A negotiation model of individual matching and zonal-based travel behavior in carpooling

Carpooling is a sustainable and ecologically acceptable transportation mode. Individuals commonly engage in coordination and negotiation processes to find matching partners and typically modify their schedules to enable cooperation. Mutual cooperation between carpooling individuals plays an important role in executing trips. Through cooperation, participants can achieve challenging agreements effectively in a repetitive manner. This paper presents a negotiation mechanism that can match individuals for carpooling using organization and agent-based concepts. It describes a matching model and a carpooling social network. It studies several aspects of multi-zonal individual behavior to identify groups of carpooling candidates. The carpooling social network is simulated on an ongoing basis for each of the following carpooling activities: interaction, negotiation, and trip execution. The interaction process enables communication between individuals within carpooling social groups in order to activate the negotiation process. During the negotiation process, participants typically modify their schedules to support cooperation by considering their personal preferences and constraints. Negotiation leads to matching of individuals based on trip start times, driver selection, detour duration, and carpool group pickup and dropoff sequences. Trip start times are established on travel, social, financial, and schedule-related factors. The carpoolers’ pickup and dropoff sequences that are feasible for an optimal carpool group are projected using specific scoring methods. Carpooling community candidates are recognized via outcomes projected using the FEATHERS activity–based model. The framework is implemented through the Janus multi-agent system.


Introduction
Carpooling is a transportation mode in which cooperation between individuals plays an important role during planning of ongoing trips.It is regarded as an efficient transportation mode that is ecologically acceptable and sustainable.Carpooling facilitates sharing of commuting costs among travelers.It allows travelers to reduce energy use and save on parking charges.It provides transportation alternatives for non-drivers and decreases both pollution growth and traffic jams.Carpooling faces many challenges including designation of in-route stops, difficulty identifying partners, security concerns, and the overall efficiency of carpooling lanes.A change to certain factors such as oil and gas prices, parking charges, and traffic policies may motivate for carpooling.For carpooling, individuals or agents must coordinate and negotiate.They typically modify their regular schedules to support cooperation.Through negotiation, individuals convey and understand information to enable cooperation in support of carpooling.Moreover, travel, social, economic, and schedule-related factors can play dynamic roles in the search for suitable carpooling partners [1][2][3][4].
The main purpose of this study was to observe the consequences of time constraints and (1) demonstrate the manner in which people cooperate by adapting their regular schedules and (2) investigate how the resulting carpool sharing arrangements develop over time.With regard to activitybased modeling, this research focused on models of information propagation, individual behavior, scheduling pressure caused by cooperation, and incentive inhibitors that affect carpooling.This was achieved by considering flexible and constraining activity arrangements.Currently, several research fields including that of transportation behavior require investigation and modeling of multifaceted behavior among individuals.Modeling communication between agents is important in current research.In carpooling simulations, older modeling implementations have difficulty handling the complexity of interaction and negotiation required for cooperation.One technique that is appropriate for modeling communication between autonomous bodies is agent-based modeling (ABM).It is fundamentally dispersed and agent-centric and can be used to identify collaboration between various objects [5,6].Agent-based models can deliver important information on the community and on the consequences of communal activities.Agent-based modeling has been useful to a variety of problems in transportation science such as simulation of automobile and pedestrian movement, path-choice models, car following models, laneshifting models, and traffic simulations.
This paper presents a Negotiation Model for Matching Individuals (NMMI) that is designed for carpooling using organization and agent-based concepts.It seeks to provide a matching system based on aggregate street addresses and a carpooling social network (CSN).It studies several properties of multi-zonal individual behavior for groups of carpooling candidates.The CSN is simulated on long-term basis for each of the following carpooling activities: (i) CSN exploration and interaction, (ii) negotiation, and (iii) trip execution (carpooling, driving alone).The CSN is explored by modeling interactions within carpooling social groups (CSGs) to allow communication between individuals to activate the negotiation process.Collections of agents who live in spatially distributed travel analysis zones (TAZs) and work in a specific TAZ are considered for interaction within a CSG.A multiple-trip-based negotiation model is presented that enables matching of individuals for carpooling.Negotiation success is affected by the lifestyle dynamics that affect trip start-time decisions.The trip start-time decision method is partially extracted from previous studies [7,8] and is based on travel, social, financial, and schedule-related factors.The daily agendas and personal profiles of the individuals, optimal path selection, and the influences of pressuring or constraining activities play vital roles in negotiation success.The negotiation process leads to matching individuals based on preferred trip start times, driver selection, detour duration, and CSG pickup and dropoff sequences.Potential carpooler pickup and dropoff sequences for an optimal CSG are scored using the following factors: (i) the trip departure time, (ii) the degree of flexibility at each intermediate stop, and (iii) the time loss.To enable cooperation in the negotiation process, agents typically modify their regular agendas according to their personal choices and restrictions.Actual trip execution (carpooling or driving alone) is performed on a long-term basis.The NMMI for carpooling is implemented using the Janus multi-agent-based system (MAS) [9].It offers effective execution of the organizationbased model (OBM) and ABM.The experiments simulate a CSN (the Flanders region of Belgium).It was established by consequences anticipated by FEATHERS [10].Travel times between TAZs were pre-generated using the within day rescheduling (WIDRS) [4] tool.
This paper is structured as follows.Section 2 reports research efforts on (i) coordination and negotiation and (ii) activity rescheduling and individual matching.Section 3 offers the NMMI for carpooling.After descriptions of the problem and some basic concepts, network exploration and communication are described briefly.Next, the negotiation process is explained in detail.This description includes negotiation and scoring components.Finally, trip execution is described.Section 4 provides the simulation setup and experimental results.Section 5 discusses conclusions and future studies.

Related work
ABM is popular in the area of transportation and is capable in examining the aggregated concerns of agents' behavioral differences.Existing research related to carpooling is reported by dividing it into two subcategories: (1) coordination and negotiation approaches and (2) rescheduling of activities and matching of individuals.

