new private ridesharing experience, and information collected from friends on social network who have similar ODs. Assumptions (a) - (e) are the same as those by Thaithatkul et al. (in press). The influence of information propagated on a social network is incorporated into the model in assumption (f). More specifically, a social network is a network of social relationships among users. A friend of a user is a person who has a direct social relationship, and who is directly connected to that user on a social network. Because a user may have time and memory limitations, that user may collect information only from specific friends. A set of friends from whom a user collects information is then assumed to contain a certain number of friends whose ODs are close to the user in physical space (within a specified distance). The information that is shared among friends is assumed as the information of expectations on DRS (e.g., expectation of fare reduction by ridesharing) in order to consider information propagated through friend-of-friend connections. A user can obtain such information by communicating using ICT or face-to-face interactions. 2.3. Model formulation The model formulation is divided into two parts. One is a within-day model (Section 2.3.1) that includes the utility function, expectation-of-utility function, travel mode choice decision, and partner choice decision. Another one is a day-to-day model (Section 2.3.2) that includes the behavior adjustment process and information collection from friends (i.e., an extension of the model proposed by Thaithatkul et al., in press). 2.3.1. Within-day model The utility of user 𝑖𝑖 ridesharing with any user 𝑗𝑗 at time 𝑡𝑡 on day 𝑘𝑘 is denoted by 𝑣𝑣𝑖𝑖,𝑘𝑘 (𝑗𝑗, 𝑡𝑡), where 𝑖𝑖 and 𝑗𝑗 are the members of a user’s arrival sequence 𝑺𝑺𝑘𝑘 . It is defined as the following deterministic function, 𝑣𝑣𝑖𝑖 (𝑗𝑗, 𝑡𝑡) = −𝑔𝑔𝑖𝑖 (𝑗𝑗) − 𝑓𝑓𝑖𝑖 (𝑗𝑗) − 𝑑𝑑𝑖𝑖 (𝜏𝜏𝑖𝑖 (𝑡𝑡) + 𝑥𝑥𝑖𝑖 (𝑗𝑗), 𝑇𝑇𝑇𝑇𝑖𝑖∗ )

for ∀𝑖𝑖, 𝑗𝑗 ∈ 𝑺𝑺.

(1)

𝐸𝐸𝐸𝐸𝑖𝑖 (𝑡𝑡) = −𝐸𝐸𝐸𝐸𝑖𝑖 − 𝐸𝐸𝐸𝐸𝑖𝑖 − 𝑑𝑑𝑖𝑖′ (𝜏𝜏𝑖𝑖 (𝑡𝑡), 𝐸𝐸𝐸𝐸𝑖𝑖 + 𝐸𝐸𝐸𝐸𝑖𝑖 , 𝑇𝑇𝑇𝑇𝑖𝑖∗ )

for ∀𝑖𝑖 ∈ 𝑺𝑺.

(2)

