A system for routing transporation and method of the same

Abstract

There is disclosed a system for routing a fleet of transportation to facilitate fleet management through collection of data from databases and calculating movement of transportation load within a defined geographical area, to achieve mobility-on-demand services. The system comprises a fleet management server, a fleet of transportations, each of the transportation in the fleet comprises at least one user's client device and a communication network in wireless communication with the fleet management server and the at least one user's client device. The fleet management server comprises a routing recommendation model having at least one processor having a memory and a set of instructions stored thereon, the routing recommendation model operable to determine at least one transportation in the fleet of transportation in a state of idle and generate a recommendation notice for transmitting to the at least one user's client device of the at least one transportation in the fleet determined to be in a state of idle. The recommendation notice comprises at least one route destination, an estimated time of travel to each of the at least one route destination, and / or an amount of power consumption rate required for the at least one transportation in the fleet of transportation determined to be in a state of idle to travel from a current location to each of the at least one route destination.

Description

[0001] 202407501

[0002] 1

[0003] A SYSTEM FOR ROUTING TRANSFORATION AND METHOD OF THE SAME

[0004] FIELD OF INVENTION

[0005] This disclosure relates to a system and method for routing a fleet of transportation within a defined geographical area and in particular routing a fleet of transportation to achieve mobility-on-demand services.

[0006] BACKGROUND

[0007] In ride-hailing system, taxi drivers use their own passenger finding strategies leading to an uncoordinated operation resulting in a spatial-temporal supply-demand imbalance problem. This leads to longer waiting times for both drivers as well as passengers.

[0008] Two types of solutions have been proposed in the literature:

[0009] One existing solution is using heatmaps where all the drivers are shown a heatmap (demand distribution over the space) of the current or the upcoming demands. Every driver makes an independent decision to reposition to his preferred location. This operation is uncoordinated and there is no control of exactly how many drivers will move to a particular location. This leads to a sub-optimal solution.

[0010] Another existing solution is the Driver State Agnostic Repositioning Recommender System, where a centralized system calculates which idle standing driver should move to which location. This calculation is done considering, i) a forecast of the upcoming demands, ii) current supply distribution. The system is agnostic to a driver’s repositioning preference and confidence in recommender system. It assumes that the driver is adherent and will follow the repositioning recommendations with complete certainty. In reality a driver may always choose to reject the system’s recommendations. Due to this missing information, the repositioning recommendations may be ineffective. 202407501

[0011] 2

[0012] There is therefore, a need to at least ameliorate the some of the problems as discussed above.

[0013] SUMMARY

[0014] A purpose of this disclosure is to ameliorate the problem of facilitating fleet management through collection of data from databases and calculating movement of transportation load within a defined geographical area, to achieve mobility-on-demand services through generating information on a route recommendation.

[0015] Further purposes of this disclosure are set out in the accompanying dependent claims.

[0016] In an aspect of this disclosure, a system for routing a fleet of transportation is disclosed. The system comprising a fleet management server, a fleet of transportations, each of the transportation in the fleet comprises at least one user’s client device; a communication network in wireless communication with the fleet management server and the at least one user’s client device. The fleet management server comprises: a routing recommendation model having at least one processor having a memory and a set of instructions stored thereon, the routing recommendation model operable to: determine at least one transportation in the fleet of transportation in a state of idle; and generate a recommendation notice for transmitting to the at least one user’s client device of the at least one transportation in the fleet determined to be in a state of idle, the recommendation notice comprising: at least one route destination; an estimated time of travel to each of the at least one route destination; an amount of power consumption rate required for the at least one transportation in the fleet of transportation determined to be in a state of idle to travel from a current location to each of the at least one route destination, or combination thereof. 202407501

[0017] 3

[0018] In an aspect of this disclosure, a method for routing a fleet of transportation is disclosed. The method comprises determining, by way of a global positioning system (GPS), at least one transport in a fleet of transportation in a state of idle; and generating, by way of a route recommendation model, a recommendation notice for transmitting to at least one user’s client device of the at least one transportation in the fleet determined to be in a state of idle via a communication network. The recommendation notice comprises: at least one route destination; an estimated time of travel to each of the at least one route destination; an amount of power consumption rate required for the at least one transportation in the fleet of transportation determined to be in a state of idle to travel from a current location to each of the at least one route destination, or combination thereof.