Coordination and negotiation
ABMs that address coordination and negotiation techniques are discussed in this section.The authors in [8] offered a negotiation mechanism that unites two-way traveling trips per day for carpooling.This was proposed by considering the opportunity for flexible activity planning.The authors measured direct collaboration among agents but bound the collaboration to small clusters established based on similarity among home and work TAZs.In Ref. [11], the same authors extended the agent interaction mechanism to negotiate carpooling by allowing agents living in dispersed TAZs but working in the same work TAZ to negotiate.The quantity of interaction among agents was minimized by forming carpooling social groups established for particular work TAZs.A cooperation mechanism for trip start times and driver selection was proposed.A constant preference for trip start times within a given interval was used in the negotiation model.The authors of Ref. [12] offered a carpool application simulation model that simulated independent entities.It also analyzed feature changes that affected infrastructure, agent behavior, and travel costs.The simulation simulated a social network of agents and used agent profiles to initiate interaction between agents.The simulation model consisted of a routing procedure and a utility method designed to activate the negotiation mechanism to enable cooperation.This study was based substantially on Ref. [13], where a theoretical proposal for an ABM for a carpool application is presented.
The authors of Ref. [14] introduced an ABM to assist ridesharing at massive industrial plants.In this study, the authors introduced (1) an ABM to study prospects and inhibitors and (2) an operational matching platform designed to match commuter profiles.The authors argued that integrating dynamic coordination between individuals is necessary to support carpooling.This is required due to consideration of the inhibiting factors like re-routing and rescheduling.In Ref. [15], a MAS-based automatic genetic approach was used to solve a regular carpooling problem by searching the study area partially.The scheme was guided by an automatic empirical cooperative learning process.It was evaluated by simulating large-scale data sets.The authors of Ref. [16] designed and presented simulation model of a dynamic carpooling system using NetLogo.The system improved transport operation by allowing carpooling between agents who share a common path.The authors claimed that their method offers a smart matching facility alongside an intelligent routing machine that enables integration of real-time information, e.g., weather and transportation information.The authors of Ref. [17] offered a simulation that managed carpooling by describing the relationships between the concepts of the MAS and optimization.This was required to respond to user queries and perform vehicle-matching assignments.A decomposition procedure was presented that divided the overall problem into numerous sub-problems by considering a realistic search space.The authors suggested dividing a geographic area into distinct TAZs, each of which was managed by an entity owning an augmented behavior.In Ref. [18], a GIS data-based ABM is presented that discovers various system formations for demand-responsive shared transport (DRST).The simulation mimicked a diverse stable or flexible path transferal service in the city of Ragusa, Italy, by considering dissimilar fleet sizes and volumes.The authors claimed that by imitating micro-interactions, it is possible to (1) visualize macroscopic system behavior and (2) develop valuable proposals to plan, manage, and optimize DRST.The authors of Ref. [19] proposed a method that supports dynamic, reflex, and optimum trip-matching processes between users.The mechanism makes decisions based on the Tabu search-based strategy.The mechanism incorporates a memory scheme and various search strategies to make ideal decisions.The system manages the transfer process and drops off passengers at a transfer node.Furthermore, detours are considered to avoid entrapment.
From the travel demand perspective, various aspects of collaboration can be applied to the execution of shared trips and activities.In Ref. [20], the authors offer an ABM that uses a negotiation approach to execute shared social activities.The projected ABM contains an organized, precise interaction procedure that integrates transport and social layers.In this research, a utility method is described based on single and collective characteristics.In Ref. [21], the authors present an ABM that schedules various events dynamically using a cooperation process.The authors describe a group and a negotiation procedure used to develop agreements within the group in order to plan schedules.Each individual is expected to state their ideal choice first and then recognize successive new plans in a non-increasing sequence.Everyone uses the private utility function.A proposed assessment method is initiated by the protocol.The authors of Ref. [22] present a utility scheme that can be used to design intra-household interactions between household associates by determining their regular cooperative or solo activities.An equilibrium model is presented for concurrent management of time-dependent trip scheduling and traffic assignment problems.In Ref. [23], a recurring carpooling problem is investigated and designed for a cluster of individuals with the same destination.An artificial bee colony method is anticipated by linking variable neighbor and Tabu search.The authors claim that this method is useful for large carpooling networks.In Ref. [24], the authors present a method that introduces the mind of a driver and examines the consequences of eco-friendly circumstances.The authors also proposed to incorporate agent collaboration in the carpooling process.In Ref. [25], large-scale carpooling forecasts are studied by considering the demand for dynamic and recurrent carpooling.A matching algorithm is used to discover ideal matching solutions.Decreases in trip counts, road network capacity, and travelling speed are also assessed.The authors of Ref. [26] describe an ABM that intelligently associates demand and supply for a recurrent ridesharing advice-giving system.The focus is on the methods needed to model agent cooperation on shared plans and the economic value of common plans.