Note that for simplicity, a subscript 𝑘𝑘 indicating the day is omitted throughout the within-day model formulation. Let 𝑔𝑔𝑖𝑖 (𝑗𝑗) and 𝑓𝑓𝑖𝑖 (𝑗𝑗) denote user 𝑖𝑖’s cost of the in-vehicle travel time and travel fare, respectively, which are the costs that are subject to detours required to rideshare with user 𝑗𝑗. The ridesharing travel fare is usually lower than that of traveling alone, which is the only benefit of ridesharing for travelers in this study. Function 𝑑𝑑𝑖𝑖 (∙) is a function of the penalty for excessive travel time, which can be incurred if the total travel time is longer than his acceptable total travel time, which is denoted as 𝑇𝑇𝑇𝑇𝑖𝑖∗ . The total travel time includes the time spent finding a partner and the in-vehicle travel time, which are denoted by 𝜏𝜏𝑖𝑖 (𝑡𝑡) and 𝑥𝑥𝑖𝑖 (𝑗𝑗), respectively. 𝑣𝑣𝑖𝑖 (𝑖𝑖, 𝑡𝑡) denotes the utility of user 𝑖𝑖 traveling alone at time 𝑡𝑡. Note that these functions must be specified by other models such as the discomfort cost of ridesharing for 𝑔𝑔𝑖𝑖 (𝑗𝑗), the fare system for 𝑓𝑓𝑖𝑖 (𝑗𝑗), the schedule delay for 𝑑𝑑𝑖𝑖 (∙), and the vehicle operational model for 𝑥𝑥𝑖𝑖 (𝑗𝑗) (see Section 3.1 for the specification used in the numerical experiments). The expectation-of-utility for ridesharing of day 𝑘𝑘 is denoted by 𝐸𝐸𝐸𝐸𝑖𝑖 (𝑡𝑡) and formulated similar to Equation 1 as Let 𝐸𝐸𝐸𝐸𝑖𝑖 , 𝐸𝐸𝐸𝐸𝑖𝑖 , 𝐸𝐸𝐸𝐸𝑖𝑖 , and 𝐸𝐸𝐸𝐸𝑖𝑖 be the expectations for ridesharing on 𝑔𝑔𝑖𝑖 (𝑗𝑗), 𝑓𝑓𝑖𝑖 (𝑗𝑗), 𝜏𝜏𝑖𝑖 (𝑡𝑡), and 𝑥𝑥𝑖𝑖 (𝑗𝑗) of day 𝑘𝑘, respectively. Note that the penalty for an excessive travel time in Equation (2) is different from that in Equation (1), where time 𝜏𝜏𝑖𝑖 (𝑡𝑡) is considered in addition to the expectation of the total travel time. This is to represent a decrease of 𝐸𝐸𝐸𝐸𝑖𝑖 (𝑡𝑡) over