[0019] Other objects, features and characteristics, as well as the models of operation and the functions of the related elements of the structure the combination of parts and economics of manufacture will become more apparent upon consideration of the following detailed description and appended claims with reference to the accompanying drawings, all of which form a part of this specification. It should be understood that the detailed description and specific examples, while indicating the non-limiting embodiments of the disclosure, are intended for purposes of illustration only and are not intended to limit the scope of the disclosure.

[0020] BRIEF DESCRIPTION OF DRAWINGS

[0021] This disclosure will become more fully understood from the detailed description and the accompanying drawings.

[0022] Fig. 1 shows a schematic diagram illustrating a driver confidence model, according to an embodiment of the invention.

[0023] Fig. 2A shows a schematic diagram illustrating repositioning probability, according to an embodiment of the invention. 202407501

[0024] 4

[0025] Fig. 2B shows a graph illustrating relationship between posterior update and success probability, according to an embodiment of the invention.

[0026] Fig. 3 shows a flowchart illustrating a method for routing a fleet transportation, according to an embodiment of the invention.

[0027] Fig. 4 shows maps illustrating a prediction model analysis, according to an embodiment of the invention.

[0028] Fig. 5 shows graphs illustrating error analysis, according to an embodiment of the invention.

[0029] Fig. 6 shows graphs illustrating spatial-temporal error analysis, according to an embodiment of the invention.

[0030] Fig. 7 shows graphs illustrating probability distribution of error in travel time prediction, according to an embodiment of the invention.

[0031] Fig. 8 shows graphs illustrating the relationship between feature and accuracy, according to an embodiment of the invention.

[0032] Fig. 9 shows graphs illustrating the impact of individual factors on the driver’s repositioning choice, according to an embodiment of the invention.

[0033] Fig. 10 shows graphs illustrating relationship between driver classes and confidence level, according to an embodiment of the invention.

[0034] Fig. 11A shows a table illustrating a model performance analysis, according to an embodiment of the invention.

[0035] Fig. 11 B shows graphs illustrating a comparison of a proposed model with the baseline models in terms of evaluation metric, according to an embodiment of the invention. 202407501

[0036] 5

[0037] Fig. 12 shows a schematic diagram illustrating a system for routing transportation, according to an embodiment of the invention.

[0038] Fig. 13 shows a schematic diagram illustrating an example mobile application of the system of Fig. 12, according to an embodiment of the invention.

[0039] Fig. 14 shows a schematic diagram illustrating an architecture of the system of Fig.

[0040] 12, according to an embodiment of the invention.

[0041] DETAILED DESCRIPTION OF EMBODIMENTS

[0042] The following detailed description is merely exemplary in nature and is not intended to limit the disclosure or the application and uses of the disclosure.

[0043] Recent urbanization trends have led to increased travel and its associated externalities (e.g., congestion levels worldwide are escalating). In this context, relying on private cars for personal mobility is becoming increasingly impractical and unsustainable. Ride-hailing services have emerged as an alternative, providing mobility-on-demand (MoD) services, raising concerns related to the exploitation of public resources, equity, profitability, and, importantly, scalability. In particular, the travel demand for such services is spatio-temporally asymmetrically distributed (e.g., commuting toward downtown in the morning), making the overall operations imbalanced and extremely sensitive to disturbances.

[0044] Fleet rebalancing has emerged as a solution to address such challenges. In this context, two main classes of approaches are contemplated. First, mathematical optimization models are studied. Here, upcoming demand is assumed to be known either exactly or is approximated leveraging demand prediction models. Subsequently, the optimization model calculates rebalancing policies based on predicted demands. Secondly, reinforcement learning techniques are employed to learn taxi rebalancing policies directly from data. Furthermore, from the 202407501

[0045] 6

[0046] decision-making perspective, the models can be categorized into two classes, i) aggregate models, and ii) agent-level models. The former generates decisions at the fleet-level, determining how many taxis should be moved from one region to another. However, such models do not consider the state of individual taxi drivers, and hence incorporating driver-level objectives such as fairness and preferences is challenging. In contrast, agent-level models possess the desired granularity, and offer greater flexibility and control over individual taxis, allowing for tailored movements based on specific criteria or constraints. However, the enhanced flexibility comes at a computational cost, due to the many variables involved in tracking each vehicle.

[0047] One possible contemplation in the domain of the taxi rebalancing problem includes an aggregate-level model for a station-based taxi fleet management. The objective is to find the rate at which the idle standing taxis should be dispatched from one station to the other to ensure that the queue length of customers waiting at the station remains bounded. Based on the formulation, the idle-standing taxis are distributed among the stations proportionally to the number of awaiting customers at each station. The excess taxis (if any) are evenly distributed among the stations at a minimum traveling cost. The primary drawback can be that it does not consider the upcoming demands while generating the rebalancing decision, and the repositioning decisions are made solely based on the number of customers waiting in the queue.