Rescheduling and matching
Some studies (e.g., Refs.[27,28]) on activity rescheduling in daily agendas have already been published.These studies consider changes in individuals' schedules in response to unplanned events.This is different from rescheduling using a cooperation process.In Ref. [4], the authors offer a framework for examination of algorithmic procedures that can be used to reschedule individual agendas on a massive scale.It permits obvious performance of information transfer between transportation facilities and commuters.It combines macroscopic traffic flow information via the commuters' microscopic model.The authors studied marginal utility, which declined monotonically with the activity duration.They also determined newly formed activity schedules by monotonically joining the relaxation algorithm.Joh et al. [29] established the Aurora model, which can generate individuals' daily schedules and make dynamic decisions related to activity rescheduling during travel.The proposed Aurora model was established on the S-shaped utility function.The best utility rate for a particular action is calculated from the product of various modeling functions.Functions use the following parameters from daily schedules: activity start times, activity sites, activity position in the daily agenda, and activity break times.Arentze et al. [30] used a thorough analysis of the Aurora model to generate and modify individual agendas.The authors propose a complete framework that can be used to make the following changes to individual schedules: addition of new activities; shifting of activities; removing and altering activities; changing locations; and connecting trip selections and transport modes.These detailed models are essential to incorporating the ideas of negotiation and cooperation in carpooling models.In Ref. [31], the authors offer a diverse linear program for activity rescheduling.The model is based on complex human decisions, i.e., activity termination, activity addition, and length modification.The model varies from existing rescheduling approaches in the following aspects: (1) rescheduling is motivated by matching growth; (2) the output organization is defined via a scheme that measures similarities and differences; and (3) the rescheduling procedure is determined by extending the similarity principle and utility maximization.Gupta and Vovsha in [32] presented a mixed discrete choice model for scheduling of work activities by designing collaborations among employees.The core objective of the model was to present inter-household interaction theory based on synchronization mechanisms.
Xia et al. [33] planned a framework for matching individuals for carpooling.The authors verified optimization-based and heuristic methodologies to determine the results.The authors claim that the newly proposed designs and related procedures allow resolution of ideal carpool groups and travel paths.Martinez et al. [34] presented a simulation of shared taxis with documented guidelines for space and time similarities.The model allowed an agent to choose the maximum deviation from its traveling path.The authors offered an objective function to elect the ideal partner for the taxi ride.In Ref. [35], the authors use the cooperative and competitive methods of several ridesharing companies to resolve linear assignment problems and make use of traveling services.Knapen et al. [36] present a computerized advisory service for carpool trip matching.A learning mechanism is used to calculate the probability of successful negotiation.The carpool matcher operates dynamically by the changing graph with regard to the weights of topologies and edges.Similarly, Knapen et al. [37] investigate the characteristics of tree-structured ideal paths in situations where some agents leave the car at the carpool parking location.An algorithmic approach was used to discover the optimum outcome for the tree (i.e., the case where passengers are picked up at carpool parking locations).Each candidate declared the maximum detour time that was acceptable for travel from home to work.The authors of Ref. [38] developed a graph-splitting method using a bipartite graph and used in the ridesharing problem.The methodology putrefies the main graph into several sub-graphs to reduce the overall computational complexity and to propose the best solutions.
The research reported above is not sufficient to model negotiation and cooperation mechanisms in carpooling platforms and between carpooling candidates.Similarly, investigation of the consequences of changes in shared schedules is essential to accomplishing shared trips.In this article, we describe an NMMI that can be used to study the concepts of negotiation and cooperation.

A negotiation model designed to match individuals for carpooling
This paper specifies an NMMI that is designed to mimic carpooling for the purpose of ongoing travel.The motivation for this research is to introduce a method of simulating individual behavior when assessments for cooperation are considered.One of the objectives of this research is to simplify the idea of multi-zone-specific collaboration within a CSN in which people reside in spatially scattered TAZs and are employed in a specific zone.A negotiation model for multiple trips is investigated by analyzing individual interactions and cooperation-related actions, as well as by considering constraints imposed by flexible activities.The iterative activities of the NMMI are network exploration and communication, negotiation, and trip execution (via carpooling or driving alone).Before the start of the iterative activities, individuals must form a CSG.Carpooling individuals who belong to the same CSG can interact to coordinate on both trips (morning and evening) required for the work day.

Carpooling problem-architecture
For a set P of identified participants, p i ∈ P is given.For each participant, there are origin-zone o i ∈ O and destina- tion-zone d i ∈ D locations.P � i is the set of participants that are mutually compatible for carpooling negotiation, where P � i ⊆ P .Participants who work in the same TAZ can interact and negotiate within the CSG of the CSN (see Fig. 1).The negotiation applies to both trips (morning and evening) and covers trip start times, selection of the driver (having car), and the passenger pickup and dropoff sequences.An individual with a trip duration T dur,p i also has a maximum detour time T maxDetour,p i , which is the upper limit of the generalized T dur,p i that p i will accept for travel from o i to d i .Individuals whose trips can be combined without exceeding the detour time can be picked up by the driver.A typical agenda for an agent is a planned series of journeys and activities with strict or relaxed timings.The trips in the individuals' regular agendas are complete and are deliberated to facilitate longterm carpooling.

Carpooling social network
A CSN comprises individuals with communal relations specified by at least one form of interdependency.A CSN varies from a common social network in the following ways.First, in addition to socio-demographic characteristics, it considers spatiotemporal characteristics like activities; trip departure times; and home and work TAZs.Second, it is intended for selection of and communication between carpool partners.The strength of association between participants can be calculated from the sum of their common characteristics.Agents may have a relationship with each other if they have any common characteristic, e.g., common trip departure or arrival time windows; routes; or home or work TAZs.
It can be difficult to find a compatible carpooling partner in a large CSN.A large CSN can be segmented into groups, each of which corresponds to a CSG.The CSG concept is used to limit interaction requirements.In this paper, CSG are designed by considering the compatible features and related work TAZ of carpooling candidates.Groups of personalities employed in a specific TAZ who live in distributed TAZs are considered for cooperation.If there are n work TAZs in the CSN, then there are n carpooling social groups (CSGs).

Framework system
To perform the iterative activities required by the carpooling process, individuals must determine their daily schedules with regard to ongoing carpooling.Once individuals share routes to the work TAZ that correspond in space and time, they are suitable for effective cooperation.Carpooling individuals interact and coordinate with other participants (with similar destination TAZs) on their trip start times and intervals, as well as on driver selection.The iterative activities that occur within the carpooling framework are shown in Fig. 2. A carpooling candidate can complete the subsequent actions: (i) CSN exploration and interaction, (ii) negotiation for cooperation, and (iii) trip execution (carpooling or driving solo).Each of these activities is described in further detail in subsequent sections.

Network exploration and communication
Each carpooling individual explores the CSG within the CSN to find partners with whom they can collaborate for execution of their regular trips.In the exploration phase, individuals may continue driving alone until they find a matching carpool partner.Each individual can interact with others using smart phones.Relationship information related to paths, profiles, activities, and travelling times is shared by the participants.Thus, every individual has a list of attributes, i.e., common interests and other necessities.For communication, common interests and other individual requirements are essential to suitable matching.In the proposed framework, each individual decides whether to invite another individual for carpooling using the parameter CPInvitation.This parameter is predicted by the character, behavior, and personal preferences of the individual because some people do not like to carpool.
Common interests I address the purpose of carpooling, matters for discussion, etc. Necessities and requirements R contains the path; trip departure and arrival times; origin and destination TAZs; commuting cost; and other social factors.
Individuals can coordinate multiple times in a day until they find matching carpooling partners.The participants typically agree to carpool after reviewing each other's personal profiles.During carpool trip execution, the driver or passengers can accept invitations to negotiate for carpooling.Carpoolers can accept or reject new participants based on the negotiation outcomes and seats available in the car.