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the time spent finding a partner. These expectation variables are realized through the day-to-day behaviour adjustment process (explained in Section 2.3.2), which are constant for each day 𝑘𝑘. The expectation-of-utility for riding alone is assumed to be known equal to 𝑣𝑣𝑖𝑖 (𝑖𝑖, 𝑡𝑡) as a conventional travel mode. Let 𝜙𝜙𝑖𝑖 (𝑡𝑡) be a decision on the use of the DRS (travel mode choice) of user 𝑖𝑖 at time 𝑡𝑡, and let the matching process be executed at every ∆𝑡𝑡 interval to involve new users (each matching is called round 𝑟𝑟). Based on the (expected) utility maximization concept, a decision on the use of DRS is given deterministic, where user 𝑖𝑖 will use DRS (𝜙𝜙𝑖𝑖 (𝑡𝑡) = 1) only if matching with someone in the next matching (at time 𝑡𝑡 + Δ𝑡𝑡) is expected to be better than immediately traveling alone (i.e., 𝐸𝐸𝐸𝐸𝑖𝑖 (𝑡𝑡 + 𝛥𝛥𝛥𝛥) > 𝑣𝑣𝑖𝑖 (𝑖𝑖, 𝑡𝑡)). Otherwise, user 𝑖𝑖 will not use DRS, and will immediately make a trip alone (𝜙𝜙𝑖𝑖 (𝑡𝑡) = 0). When a user makes a trip alone, the following information is recorded: actual travel mode 𝜙𝜙𝑖𝑖𝑒𝑒 , time exiting DRS 𝑡𝑡𝑖𝑖𝑒𝑒 , time spent in DRS 𝜏𝜏𝑖𝑖𝑒𝑒 , and utility 𝑣𝑣𝑖𝑖 (𝑖𝑖, 𝑡𝑡𝑖𝑖𝑒𝑒 ). With respect to the partner choice for users who decide to use DRS, decision strategy is to match with the user who maximizes his/her utility at the present time 𝑡𝑡. Consequently, the spontaneous matching result can reach the so-called stable matching (Gale and Shapley, 1962), which is a set of matching pairs where no one can increase the utility by changing the partner, if it is possible. Moreover, matching with that partner must be better than immediately traveling alone 𝑣𝑣𝑖𝑖 (𝑖𝑖, 𝑡𝑡) as well as waiting for the next matching round 𝐸𝐸𝐸𝐸𝑖𝑖 (𝑡𝑡 + Δ𝑡𝑡). To represent this matching process for each round 𝑟𝑟, we employ the static one-to-one passenger matching (Thaithatkul et al., 2015), which is a modification of the stable roommate problem (Knuth, 1997). The stable matching is obtained by using the algorithm proposed by Irving (1985) if it exists; otherwise, the matching result will be a matching with oneself. As a result of the above described matching process, at each round 𝑟𝑟, user 𝑖𝑖 will be matched with a partner denoted by 𝑚𝑚𝑖𝑖𝑟𝑟 . In the case of 𝑚𝑚𝑖𝑖𝑟𝑟 = 𝑗𝑗, where 𝑖𝑖 ≠ 𝑗𝑗, it represents a ridesharing pair (a solution of stable matching). In other words, both of them prefer to rideshare together, and are called ridesharing users. A user with a successful matching then stops seeking a partner, and starts to rideshare with the matched partner. The following information is recorded: actual matched partner 𝑚𝑚𝑖𝑖𝑒𝑒 , actual travel mode 𝜙𝜙𝑖𝑖𝑒𝑒 , successful matching time 𝑡𝑡𝑖𝑖𝑒𝑒 , time spent in DRS 𝜏𝜏𝑖𝑖𝑒𝑒 , and utility 𝑣𝑣𝑖𝑖 (𝑚𝑚𝑖𝑖𝑒𝑒 , 𝑡𝑡𝑖𝑖𝑒𝑒 ). Note that the matched partner of user 𝑖𝑖 can differ over days depending on the arrival sequence 𝑺𝑺 of each day 𝑘𝑘. For 𝑚𝑚𝑖𝑖𝑟𝑟 = 𝑖𝑖, it means that user 𝑖𝑖 is not stably matched with anyone in the current matching round. User 𝑖𝑖 then makes a decision about whether to wait for the next matching by repeating the mode choice. 2.3.2. Day-to-day model For each day, every user updates her/his expectations for decision making on day 𝑘𝑘 using the same behavior adjustment process as follows. For user 𝑖𝑖, 𝑔𝑔

(3)

𝑒𝑒 ) + (1 − 𝛾𝛾𝑘𝑘 )𝛼𝛼̅𝑘𝑘−1 𝑓𝑓(𝑖𝑖) ] + (1 − 𝛽𝛽𝑘𝑘 )𝐸𝐸𝐸𝐸𝑘𝑘−1 , 𝐸𝐸𝐸𝐸𝑘𝑘 = 𝛽𝛽𝑘𝑘 [𝛾𝛾𝑘𝑘 𝑓𝑓(𝑚𝑚𝑘𝑘−1

𝑓𝑓

(4)

𝑒𝑒 𝑥𝑥 ) + (1 − 𝛾𝛾𝑘𝑘 )𝛼𝛼̅𝑘𝑘−1 𝑥𝑥(𝑖𝑖) ] + (1 − 𝛽𝛽𝑘𝑘 )𝐸𝐸𝐸𝐸𝑘𝑘−1 , 𝐸𝐸𝐸𝐸𝑘𝑘 = 𝛽𝛽𝑘𝑘 [𝛾𝛾𝑘𝑘 𝑥𝑥(𝑚𝑚𝑘𝑘−1

(6)

𝑒𝑒 ) + (1 − 𝛾𝛾𝑘𝑘 )𝛼𝛼̅𝑘𝑘−1 𝑔𝑔(𝑖𝑖) ] + (1 − 𝛽𝛽𝑘𝑘 )𝐸𝐸𝐸𝐸𝑘𝑘−1 , 𝐸𝐸𝐸𝐸𝑘𝑘 = 𝛽𝛽𝑘𝑘 [𝛾𝛾𝑘𝑘 𝑔𝑔(𝑚𝑚𝑘𝑘−1