[0048] Further possible contemplations introduce a more complex model, by accounting for both awaiting customers and expected future customer requests in the decision-making process. Taxis are assigned to stations to guarantee that each station has at least as many taxis as there are awaiting customers. Furthermore, following the allocation for awaiting customers, any remaining taxis are distributed proportionally based on demand forecasts at each station. A major shortcoming of this is that the proposed model does not account for the uncertainties in the demand forecasts. This is critical, because recommendations might be overly optimistic and cause drivers to head to locations with insufficient demand. This may cause distrust 202407501

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[0050] among drivers and hence lead to poor adherence to system recommendations in the future.

[0051] The aggregate-level taxi rebalancing solution can be further enhanced by formulating a multi-period stochastic rebalancing problem considering uncertainties in demand forecasts. The objective is to ensure that the supply-demand ratio at each station is the same as the overall supply-demand ratio at the network level while minimizing the traveling cost. Formulating the taxi rebalancing problem as a multi-period problem has the advantage of accounting for the downstream effects of decisions made in the planning horizon. However, this may not always be beneficial due to the underlying uncertainties in the forecasts for mobility patterns. It is a possibility to discuss an upper-confidence-bound based approach to determine optimal parameters, such as the rebalancing frequency, and the length of the planning horizon, to ensure the effective implementation of the aggregate-level models sequentially.

[0052] The models as discussed above are aggregate models and are unable to generate taxi-level decisions. It is contemplated the possibility that the agent level version of the aggregate model may enable decision-making at the individual taxi level. A notable limitation of this is its failure to account for uncertainties in travel time and their potential impact on taxi availability at the destination. A possible method and system can greatly improve on this aspect and account for the impact of the travel time on taxi availability at the destination station. The availability of a taxi at the destination was represented as a fraction of the planning horizon’s time during which the taxi is expected to be present at the destination. This fraction is determined by utilizing pre-calculated inter-station travel time. It is contemplated that agent-level models may not incorporate any driver-centric objectives, rather the objective still remains to balance network-level supply and demand. A possible contemplation includes incorporating fairness in providing rebalancing recommendations and discussion of the impact of the charging-related constraints on the taxi rebalancing problem. Research on the impact of human factors on recommender systems is limited. In particular, little attention is given to the analysis 202407501

[0053] 8

[0054] of confidence level of taxi drivers and on the effectiveness of rebalancing strategies suggested by the recommender systems.

[0055] Existing taxi rebalancing models are agnostic to taxi driver’s confidence levels as well as their repositioning preferences. Due to this, the rebalancing recommendations given by the model may not be effective in practice because the driver may discard the recommendation if they are not confident about the recommender system or if the recommendation is not aligned with their preference. Additionally, learning taxi drivers’ preferences also helps one modelling the repositioning choice of the drivers more realistically. Driver’s confidence levels are impacted by the outcome of the repositioning recommendation. In other words, if the recommendation leads to a higher reward, the confidence level increases and vice-versa. Additionally, at any particular time instant, the confidence level impacts the likelihood of the driver accepting the repositioning recommendation from the system. The dynamics of an agent’s confidence while interacting with a recommender system can be a possible contemplation.

[0056] Another example contemplation includes a Thompson Sampling-based decision-making and confidence update mechanism. This approach has been successfully applied in improving the exploration-exploitation trade-off in recommendation systems. However, the implementation of such methods in taxi recommender systems remains limited. It can be shown that taxi drivers display a preference in terms of their passenger-finding strategies. One possible contemplation includes the driver cruising strategies between the trips and highlights that taxi drivers tend to make reasonable choices between rebalancing and parking, heading to high-demand locations based on the time of day. It is contemplated there is a possibility of a multinomial logit model to learn the probability distribution over the driver’s choice to head to one of the neighbouring zones. Furthermore, another possible contemplation includes a model that explores the behaviour of taxi drivers when searching for passengers under uncertain conditions and three distinct strategies can be studied, i.e. random search, maximum anticipated pick-up probability search, and maximum anticipated revenue search. In an embodiment, there can be a new detailed model for the behaviour of 202407501

[0057] 9

[0058] taxi drivers, and tools to compute recommendations for such drivers, so that they can reposition their vehicles to increase their returns.