Negotiation process
In the negotiation phase, similarity measures are applied to identify optimal carpool groups.The optimal carpool groups meet requirements defined by the candidate members.The proposed framework contains information regarding frequent trips and is intended to be accurate and to provide strict supplemental time limitations.This is because it avoids the extensive mental work required for multi-party cooperation.Participants cooperate on multi-trip departure time intervals; pickup and dropoff sequences; and driver selection.Limitations imposed by adaptable or stable activity development are considered.The overlapping of time windows for corresponding individuals is considered when trip departure time intervals are proposed in a particular TAZ.A person who holds a car and has a driving license can be a potential carpool group driver.Each individual knows the duration of a trip taken alone and maximum acceptable detour duration and distance.The latter are introduced via drive path and time-matching concepts and are applied to both trips.The carpool group distance determination is driven by the driver selection process since the driver must pick up every passenger.A carpooling individual can be part of a carpool group in any sequence.A carpool sequence order is considered as a feasible if the first agent can act as a driver.A carpool sequence order of carpooling individuals is assessed using personal preferences, of which the most important are schedule-related requirements.The negotiation process leads to matching of individuals based on trip departure time choices, detours, maximum access durations, and driver and car selection.Feasible carpool group pickup and dropoff sequences are evaluated and the optimal sequence is selected.

Departure time choice
Departure time choice (DTC) is a significant component of the decision to travel.DTCs are preserved as an iterative supportive decision established upon the maximum travelers' utility with each combination.The time preferences revealed by carpooling individuals at various times are fixed by their individual choices.For an individual, two features may affect the time preferences involved in determining start times: (a) socio-economic characteristics (i.e., the proportion of commute expenses to yearly earnings) may help to measure the value of time at a specific moment for trip departure times within a specified time window and (b) the participants' willingness to reach the pickup location, which shows their level of inflexibility with respect to departure times.

A. Time preference function
To develop a feasible scheme for trip departure times, Hendrickson's multinomial logit model [7] is used for work activity trips.Hendrickson and Plank used data collected in Pittsburgh, PA, to study large service-level deviations and trip start time decisions.Data collection and measurements involved travel and transfer waiting times for commutes to the Central Business City in Pittsburgh.The state-of-theart approach presented by Hendrickson involved up to 28 choices in groupings of four modes (driving solo, ride sharing, transit through a pedestrian entrance, and transit through a vehicle entrance) with seven different trip departure time intervals of 10 min each.For various reasons, e.g., time pressure, individuals did not express consistent preferences for specific time intervals.
The utility is associated with the daily agenda and is influenced by the timing of the activities and trips, as well as the time spent at activity locations and traveling between them.Changing the trip start time impacts the actual utility value according to the marginal utility of transport and the reduction in activity participation.Individuals may arrange their daily agendas efficiently during negotiation to capture the impact of an exogenous change on the cooperation scheme.The definite utility value of a specific individual leaving for work at particular time within an offered time window is determined by Eq. ( 1).
Consider N agents througha 1 ,a 2 ,...,a N .The trip start time intervals t 1 , t 2 , t 3 ..., t T are accessible between the established trip start timeT .The preference (utility) V a i t j for a specific time interval t j of a i is indicated by: For a i , the constants mentioned in Eq. ( 1) are extracted from Hendrickson's research study for particular mutual trips and the elements are defined in Table 1.
The probability that an individual selects a trip departure time alternate P a i t j is calculated by Eq. ( 2): The probability can be considered for the specific cases identified in Hendrickson's study.Outcomes from Hendrickson's study are re-used to establish the utility preference (1) Table 1 The elements (parameters) used in Eq. ( 1) and their descriptions Parameters Meanings and descriptions The free flow travel time (FFTT) is defined by the vehicle travel time during carpooling and may be 75% during peak times and 90% during off-peak periods.A negative constant is estimated because travel duration increases would disappoint agents who engage in carpool sharing CONG t j The share of the carpooling trip duration that is related to congestion, calculated based on the departure time, e.g., 25% (peakperiod travel) and 10% (off-peak travel) is the ratio of the yearly carpooling cost to the annual income.It is influenced by the day intervals because other costs such as tolls and parking depend on them ACC a i t j ACC a i t j is the transit time required to reach the work location at the end of the trip and is related to the trip departure time.It offers a degree of approachability to the work desk and is contained within for the transfer with walking mode.The parameter t j permits for changes in transit times due to trip start time changes WAIT a i t j WAIT a i t j is the waiting time with respect to an agent's best trip departure time choice LATE a i t j LATE a i t j is associated with the trip departure time because agents may arrive late at the workplace by a number of minutes.The parameter LATE ai tj 2 is used to represent the agent's perception of late arrival at the workplace EARLY a i t j EARLY a i t j is related to the trip start time because agents may arrive a number of minutes early at the workplace.In this paper, the constant coefficient EARLY a i t j is taken as 0.01.This is smaller than the coefficient LATE a i t j because late arrival is more problematic than early arrival.EARLY ai tj 2 as with LATE ai tj 2 ; however, a destructive constant is predicted to reveal the growing disutility related to the prior arrival 1 3 .For various reasons, numerical incorporation is achieved by assuming a constant probability across the various 1-min time periods.The likelihood density for the trip departure time is designed by normalizing P a i , whose integral is 1.It is specified by Eq. (3).
The P a i for the evening trip case is produced by taking the mirror of the morning trip P a i .In both cases, the value of time is analyzed based on the significance for which the best probabilistic value is achieved (Fig. 3).
The preference function established using the factors described in Table 1 is assigned to each individual to determine the trip departure times.The time intervals for each trip departure time are anticipated by considering activities that exert schedule-related influence.

B. The influence of constraining activities on trip departure time intervals
When determining the desired trip departure times, each individual is expected to consider a maximum symmetric , respectively.The desired trip departure time is t a i for each a i .Parameter symbols and their meanings are defined in Table 2.
The promising circumstances for the pressuring activities are described as follows: 1.The probable leftmost T b a i and rightmost T e a i time intervals of the specific departure T for the preferences of a i with- out considering any pressuring activities are specified by Eq. (4).