𝑒𝑒 + (1 − 𝛾𝛾𝑘𝑘 )𝜏𝜏̅𝑘𝑘−1 ] + (1 − 𝛽𝛽𝑘𝑘 )𝐸𝐸𝐸𝐸𝑘𝑘−1 , 𝐸𝐸𝐸𝐸𝑘𝑘 = 𝛽𝛽𝑘𝑘 [𝛾𝛾𝑘𝑘 𝜏𝜏𝑘𝑘−1

𝛽𝛽 𝛽𝛽𝑘𝑘 = { 0 𝛾𝛾 𝛾𝛾𝑘𝑘 = {1 0

𝑒𝑒 = 1 𝑜𝑜𝑜𝑜 |𝑯𝑯∗ | > 0, 𝑖𝑖𝑖𝑖 𝜙𝜙𝑘𝑘−1 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒,

𝑒𝑒 𝑖𝑖𝑖𝑖 𝜙𝜙𝑘𝑘−1 = 1 𝑎𝑎𝑎𝑎𝑎𝑎 |𝑯𝑯∗ | > 0, 𝑒𝑒 𝑖𝑖𝑖𝑖 𝜙𝜙𝑘𝑘−1 = 1 𝑎𝑎𝑎𝑎𝑎𝑎 |𝑯𝑯∗ | = 0, 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒.

(5)

(7)

(8)

Note that the subscript 𝑖𝑖 is omitted throughout day-to-day model formulation for simplicity. A user adjusts his/her behavior according to new information obtained by updating his/her previous expectations of day 𝑘𝑘 − 1 (second terms in Equations (3) – (6)) with new information (first terms) using the exponential moving average with update rate 𝛽𝛽𝑘𝑘 (where 0 ≤ 𝛽𝛽𝑘𝑘 ≤ 1 ) if such information exists. The new information is obtained from the private ridesharing