[0059] Taxi drivers are modelled as agents characterized by a repositioning preference as well as a confidence level. A dataset can be leveraged to extract the taxi demands as well as driver preferences. According to an embodiment of the invention, there is a taxi rebalancing model which provides repositioning recommendations by predicting the upcoming taxi demands, travel times, driver position, repositioning preference, and confidence in the recommender system. Repositioning recommendations are made sequentially, and the agent’s confidence level is updated depending on the reward received after reaching the destination. To learn the taxi driver preference, the features that can describe the repositioning decision of a driver can be identified (e.g., the distance of the driver to the recommended destination, time of the day, day of the week, the expected number of requests at the destination, expected revenue from the ride originating at the destination, etc.). Subsequently, the probability of the driver moving to the destination can be learned using a logistic model and identify the top-k most likely destinations. When a driver is standing idle after dropping off a passenger, their next location is a function of the repositioning recommendation, their confidence level, and their preference. The confidence level of a taxi driver is modelled using the Thompson sampling-based Beta-Bernoulli Bandits. The performance of the confidence and preference-aware repositioning model is compared with the agnostic repositioning model. Additionally, three other baseline models that have partial availability of information regarding taxi driver preference or confidence level are reported.

[0060] Embodiments of the present invention can include:

[0061] 1) Learning the taxi driver preferences using logistic regression and model the taxi driver confidence as a dynamic process using Thompson sampling-based Beta-Bernoulli Bandits. This may include modelling the taxi drivers’ confidence in the recommender system and its impact on rebalancing recommendations.

[0062] 2) Formulating and solving a novel taxi rebalancing optimization model that predicts the upcoming demands, travel times, driver positions, driver rebalancing 202407501

[0063] 10

[0064] preferences, and driver confidence, and uses that as an input to generate taxi rebalancing decisions to maximize profit.

[0065] 3) Analyzing the proposed strategy in a simulated taxi network derived from real taxi data from a state-of-the art New York City dataset, and illustrate its effectiveness in comparison to preference and confidence-agnostic taxi rebalancing models. A rigorous mathematical formulation of the proposed preference and confidence-aware rebalancing model is introduced, followed by the detailed presentation of the architecture for the rebalancing recommender system. Detailed simulation-based case studies can be presented and conclusions can be drawn.

[0066] MATHEMATICAL FORMULATION

[0067] An embodiment of the present invention includes a detailed mathematical formulation of the proposed taxi drivers’ state aware repositioning recommender system. The system consists of a set of regions denoted as R, and a set of idle taxi drivers denoted as C. Drivers transport the passengers from one region to the other. Idle standing drivers receive a repositioning recommendation which they can either accept or reject. The driver moves to the recommended region if he accepts the system recommendation or moves to his preferred region if he rejects the system recommendation. Upon reaching, the driver either gets allocated to transport a passenger, or remains idle. This sequential decision-making process for driver c e C is modelled as a random experiment with a probability space (Q, F, Pc) and is shown in Fig. 1. The sample space of the random experiment is Q = {0, 1} x R x {0, 1}, where an outcome is a tuple co = (col, co2, co3) e Q. Here, col = 0 indicates that the driver rejected the system recommendation, while col = 1 indicates that the driver accepted the system recommendation. Additionally, co2 = j implies that the driver moved to region j e R. Finally, co3 = 1 implies that the driver was allocated, whereas co3 = 0 indicates that the driver remained idle. The o-algebra, i.e., a set of all the subsets of sample space (also known as events), is denoted as F. For brevity, the following notation is used: {col = a} = {(col, co2, co3) e Q | col = a}. Similarly, this notation can be extended to other combinations of col, co2, and co3 to represent events involving multiple conditions. The probability measure is defined such that Pc({co1 = 1}) represents the probability of the driver accepting the system 202407501

[0068] 11

[0069] recommendation, while Pc({co1 = 0}) represents the probability of the driver rejecting the system recommendation. Furthermore, Pc({co2 = j} | {col = 0}) denotes the probability of the driver moving to destination j e R given that the driver has rejected the system recommendation, and Pc({co2 = j} | {col = 1}) denotes the probability of the driver moving to destination j e R given that the driver has accepted the system recommendation. Finally, the probability of the driver getting allocated is defined such that if the driver rejected the system recommendation and moved to region j e R, the probability that the driver remains idle is Pc({co3 = 0} | {col = 0}, {co2 = j}) = 1 -0c, and the probability that the driver gets allocated is Pc({co3 = 1} | {col = 0}, {co2 = j}) = 0c. Note that the value of 0c is unique to the driver c e C. Similarly, if the driver accepted the system recommendation and moved to region j e R, the probability that the driver remains idle is Pc({co3 = 0} | {col = 1}, {co2 = j}) = 1 — 0r, and the probability that the driver gets allocated is Pc({co3 = 1} | {col = 1}, {co2 = j}) = 0r. The state of the taxi driver is defined as tuple containing i) probability of the driver going to region j e R by following his own preference, and ii) probability of the driver accepting the reposition recommendation from the system.