Equation (5) enables calculation of the leftmost and
rightmost intervals of the departure T for the morning trip.The a i has noted a stable pressuring activity prior to the morning trip.The tolerance period ΔT is reflected in the morning departure T.

If C instantly follows the work activity at l, the leftmost interval T b WH,a i
for the evening departure T is C f inTime,a i for a given a i , as shown in Eq. ( 6).Thus, T b WH,a i is the finishing time of C, which is executed after the work activity. (4) HW,a i = t HW,a i + ΔT Fig. 3 The departure-time probabilistic curve for the morning trip (for an individual) The rightmost interval T e WH,a i for the same T is t WH,a i + ΔT and is shown by Eq. ( 6). 4. Sometimes, C is planned subsequent to the work activity but at a TAZ that is different from the work TAZ.In addition, application of the appropriate arrival is also essential for C. Therefore, the rightmost interval of the departure T for the evening trip is influenced by the C startTIme,a i , as shown in Eq. ( 7).Here, 1 , is trip duration to any other TAZ from the work TAZ and W * is the time obligatory for an a i to move from the work loca- tion to the specific TAZ where the pressuring activity is performed.
For successful negotiation of trip departure times, the time intervals of the trip departure time windows (for both negotiated trips) must intersect at the TAZ location of every individual within a carpool group.

A. Departure time choices
The arrival T (time window) for all of the carpool group participants at the work TAZ location is denoted as T carpool,l N .The T carpool,l N is basically the overridden time interval of T for all the carpooling agents to arrive at the work l.The leftmost T b carpool,l N and the rightmost T e carpool,l N of the arrival T can be determined using Eq. ( 8).The keys are used to represent the max() and min() functions, which cover the set of individuals who belong to the same carpool group.) is considered.The summation corresponds to the integration of the preference function for a particular individual over the available time interval.The likelihood of discovering the time that a carpool group  The arriving T at the work site or TAZ T carpool,l The possible T at a specific l for a CSG d l i The solo-drive duration for a trip between l i and a destination T a i ,l i T of an agent at an identified l i T e carpool,l k The rightmost bound of a feasible T for a CSG at l k The leftmost bound of a feasible T for a CSG at l k t 0 Indicates the trip departure time at l 0 reaches the work TAZ is specified by the product of the probabilities of the participants and is shown by Eq. ( 9).
The probability distribution of the WH (evening trip) start time window can be created by mirroring the function given by Eq. ( 9).
The time window T carpool,l for any TAZ site l in HW carpool group journey is designed in the reverse TAZ stay sequence.The T carpool,l for a specific l monitors from l + 1 by deducting the estimated travel period d l i +1 .It is evaluated by determining the intersection of the Ts stated by the individuals to pickup from their particular locations (Eq.( 10)).The 1 is applicable to a T and a scalar indicates successive shifting of time windows over various locations.
The leftmost T b carpool,l i and the rightmost T e carpool,l i intervals of intersecting Ts at location l i are specified by Eq. (11).
The likelihood of finding a feasible trip departure time for each individual is calculated by taking the product of the sum of the probabilistic values of the intersecting intervals (between T b carpool,l i and T e carpool,l i ) within a carpool group.It is determined using Eq. ( 12). ( 9)

B. The detour duration relative to the solo driving duration
A candidate with a solo travel duration d a i ,solo may accept a higher d a i ,detour as the maximum morning work-trip delay.The relative excess is handled as follows: (a) for small trips, a higher comparative detour value is deliberated, and (b) if the distance d a i ,solo is less than d min , an associated surplus of 1 is accepted (i.e., double the trip length is assumed).Trips with lengths higher than or equivalent to d max accept a comparative error of r min .For time intervals between d min and d max , an exponential decay is used.In this paper, individual profiles are used to aid in choosing the carpool group driver and vehicle.A candidate who possesses a vehicle and driver's license is a potential driver.The driver's role within a carpool group is to pick up each passenger from their home TAZs.The driver of the carpool group is the first to board their own vehicle.The driver selection and timing constraints are interrelated.

Achieving negotiation
The carpool group size is typically restricted to four or five carpoolers.It is useful to examine each pick-up sequence using the permutation method.The first member to board in the permutation process is the driver.Any sequence in which the driver is not found is infeasible.Infeasible sequences can be discarded immediately to save on computation time.A feasible carpooling agent sequence provides pickup ( morning trip) and dropoff ( evening trip) sequences.
Other infeasible sequences include those where at any l i , the time window T carpool,l i for the negotiating participants is empty.This means that the time windows of the participating individuals do not intersect (at least once) at any l i in the sequence.Hence, the sequence is infeasible and negotiation between sequencing participants fails for the specific trip departure times that are identified.Moreover, the combined preferences of all carpoolers are calculated based on their intersecting time intervals at every (15) location and by considering both morning and evening trips.This process is described by Eq. ( 16).
For eacha i , the carpool duration must be ≤ to the agent's maximum detour travel durationd a i ,maxDetour .Sinced a i ,maxDetour = d a i ,solo . 1 + r d a i ,solo .
Negotiation among individuals succeeds when all constraints are satisfied and the final assessed value is greater than the specified threshold value, as shown in Eq. ( 18). Figure 5 characterizes the negotiation success values, which are estimated using the product of (1) time preferences, (2) the effects of detours (same as the time loss function), and (3) the driver availability functions.The x-axis, y-axis, and x-axis show time preferences, the effects of detours, and the driver availability,values respectively, whereas the y-axis shows the negotiation success values.On the x-axis, the negotiation fails when the driver availability value is zero (the driver is not available).On the other hand, the negotiation succeeds when driver availability is 1 and the negotiation success value is between 0 and 1 (see the ( 16) bar chart in Fig. 5).When negotiation among the candidates succeeds, the respective sequence is a candidate solution.

timePreference().detourEffect().driverAvailable() > threshold
Due to the permutation process, there can be more than one candidate solution for the same carpool participants.Differences between these solutions can include different driving agents or the pickup and dropoff sequences of participating agents.To identify the optimal solution from the candidate solutions, the trip start time, degree of f lexibility and detour scoring methods are used as scoring functions.