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experience (first terms in brackets) and information collected from friends (second terms in brackets) on day 𝑘𝑘 − 1 as a weighted sum with rate 𝛾𝛾𝑘𝑘 and (1 − 𝛾𝛾𝑘𝑘 ), respectively (where 0 ≤ 𝛾𝛾𝑘𝑘 ≤ 1). However, if any one of these two 𝑔𝑔 𝑓𝑓 information sources is not available, users adjust behavior based entirely on the other one. Let 𝛼𝛼̅𝑘𝑘−1 , 𝛼𝛼̅𝑘𝑘−1 , 𝜏𝜏̅𝑘𝑘−1 , and 𝑥𝑥 ∗ 𝛼𝛼̅𝑘𝑘−1 denote collected information for 𝐸𝐸𝐸𝐸𝑘𝑘 , 𝐸𝐸𝐸𝐸𝑘𝑘 , 𝐸𝐸𝐸𝐸𝑘𝑘 , and 𝐸𝐸𝐸𝐸𝑘𝑘 , respectively; and let 𝑯𝑯 denote user 𝑖𝑖’s set of friends from whom s/he collects information. Specifically, 𝑯𝑯∗ is a set of some friends of user 𝑖𝑖 on social network who are close to the user in physical space. The user obtains information of expectations from those friends by averaging. For expectations that depends on individual OD (i.e., 𝐸𝐸𝐸𝐸𝑘𝑘 , 𝐸𝐸𝐸𝐸𝑘𝑘 , and 𝐸𝐸𝐸𝐸𝑘𝑘 ), the difference in the OD is normalized by comparing the expectations of ridesharing with that of riding alone. For instance, user 𝑖𝑖’s expectation-of-fare is normalized as 𝐸𝐸𝐸𝐸𝑘𝑘 ⁄𝑓𝑓(𝑖𝑖). However, information of 𝐸𝐸𝐸𝐸𝑘𝑘 is obtained by averaging directly as it is independent of OD. With this behaviour adjustment process, the newly perceived information influences the decisions of the following day, which then affect the entire DRS performance. Therefore, the number of ridesharing users is expected to vary over days, and may reach the stationary state if all users realize that they cannot realize additional incentives by changing their travel mode. Note that the initial user’s expectations of the first day of executing DRS must be given. 3. Numerical experiments 3.1. Model specification The functions 𝑔𝑔𝑖𝑖 (𝑗𝑗), 𝑓𝑓𝑖𝑖 (𝑗𝑗), 𝑥𝑥𝑖𝑖 (𝑗𝑗), 𝑑𝑑𝑖𝑖 (⋅), and 𝑑𝑑′𝑖𝑖 (∙) as well as other parameters are specified in the same way as in Thaithatkul et al. (in press) as follows. Let the travel times be proportional to the (Euclidian) distance. For 𝑔𝑔𝑖𝑖 (𝑗𝑗), the cost per unit time in a vehicle is different between time spent riding alone and ridesharing time at 𝜇𝜇1 and 𝜇𝜇2 , respectively. Given that 𝜇𝜇1 is equal to 0.1 unit of money/unit of time, and ridesharing costs 50% more than that of riding alone (𝜇𝜇2 = 0.15). The cost difference between 𝜇𝜇1 and 𝜇𝜇2 can represent a discomfort cost that may be incurred when travelers share their private space with others. For 𝑓𝑓𝑖𝑖 (𝑗𝑗), the fare rate is given at 𝛼𝛼 unit of money/unit of travel time, which can be equally shared with a partner during the time that both of them are in the vehicle. The fare rate 𝛼𝛼 is 10 times larger than 𝜇𝜇1 (𝛼𝛼 = 1). The vehicles are assumed to be effectively operated (no dispatching time), and the in-vehicle travel time 𝑥𝑥𝑖𝑖 (𝑗𝑗) is obtained from the shortest path that serves both user 𝑖𝑖 and user 𝑗𝑗 (including the detour required for picking up the partner). Penalty 𝑑𝑑𝑖𝑖 (⋅) in Equation (1) is given as 𝜇𝜇1 (𝜏𝜏𝑖𝑖 (𝑡𝑡) + 𝑥𝑥𝑖𝑖 (𝑗𝑗) − 𝑇𝑇𝑇𝑇𝑖𝑖∗ )2 if the total travel time exceeds the acceptable travel time ( 𝜏𝜏𝑖𝑖 (𝑡𝑡) + 𝑥𝑥𝑖𝑖 (𝑗𝑗) − 𝑇𝑇𝑇𝑇𝑖𝑖∗ > 0 ); otherwise, there is no penalty. The acceptable travel time is given to be 10% longer than a trip without using DRS. Similarly, penalty 𝑑𝑑′𝑖𝑖 (∙) in Equation (2) is given as 𝜇𝜇1 (𝜏𝜏𝑖𝑖 (𝑡𝑡) + 𝐸𝐸𝐸𝐸𝑖𝑖 + 𝐸𝐸𝐸𝐸𝑖𝑖 − 𝑇𝑇𝑇𝑇𝑖𝑖∗ )2 if 𝜏𝜏𝑖𝑖 (𝑡𝑡) + 𝐸𝐸𝐸𝐸𝑖𝑖 + 𝐸𝐸𝐸𝐸𝑖𝑖 − 𝑇𝑇𝑇𝑇𝑖𝑖∗ > 0; otherwise, it is zero. The matching is executed at every unit of time (∆𝑡𝑡 = 1). Parameters 𝛽𝛽 and 𝛾𝛾 are the same for all users at 0.8 and 0.5, respectively, and represent the moderate adjustment behaviour corresponding to the investigation by Thaithatkul et al. (in press). The social network-related parameters are specified as follows. 𝑯𝑯∗ is defined as a set with a maximum number of 𝑛𝑛 friends whose OD values are closest to those of the user, and its difference is not larger than the Euclidean distance 𝑑𝑑. A social network is represented as a well-known scale-free network as some real-world social networks were revealed to have scale-free properties (Li et al., 2005). A scale-free social network is generated using the BarabasiAlbert algorithm (Barabási and Albert, 1999), where each user is connected to at least 𝑙𝑙 friends. Parameters 𝑛𝑛, 𝑑𝑑, and 𝑙𝑙 are determined differently for the scenarios explained in the following section. 3.2. Scenario and experimental design