[0070] (Pc(co2 = j |w1 = 0), Pc(w1 = 1 )) (1 )

[0071] can be the formulation of the state of the driver and the driver state aware repositioning recommendation model can then be evaluated.

[0072] Taxi Driver’s Preference to Repositioning to a Region

[0073] Assuming that the driver c e C has rejected the system recommendation, i.e., col = 0, the driver will next reposition to his preferred destination, with the probability of moving to the region j e R given as follows:

[0074] Pc({co2 = j}|{co 1 = 0}) = Lcj (2)

[0075] where Lcj e [0, 1] is defined as follows:

[0076] Lcj = oc(zj) P ieR oc(zi) and oc(zj) = 1 1 + e-wc zj (3). 202407501

[0077] 12

[0078]

[0079] Logistic function oc maps a vector of featuresl zj associated with region j e R to a score which lies in the interval [0, 1], This score is indicative of the the attractiveness of region j e R for driver c e C. Parameter wc e R |zj | +1 is unique to each driver c e C and is learned by separately fitting a logistic function to the historic repositioning decisions of each driver using the dataset. Alternately, if the driver accepts the system recommendation, i.e., co2 = 1, the driver will move to the recommended destination. Once, the driver has accepted the system recommendation, there is no uncertainty in his selection of the destination region.

[0080] Pc({cu2 = j}|{cu1 = 1}) = xcj (4)

[0081] where, xcj = ( 1 c e C is recommended to j e R 0 c e C is not recommended to j e R. (5) Note, xcj e {0, 1} is a decision variable, that must be calculated to achieve an optimal dispatch solution. Each taxi driver is recommended only one destination region

[0082] j e R: X jeR xcj = 1 vc e C. (6)

[0083] Taxi Drivers’ Confidence in the Recommender System

[0084] An embodiment of the invention includes modelling how taxi drivers update their confidence in a recommender system with experience, using a Bayesian 202407501

[0085] 13

[0086] decision-making approach, which relies on posterior distributions for decision-making. The driver’s personal success probability 9c is known to the driver from his prior experience, while the recommender system’s success probability 9r is initially unknown. The drivers update their estimate of 9r over time as they observe the outcomes of the system’s recommendations. Let 0r(c) represent driver c’s estimate of 9r. The driver’s prior belief about 9r is modelled using a Beta random variable:

[0087] 0r(c) ~ Beta(ar(c), |3r(c)) (7)

[0088] Recommendation outcome is modelled as a Bernoulli trial, where yc(k) e {0, 1} denotes the outcome of the k-th trial: yc(k) = ( 1, if driver c gets allocated in the planning horizon 0, if driver c remains idle in the planning horizon (8) After observing k trials, the posterior distribution is updated using the Beta distribution’s conjugate updating rule:

[0089] 0r(c) | yc(1 ),..., yc(k) ~ Beta a0 + e1 X k i=1 yc(i), (30 + eO k - X k i=1 yc(i)!! (9)

[0090] Here, eO, e1 are the weights used for updating the parameters of the confidence model. The driver’s updated estimate of the success probability after k trials is given as follows:

[0091] E[0r(c)] = a0 + e1 Pk i=1 yc(i) aO + [30 + eO ■ k + (e1 - eO) ■ Pk i=1 yc(i)

[0092] Each successful recommendation increases the driver’s confidence in the system, moving the estimate right, while each failure decreases it, moving the estimate left. Weights, eO, e1 decide how rapidly the curve shifts left and right respectively. Figure 2 shows how the Beta distribution evolves with successive successful recommendations. As the driver accumulates more data, their estimate 0r(c) converges toward the true value 9r, with the speed of convergence depending on the observed outcomes’ consistency. Rather than always selecting the option with the highest expected success probability, the driver’s decision-making process can be modelled as probabilistic. The driver accepts the system’s recommendation with 202407501

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[0094] a probability pc, which represents the probability that the system’s success rate is higher than the driver’s personal success rate:

[0095] p(c) = P (0r(c) > 0c) = Z 1 0cf0r(c)(t) dt, (10)

[0096] where f0r(c) is the probability density function (PDF) of the Beta distribution:

[0097] f0r(c)(t) = t ar(c)-1 (1 - t) pr(c)-1 B(ar(c), pr(c) ), (11)

[0098] and B(ar(c), |3r(c)) is the Beta function, defined as:

[0099] B(ar(c), [3r(c)) = Z 1 0 t ar(c)-1 (1 - t) pr(c)-1 dt. (12)

[0100] The use of this probability reflects risk aversion and how the driver weighs the risk of failure. If the probability p(c) is high, the driver is more confident that the system will succeed, and they are more likely to follow the recommendation. Conversely, if p(c) is low, the driver is less confident in the system and less likely to accept the recommendation. Let dj denote the total number of passenger requests in region j e R and sj denote the total number of taxis in region j e R in the planning horizon H. The number of taxis that will get allocated is given as: min(dj, sj). The taxis that will be allocated are randomly selected using uniform random selection by performing min(dj, sj ) independent trials. The probability of a driver getting allocated after following the repositioning recommendation is defined as a steady-state fraction of drivers that got allocated out of the total number of drivers who accepted the repositioning recommendation:

[0101] 0r = lim k— >°° P ceC yc(k) |C| (13)

[0102] Driver State Aware Repositioning Recommendation Model

[0103] According to embodiments of the invention, the repositioning recommendation model can be used to provide recommendations to the idle-standing taxi drivers. Decision variable x as specified in equation (5) is used to calculate the optimal repositioning recommendations that will maximize the expected profit accumulated by successful allocations of the drivers in the planning horizon. 202407501

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[0105] 1) Supply Vector. A supply vector s e Z |R| is a random vector consisting of the number of taxi drivers that will be available in each region after the repositioning is completed based on the drivers’ choices and element sj denotes the number of taxi drivers available in the region j e R in the planning horizon H. Random variable Xcj is a defined on the probability space associated with the driver c e C, which is denoted as (Q, F, Pc) such that:

[0106] Xcj = ( 1 with probability Pc({co2 = j}) 0 with probability 1 - Pc({co2 = j}) (14)

[0107] Where, Pc({co2 = j}) is the total probability of the driver c e C moving to region j e R: Pc({co2 = j}) = p(c) ■ xcj + (1 - p(c)) ■ Lcj (15) To determine the total number of taxis that will be available in each region, the probabilistic behavior of each taxi driver is considered and is aggregated across all drivers, sj = X ceC Xcj (16). Since, Xcj are independent Bernoulli random variables, the total taxi count sj follows a Poisson binomial distribution, which is a generalization of the binomial distribution where the probability of success is not the same for each trial. The probability mass function P({sj = b}) of the Poisson binomial distribution is given by:

[0108] X CbcC Y ceCb Pc({co2 = j}) Y c / eCb (1 - Pc({co2 = j}))_ (17)

[0109] where Cb is a subset of {1, 2,..., m} with b elements. Obtaining the probability distribution of the Poisson binomial distribution is computationally hard, due to the necessity of evaluating all possible subsets of drivers. This complexity arises from the fact that the number of subsets grows exponentially with the number of drivers m. Specifically, the probability mass function involves summing over (™) terms, making it impractical for large values of m. Moreover, unlike the binomial distribution, the Poisson binomial distribution lacks a simple closed-form expression for its probability mass function, further complicating its use in analytical studies and practical applications. Despite the computational complexity, the expected value of sj can be derived due to the linearity of expectation and assuming independence of the Bernoulli trials. The expected value of sj is given by: 202407501

[0110] 16

[0111] E[sj ] = Xm c=1 E[Xcj] = X ceC p(c) ■ xcj + (1 - p(c)) ■ Lcj (18)

[0112] 2) Demand Vector. A demand vector d e Z |R| is a random vector consisting of the number of requests that will appear in each region in the planning horizon. Demand is assumed to be a Gaussian random variable, whose parameters are unknown and need to be estimated.