A. Trip start time determination
It is important to regulate the final trip departure times at each pickup and dropoff TAZ location once it becomes clear that the participants will carpool.Therefore, a preference function is used.In this paper, the candidates do not require a constant preference in order to have a feasible T. The trip departure times are planned using the following method.
Let d k represent the travel time for solo driving from l k−1 to l k .Then, the departure time at l k is given by t 0 + ∑ k i=1 d k .For every l, the departure intervals must be in realistic or preferred T. Therefore, at l k : The T for carpool group arrival is shown by Eq. ( 20): The leftmost time intervals of T are lower than the sum of travel times for the trip departure intervals at the specified l k .
For the rightmost time interval of T, one finds: The leftmost and rightmost time intervals at the TAZ l k are represented by Eqs. ( 25) and (26), respectively.
The trip departure time t 0 at TAZ l 0 is within the left- most and rightmost time intervals of T and is specified using Eq. ( 27).
In the same way, the trip departure time t k for each agent location l k is: In Eq. ( 29), the proportionality constant is used.It is used because the given preferred start time is proportionate to the likelihood that the carpooling agent will choose.This occurs because of the normalization process described above.
The optimal trip departure time at a specified TAZ location is determined by calculating the leading mutual preference probability.It is specified by Eq. ( 30): The final trip departure time score for both trips is calculated via multiplying the individual scores.

B. Degree of flexibility
The degreeofflexibility (DoF) is described by Eq. (32)  and calculated for each carpooling participant in the carpool group.The DoF signifies the lowest quantity calculated over all TAZ locations.The carpooling participant with the largest score is reserved.The DoF is calculated at each location for each valid trip departure time interval length.The ability to execute the planned schedule exists because there may be uncertain travel times.Equation ( 32) is used to determine the DoF when ΔT is the minimum interval length required to set a value; e.g., (25) for ΔT = 5[min] if the required value is 0.9, then can be determined using Eq.(33).
The final DoF score for the trip start times of both trips is calculated by multiplying the individual DoFs.

C. Time loss
The scoring function is used to evaluate time loss due to the difference between the detour duration and the solo-driving duration.Let L C j denote the time loss for participant j due to carpooling and let L A j denote the maximum acceptable detour duration specified by participant j .The time loss score for the carpool is given by: The time loss score for both of the carpooling trips that occur in a day is the product of the individual scores.
The optimal scoring values are estimated by taking the product of each score as shown in Eq. (37).
Figure 6 shows optimal scoring values estimated by taking product of (1) the trip start time, (2) the degree of flexibility, and (3) the time loss.The x-axis, x-axis, and y -axis, respectively, show these scoring functions, whereas the y-axis displays optimal scores.The optimal scores are estimated between 0 and 1 (see the bar chart in Fig. 6) by taking the product of the scoring function values.The candidates that exhibit the maximum optimal score are kept and this solution should be chosen as the optimal solution.

Joining a carpool
When negotiation between participants succeeds, the carpooling members may change their daily schedules to match the coordinated (optimal sequence) solution.During the negotiation phase, each carpooling individual agrees to the period through which they will carpool with the newly formed carpool group.The carpool group is considered for the optimal solution, whose optimalScore() is sufficiently large in the negotiation process.The carpoolers become participants in the carpool group by engaging in their individual roles.Remember that carpooling members (driver or passengers) who are already participating in a carpool group can find further partners to fill the remaining seats in the car.Carpooling candidates who commute by driving alone can continue exploring the CSN to find feasible carpooling partners.Typically, this happens when a person needs to join a new carpool group after leaving the previous one due to expiry of the carpooling period.Once this occurs, the negotiation process defined in the above sections is executed again until at least two carpooling candidates are in the carpool group, one of whom can perform the role of driver.This implies a new TAZ stay pickup and dropoff order and timing.

Trip execution -traveling solo or carpooling
Carpooling resembles execution of recurring trips over numerous days.The presented model assumes that (1) traffic is not reduced considerably and (2) the travel time is unresponsive to the carpooling level.The pre-calculated TAZ-based travel times for the peak period are used and presumed to be time independent.The time reliant on travel times are recycled to enable cooperation.The agents' daily work trip schedules (with constraining activities) are considered and repeated across all working days until the end of the specified period.
Throughout the carpooling period, when a carpooler leaves or a new one joins the carpool group, the remaining carpoolers may re-negotiate and adjust their day-to-day schedules.This renegotiation can fail.If the driver agrees to leave, a new driver is to be selected among the passengers having a car and a driving license.This is achieved by again executing the permutation procedure described above.Incoming carpool requests can be managed throughout the lifetime of the carpool group.Hence, carpooling agents and the newly applying agent require further negotiation.The agent who left the carpool group may explore the CSN again to interact with other candidates of his or her interest in order to arrange carpooling.
Any carpooler may leave carpool group when their carpooling period expires.A carpool group is dismissed when there is only one remaining participant or there is no person with a driver's license.After leaving the carpool group, an agent may immediately start to explore the CSN to become part of the same or a new carpool group.

An agent-oriented framework for carpooling
The scheme of an agent-oriented model is presented as a solution to the framework described in Section 3.1.Agents represent individuals with properties and common relations, are automated at a distinct level, and can act autonomously.In this model, an agent is located in a CSN and performs its daily tasks.Groups are partitioned via organizational concepts.Each member of a particular group is capable of communicating based on specific interaction properties and rules.The roles are considered to identify the shared norms and are cooperatively referred by groups.

OBM for carpooling social groups and carpool groups
Based on the organizational methodology, agents that cooperate in carpooling are associated with similar organizations.Organizational concepts are considered during the decision to form a CSG and used to bind the necessary interactions between individuals in the CSN.After creation of a CSG, each agent joins it by starting a Social.classrole.Within these CSGs, agents can interact and negotiate for carpooling.
Once the negotiation is successful, the carpooling agent (receiver) forms the carpool group using organizational concepts and shares it with the sender, allowing the latter to join the group.The driving agent joins this carpool group by starting and playing the Driver.classrole, whereas passengers join by performing their Passenger.classroles.Multiple trip-based long-term carpooling is performed by each agent in this carpool group.
Day switching groups are formed by using organizationbased concepts to model the states at which the carpoolers exchange activities at the end of the day.Each carpooler travels in its particular carpool group until its carpooling period expires.Each agent joins this group toward the completion of the day and starts the following day by leaving this group.The process continues each day until the simulated period is complete.