The experimental scenarios are explained as follows. There is a total of 500 users. Their ODs are randomly, uniformly, and independently sampled within the same square area with a size of 200 × 200 units of distance. Each user has the same OD, but with different arrival times over days. The user’s arrival time is completely random (Poisson arrival) with an average of 5 users/unit of time. Twelve scenarios are considered, where parameter 𝑙𝑙 of a scale-free network is given at 20, 50, and 100 (to investigate the influence of the social network, where low 𝑙𝑙 is intended to represent an offline social network); 𝑑𝑑 is given at 50, 60, 70, and 80 (to investigate the effects of information collected from spatially close friends); 𝑛𝑛 is given at 5 (the increasing 𝑛𝑛 was tested to have insignificant effects on DRS adoption). For scenarios with 𝑙𝑙 at 20, 50, and 100, the average total numbers of friends of all users are 38, 90, and 160 friends,

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respectively. Moreover, there are 3 additional scenarios in which 𝑑𝑑 and 𝑛𝑛 are set to infinity for all 𝑙𝑙 considered to represent situations when the collected information is not limited by the similarity of OD and memory, respectively. All scenarios were experimented for 10 replications using 10 sets of users with different sampled ODs. Each replication was conducted for 200 consecutive iterations (days). Each iteration has a finite time length that is equal to the time that the last user appears in the transport system. For the first iteration, users are assumed to have the same 𝑔𝑔 𝑓𝑓 initial collected information of the best performance of DRS: 𝛼𝛼̅0 = 1.5, 𝛼𝛼̅0 = 0.5, 𝜏𝜏̅0 = 0 and 𝛼𝛼̅0𝑥𝑥 = 1. The DRS evolution in terms of the adoption level (number of ridesharing users) was obtained by averaging the numbers of ridesharing users in each iteration from 10 replications. 3.3. Results The evolutions of scenarios with different values of 𝑑𝑑 were compared to investigate the effects of collecting information from spatially close friends. Figure 1 shows that the adoption levels for scenarios with information collected from spatially close friends tend to evolve to the same state as the scenarios in which the OD similarity of the collected information is neglected (𝑑𝑑 = ∞). This means that the OD similarity of collected information did not significantly influence the adoption level. This can be clearly seen from the comparison done among scenarios with 𝑙𝑙 = 100 (Fig. 1(c)). However, a different evolution appeared in the results of scenarios with 𝑙𝑙 = 20, 50 (Fig. 1(a) – (b)) was actually caused by the insufficient collected information. Figure 2(a) – (c) shows the number of users (y-axis) according to the number of friends from whom users collect information (x-axis) for scenarios with 𝑙𝑙 = 20, 50, and 100, respectively. By comparing scenarios with 𝑑𝑑 at 50, scenarios with 𝑙𝑙 = 20, where the average user had a small amount of collected information, tended to evolve to the state with a lower adoption than the other two scenarios (𝑙𝑙 = 50, 100) where the average user collected information from more friends. However, if users had sufficient information,

(a)

Scenarios where travelers are connected to at least 20 friends in a social network (𝑙𝑙 = 20).

(b)

Scenarios where travelers are connected to at least 50 friends in a social network (𝑙𝑙 = 50).

(c) Scenarios where travelers are connected to at least 100 friends in a social network (𝑙𝑙 = 100). Fig. 1. Evolution of number of ridesharing users for scenarios with spatially different information collected from friends.