ABM for agent behavior
The behavior of an agent is modeled via a finite state machine.The agents in the carpooling social network can exchange messages.Negotiation between agents is performed via text message.The release of invitation messages is performed based on the CPInvitation factor.CPInvitation returns a value between 0 and 1.The text messages invite(), accept(), and reject() are used in communication.An agent state transition machine is shown in Fig. 7 and described below.The agent has the following states: exploring, waiting, and carpooling.

Exploring
In the exploring state, each agent (non-carpooling) searches the CSN for a carpool partner.Agents communicate with other (non-)carpooling agents within the same CSG by emitting and accepting text messages.During these interactions, agents can share their daily schedules.Generation of carpooling invitations is determined by the CPInvitation parameter.When an invite() message is produced by the sending agent, it immediately transitions to the WAITING state.The sending agent waits for an accept() or reject() response from the receiving agent.Agents can receive invite() messages in the exploring state and answer appropriately depending on the negotiation result.The receiving agent typically agrees to carpool with the sending agent after reviewing his or her personal profile.Once the negotiation is successful, the receiving agent forms a carpool group and starts its role.Based on successful negotiations and their outcomes, the participants join the particular carpool groups by executing their particular roles (the Driver.class and Passenger.classroles).When a non-carpooling agent does not succeed in finding a carpooling companion, it remains in the same state and continues driving alone or using alternate transportation during the simulation period.A non-carpooling agent can emit multiple invite() messages in a day and may switch between exploring and waiting states multiple times.A factor is used to bind a determined amount of invite() messages in a day.

Waiting
In the waiting state, the sending agent is able to receive messages whose content depends on the negotiation process.Once an accept() is received, the sender (i) joins the same carpool group as the receiving agent, (ii) starts playing its negotiated role, and (iii) moves to the CARPOOLING state.The accept() identifies the carpool group and the role played is decided during the subsequent negotiation process.When a reject() is received, the sender immediately returns to the EXPLORING state.When an agent receives an invite() message while in the WAITING state, it rejects the offer by replying with a reject().

Carpooling
In the carpooling state, the carpooling agents play their respective Driver.class and Passenger.classroles in the carpool group.During carpooling, driver and passenger agents can accept invite() messages and trigger new negotiations.Carpoolers can answer invite() messages by using accept() or reject() text messages subject to seat availability and the results of further negotiations.When a negotiation is successful, the sending agent joins the carpool group.Negotiators can also coordinate during negotiations to identify a new driver.If the sending agent is nominated as a driving agent, the current driver withdraws from the Driver.classrole and switches to its Passenger.classrole.When the driving agent's assignment is complete, the driver can withdraw from its driving responsibilities by simply leaving its Driver.class role and moving to the EXPLORING state.When more than one carpooling agent exists in the carpooling group, the remaining agents re-negotiate to identify a new driver.The newly nominated driver takes over driving responsibilities by playing its Driver.classrole and withdrawing from the Passenger.classrole.Once a passenger leaves and the driving agent is the only candidate in the carpool group, it leaves the Driver.classrole, terminates the carpool group, and moves to the EXPLORING state.In the exploring state, it tries again to find a carpooling partner, attempts to join another carpool group, or continues driving alone.

Dataset: carpooling social network and origindestination (OD)-based travel times
A synthetic population (CSN) is generated using the results anticipated by FEATHERS.A daily schedule that covers 24 h is produced for each agent in the CSN.The Fig. 7 (Non-)Carpooling agent's behavior using state machine and playing their roles in different groups formed configuration claims that agents may pass the daytime at some locations and traveling between these locations.The primary agenda for each agent is intended to be optimal and thus to produce the highest utility and reflect agent preferences.The predicted daily agenda is a group of activities and their corresponding trips.The starting time, duration, and associated trip of each activity are stated in the agenda.The FEATHERS [10] model is specifically characterized by approximately six million populations for the Flanders region.The region is segmented into 2386 TAZs.Each TAZ contains an average area of 5 km 2 .
A pre-planned travel-time (TAZ-based) matrix produced from the WIDRS framework [4] is used.The travel times apply to peak periods between TAZ segments in the Flanders region.The estimation of predictable travel times signifies the time-periods for the carpooling trips.
In the presented framework, agents' daily commuting trips are complete and intended for recurrent carpooling.Other activities, i.e., pick-drop and shopping, are also measured within the commuting trips, as they can affect timing constraints.An agent's profile consists of the following information: household and work-place TAZs; trip and activity beginning times; the time-period of every activity and trip; and SEC attributes including car ownership and driver's license status.The NMMI is established on traffic movement among the TAZs.It is presumed that agents picked up from home and dropped off at work TAZs.Agents employed in the TAZ in which they live are not considered as the carpool applicants.

Experiments and results
Experiments were conducted based on the synthetic population of the Flanders region.Belgium created FEATHERS.Particular TAZs in the Brussels region to which people commute daily for work were treated as work areas.Individuals whose transportation mode was a car and who had at least one daily work activity at one of the selected work TAZs were considered as candidate carpoolers.Note that only individuals with a common destination or work TAZ can carpool with each other.In these experiments, the carpooling social network was characterized by: Individuals: 18,218 whose only transportation mode was a car Home zones: 2386 TAZs

Work zones: 22 TAZs
To analyze the actions of the carpooling agents, the proposed carpooling NMMI was simulated for 3 years (660 working days) with the following constraints applied (Table 3).
Carpooling agents can decide their carpooling periods or how long they can carpool with the chosen carpool group, by selecting a number between 30 and 660 through random-sample from a uniform distribution.The trip start times for each agent are affected by further constraining activities (e.g., pick-drop, shopping, etc.) that occur before or after work-activity trips.To address the constraining activities, agents can adjust their trip start times within particular time windows to cooperate for carpooling.The carpool group size is set using the car capacity.In the NMMI presented in this experiment, a maximum of five agents (driver and passengers) can share a carpool.
Figure 8 shows the numbers of active carpoolers and driving agents or CSGs throughout the simulation period based on the constraints presented in Table 3.The x-axis displays the no. of operational days that the agents carpool, whereas the y-axis indicates the no. of dynamic carpooling-agents (blue line) and the number of active or live CSGs (red line) intended for each day.The numbers of active carpoolers, drivers, and carpools rises quickly between the start of the experiment and the end of the minimum carpooling period, which is 30 days.This rapid increase occurs because each non-carpooling agent attempts to be part of a carpool group and nobody leaves a carpool group.After 30 days, a few agents agree to leave their carpool groups.The carpooling agent growth rate is lower until completion of the simulation period.It appears to be easier for agents to be part of a currently active carpooling cluster than to form a new carpool group.After the early period, the remainder of the curves exhibit slight variations until expiry of the simulation period.Overall, 7% of the agents in the simulated population carpool successfully and nearly 40% of carpoolers drive their own cars for carpooling.
The scatter chart in Fig. 9 shows the distribution of the amount of carpooling days for each simulated individual.The x-axis shows all of the simulated individuals (userids), whereas the y-axis shows the amount of carpooling days for each agent.Individuals are categorized by the number of carpool groups that they share on the x-axis (Fig. 9).Carpooling individuals are divided into eight carpool groups (seven of these are carpool groups, while group 0 contains individuals who drive alone because they did not find a carpool group).The specified masses of the carpooling days are shown using density ellipses for each carpool group.The density ellipsoid is computed from a bivariate normal distribution that is fit to the individuals and the carpooling days that they travel.The graph shows that individuals who share larger numbers of carpool groups carpool for longer periods.The mean value for each carpool group is also given at their particular section in Fig. 9 and shows how long each individual travels via carpooling on average.
Carpoolers who carpool for fewer than 30 days are not able to complete the intended carpool duration either because the simulation ends or because they join a group from which the driver resigns soon after.When a carpool group contains fewer than two people, it is terminated and the person who is left alone stops carpooling as well.Other reason can be they cannot be part of the any carpool group either with the same participants or with different participant because they carpooled with different candidates who are not compatible with this one.
The boxplots in Fig. 10 show the number of carpooling days that the carpoolers travel during their carpooling periods.Figure 10 presents the time spent as a driver, a passenger, or both as a function of the number of carpool groups joined.In the case shown, boxplots are useful for comparing distributions.The mean values for the carpool groups joined (1st, 2nd), carpoolers traveled for more days as both driver and passenger than as either driver or passenger only.Carpoolers who join three and four carpool groups as drivers during their carpooling period travel for more days as drivers than as passengers.A Fig. 10 Boxplot showing the number of carpool days that carpoolers travel arranged by the number of carpool groups joined as a driver, passenger, or both smaller number of carpoolers join six and seven carpool groups; each of these carpoolers travels for almost the full simulated period.The boxplots in the block in the lower-right corner of Fig. 10 show the overall number of carpool days for all of the carpool groups.It includes carpoolers who travel as both driver and passenger, as well as those who travel exclusively as either drivers or passengers.The overall mean value for these situations is 415.7.Thus, the average carpooler travels for 415 days of the simulated period.The mean value for carpoolers who travel as both driver and passenger exceeds those of carpoolers who travel as either driver or as passenger.We note that an individual can be part of a carpool group for a minimum of 30 days but must leave when the carpool group terminates.
Figure 11 shows the average size of a carpool group.On average, 2.49 carpoolers share a car.According to the 2012 and 2013 Flemish travel study ["Onderzoek Verplaatsingsgedrag Vlaanderen" (OVG, travel behavior research in Dutch)], an average car was occupied by 2.4 people (in the 2012 OVG) and 2.46 people (in the 2013 OVG) [41].
The results show that the current framework works well within the given constraints and factors.Certainly, it is essential to deliberate appropriately the large area to assess the presented simulation model.In addition to addressing scalability concerns, future research should emphasize the consequences of changes in individual schedules and improving the cooperation model.

Fig. 1
Fig. 1 A carpooling-problem architecture.Individuals are distributed across a populated area that is divided into TAZs, which represent origins.The decorated area with buildings indicates the work TAZ

Fig. 2
Fig. 2 Iterative activities that an individual performs to support their work trips method.The continuous preference function for the circumstances of the morning time window T is presented in Fig.3.The preference function is established by calculating an individual's likelihood values for each moment in a particular T. The carpooling candidate is expected to agree to a symmetric deviance ±ΔT with respect to the desired trip start times.The area of variation of any particular time window is between time intervals T b a i and T e a i t j = 1 deviance ±ΔT .The resulting case is a modest one because prior or subsequent activities can induce scheduling limitations.For an individual a i , the leftmost and rightmost inter- vals of each trip are T b a i and T e a i The negotiation prerequisite is that the carpooler arrival time intervals are between T b carpool,l N and T e carpool,l N .To determine an appropriate outcome for each participant in the carpool group, the sum of the intersecting time intervals for T (between T b carpool,l N and T e carpool,l N

Figure 4
Figure 4 demonstrates the maximum detour overhead with respect to solo traveling times.The various parameters and their values are as follows: d min = 5min , d max = 90min , and r min = 0.15.C.Driver selection

Fig. 4
Fig.4 The maximum detour durations relative to the solo trip durations

Fig. 5
Fig. 5 Possible negotiation success values as functions of time preferences, detour effects (time loss), and driver availability S DoF = S DoF,HW .S DoF,WH

Fig. 6
Fig. 6 Optimal scoring values estimated using the , , and scoring methods

Fig. 8 Fig. 9
Fig. 8 Numbers of active carpoolers and carpool drivers during the simulated period

Table 2
Parameters used: symbols and their definitions The possible leftmost and rightmost bounded values of a time window for morning (HW) and evening (WH) trips (b indicates the beginning and e indicates the end of a time window)

Table 3
Simulation parameter settings and values