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(a)

Scenarios where travelers are connected to at least 20 friends in a social network (𝑙𝑙 = 20).

(b)

Scenarios where travelers are connected to at least 50 friends in a social network (𝑙𝑙 = 50).

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(c) Scenarios where travelers are connected to at least 100 friends in a social network (𝑙𝑙 = 100). Fig. 2. Average number of users categorized by number of friends from whom a user collects information.

DRS tended to evolve to a similar state, such as the scenario with 𝑙𝑙 = 50, 𝑑𝑑 = 80 and scenarios with 𝑙𝑙 = 100, 𝑑𝑑 = 60, 70, 80. This result answered our research questions regarding how social networks affect DRS adoption. Sufficient collected information mentioned above is important because it could convince users with worse private ridesharing experience than their expectation to continue using DRS with the good information. For instance, for the scenario with 𝑙𝑙 = 20, 𝑑𝑑 = 80, 𝑛𝑛 = 5, during the last 50 days of all replications, there were 58% of 64,520 ridesharing trips in which the actual experiences were worse than the expectation from collected information. Moreover, to further investigate the effects of social networks, the average normalized expectations on DRS (i.e., the average of 𝐸𝐸𝐸𝐸𝑘𝑘 ⁄𝑔𝑔(𝑖𝑖), 𝐸𝐸𝐸𝐸𝑘𝑘 ⁄𝑓𝑓(𝑖𝑖), and 𝐸𝐸𝐸𝐸𝑘𝑘 ⁄𝑥𝑥(𝑖𝑖) of all users, and 𝐸𝐸𝐸𝐸𝑘𝑘 ) with their standard deviation were compared among scenarios with 𝑙𝑙 = 20, 50, and 100. The results showed that the more friends a user had, the less diverse were the normalized expectations (i.e., smaller standard deviation). This led to a smaller fluctuation in the DRS evolution, as shown in Fig. 1. However, a small number of friends raised various expectations over days, further causing the adoption level to gradually decrease over days, as shown in Fig. 1(a). 3.4. Discussion According to the results, the amount of information collected from friends on social networks affected the DRS adoption (Fig. 1 and Fig. 2). The results showed that the greater the number of friends that a traveler had in a social network, the greater the likelihood that DRS was adopted. This was because the information that propagated through the social network could convince travelers who actually had negative ridesharing experiences to continue ridesharing. However, this may be caused by the model’s limitations: 1) travelers trust the collected information even though it is different from their actual experience, and 2) travelers only obtain information collected from successful ridesharing trips. However, the OD similarity of information was revealed to have an insignificant effect on the DRS adoption

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level. This may have been caused by the influence of information propagation through social networks—the user also implicitly perceived the information through friends-of-friends’ connections whose OD may not be similar to that of the user—which could decrease the effects of the difference in the distance in physical space. However, further investigations on non-uniform OD distribution should be considered to confirm that this effect of information propagation on social networks exists for any OD distribution. 4. Conclusion In this study, we investigated the influence of the propagation of information through social networks on the longterm adoption of DRS. Moreover, we also investigated the effects when travelers only collect information from friends who have similar ODs. Information propagation may have positive or negative effects on DRS (more or less travelers who rideshare) depending on information that is shared among travelers. The results obtained from numerical experiments highlighted the influence of social network on DRS adoption in that the greater the number of friends that a traveler had, the more likely would it be that that traveler would rideshare. This could be because positive feedback about DRS that is propagated through social network could induce more travelers to rideshare. However, the collection of information only from friends who had very similar ODs did not significantly influence the DRS adoption when DRS was operated in areas with uniform OD distribution. This could be caused by the effects of the distance difference among travelers in physical space becoming smaller owing to the information propagation on social network as travelers did not only collect information from friends who were near in physical space; however, travelers also implicitly perceived the information from friends of friends who had less similar ODs through information propagation mechanism in social networks. 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