[0113] <i, i < ■..■»* i,,,\‘ iL.r i i

[0114]

[0115] First, a function gj: d~j — vj is learnt using a gradient-boosted tree-based regression model for each region j e R using the historical demand data. This function maps a vector d~j, that contains tuples of demand and covariate information of previous planning horizons to the forecast:

[0116] gj (d~j) = vj (20)

[0117] Where,

[0118] ll|, 7 ‘! 'Ji ' ' ' ‘ |1*. ’’ » ■ >

[0119]

[0120] Each variable dj (h - t) denotes the realization of the random variable dj(h - t), i.e., the number of passenger demands that appeared in the region j e R in the planning horizon h - t and "d(h - t) denotes the covariate information, which contains three additional features, namely i) hour of the day, ii) day of the week, and iii) day of the month. Walk-forward validation is used to refine the trained model as the new data corresponding to the current time step is available. Parameter o 2 j of the error distribution N (0, o2 j ) is estimated using the residuals from the test dataset, and is defined as the expected value of the squared residuals:

[0121]

[0122] • \ « 11,1, ■ ' 121 >

[0123] 3) Travel Time Matrix. Travel time matrix T e R nxn is a random matrix, where Tij is the time it will take to travel from region i e R to region j e R. Tij is modelled as a Gaussian ransom variable:

[0124]

[0125] 202407501

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[0127] Function h: Tij — Tij is learnt using a gradient-boosted tree-based regression for the inter-region pairs (i, j) e R x R using the historical trips data. The function maps the feature vector Tij that contains i) historic travel times between the region i to j, ii) distance between the region i to j, iii) hour of the day, and iv) day of the week, to the expected value of the travel time:

[0128]

[0129] :• Tr, r < 2n

[0130] The error distribution is modelled as Gaussian N (0, sij) and the parameter, sij) is learned using the residuals from the test dataset, and is defined as the difference between the realization of random variable Tij and the predicted demand value:

[0131]

[0132] i. 2 •

[0133] Travel time for c e C, standing in region i e R for region j e R is denoted as:

[0134]

[0135] J 125?

[0136] To ensure that the taxis recommended to go to a particular destination j e R reach the destination within the planning horizon, the travel time forecasted using the travel time prediction model Tcj for taxi driver c e C, must be no more than the length of the duration of the planning horizon:

[0137]

[0138] ■,; T H i ft <2oi

[0139] 4) Objective Function. The expected number of taxis that will be allocated in region j e R in the planning horizon is given as follows:

[0140]

[0141] t <1, II I 2" i

[0142] where sj is a Poisson binomial distributed random variable and dj is a normally distributed random variable as discussed previously. Obtaining a closed-form expression for

[0143]

[0144] :1-!1■ Tfl,may be difficult due to the computational complexity of deriving the probability distribution of sj. Therefore, the expected supply E[sj] is being relied upon, and define an approximation to the expected allocation. This is 202407501

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[0146] determined using the expected supply E[sj] and a sampled demand,\ d ’

[0147] - Y - <2SI

[0148]

[0149] One possible objective for rebalancing is to maximize the expected allocation in Eq. (28). However, the fuel cost associated with repositioning idle-standing taxis can be considered. Maximizing profit, which is a function of earnings from allocated taxis and taxi rebalancing costs, can be focused to ensure overall benefit. The expected ride fare Pj for the trips starting in region j e R can be calculated using historical data. The cost Qcj of moving a taxi from its current location, say region i e R to region j e R, is calculated based on the distance between the regions, the average taxi mileage, and the fuel cost. This cost represents the expense incurred in repositioning taxis to meet demand. Expected profit is defined as the difference between the expected earnings and rebalancing costs:

[0150]

[0151] 5) Repositioning Recommendation Model. The repositioning recommendation model (30) generates an optimal taxi-destination match, ensuring the taxis are dispatched to destinations with a higher chance of getting allocated during the planning horizon. Using Eq. (6), Eq. (26), as constraints and Eq. (29) as the objective function, where tjj is given by Eq. (28), the proposed model can be written as:

[0152] . \ ’ • \ \ '

[0153] w X", I (’ <

[0154]

[0155] >!. x: i*. p ■ i’. »

[0156] It is contemplated there can be a possibility of an optimization problem of the taxi rebalancing recommender system. 202407501

[0157] 19

[0158] III. ALGORITHM

[0159] According to an embodiment of the invention, the driver state-aware reposition recommendation algorithm takes as input, i) confidence model parameters ar, |3r, ii) allocation probabilities 0, iii) features used for preference prediction z, iv) variance of demand forecast error o, v) features used for demand prediction ~d, vi) features used for travel time prediction T~, vii) inter-region travel distance 5, and viii) expected profits in planning horizon P, and returns the repositioning recommendations. This algorithm is executed at a fixed rate, i.e., after every H minutes. An example of such an algorithm is shown below. It is contemplated that a detailed analysis on repositioning frequency optimization can be performed. 202407501

[0160] 20

[0161] Uuorithrn 1 i i -.-r Mate \warc Reposition Rexumiiicnd.iiion

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[0218]

[0219] Rt turn:

[0220] CASE STUDIES

[0221] Experiments are performed to test the proposed driver state aware repositioning recommendation algorithm using 7,000 taxis to simulate large-scale fleet operations. Operational details of the proposed driver preference and confidence-aware taxi rebalancing system are analysed and the components that will become the key ingredients of a realistic test-bed used for simulation case 202407501

[0222] 21

[0223] studies can be determined. A simulated taxi network can be developed based on real data from New York City. The repositioning recommendation model (30) was triggered every H = 60 minutes. In order to generate the road network, city Manhattan was partitioned into regions denoted by the set R. The centers of each region is determined using the k-means clustering algorithm. The road network is then leveraged to define a directed graph with the nodes representing the road junctions, and the edges representing the links between the road junctions. Dijkstra’s shortest path algorithm is used to calculate the shortest distance route between the region centers. 5 represents a matrix that stores the shortest path distance 5ij between region i, j e R. Taxi drivers pick up passengers from one region and drop them off at the other region. After dropping off the customer, a driver has a choice to either keep waiting or reposition to a new region. Fig. 4 shows maps illustrating a prediction model analysis and an idle-standing driver and the top 3 potential destinations which will maximize his likelihood of getting the ride in next H minutes. For example and as shown in Fig. 4, the driver is standing idle in the highlighted region, and the neighbouring regions represent places where the taxi driver had re-positioned in the past.

[0224] Demand Prediction

[0225] The demand prediction problem can be formulated as a time-series forecasting problem. Various features can be used for training an XGBoost model. To determine the optimal look-back window size, i.e., the number of previous hours of demand to consider for training, the window size was defined as a parameter alongside three other model parameters: (i) the number of estimators, (ii) max depth, and (iii) learning rate. Grid search-based approach was employed to identify the best model parameters. As baselines, two pretrained deep learning-based large language models were used: CHRONOS, and MOIRAI. Traditionally, deep learning for time series forecasting has adhered to a one-model-per-dataset framework, restricting its ability to capitalize on the impact of large pre-trained models. The emerging concept of universal forecasting, which involves pre-training on an extensive collection of time series datasets, envisions a single Large Time Series Model capable of tackling diverse downstream forecasting tasks. CHRONOS exemplifies this approach as a probabilistic time series model that converts time series values into a 202407501

[0226] 22

[0227] fixed vocabulary through scaling and quantization. It then trains transformer-based language model architectures on these tokenized values using cross-entropy loss. Pre-trained on the T5 family with parameter sizes ranging from 20M to 710M, CHRONOS utilizes a vast collection of publicly available datasets and a synthetic dataset generated via Gaussian processes to enhance generalization. Another pre-trained model, Masked EncOder-based UnlveRsAI Time Series Forecasting Trans_former (MOIRAI), is trained on the Large-scale Open Time Series Archive (LOTSA), which includes over 27 billion observations across nine domains.

[0228] The evaluation of demand prediction models shows that XGBoost outperformed both MOIRAI and CHRONOS across various error metrics, demonstrating a lower mean error and median error and the highest correlation with actual demand values. Fig. 5 shows graphs illustrating error analysis, according to an embodiment of the invention. In particular, the graphs of Fig. 5 show a relationship between density and error and a relationship between density and absolute error for the different models. Specifically, 1 ) XGBoost had a mean error of -0.123, a median error of -0.003, and a correlation of 0.981 with the actual values, while MOIRAI had a mean error of -3.344, a median error of -0.911, and a correlation of 0.971, and CHRONOS had a mean error of -4.047, a median error of -0.718, and a correlation of 0.889. 2) Despite mean errors being affected by outliers, the median error for all three models is close to zero, indicating that none of the predictors are biased towards over / under prediction. 3) MOIRAI performed slightly better in terms of skewness (0.08) compared to XGBoost (0.45), suggesting MOIRAI has fewer instances of frequent underestimation of demand. 4) Absolute error statistics further highlighted XGBoost’s superior performance, with a median absolute error of 3.92, a 25th percentile error of 0.97, a 75th percentile error of 11.02, and a 95th percentile error of 31.79. 5) Fig. 6 shows graphs illustrating spatial-temporal error analysis, according to an embodiment of the invention. Specifically, Fig. 6 shows spatial-temporal error plots, such as the distribution of error for three models and the distribution of absolute errors for three models. The percentage error is evaluated by dividing the median error by the median demand in the region. As seen in the first plot (median error vs region) in Fig. 6, the mean of the median errors across the regions is 3.91, and the mean demand across the regions is around 57.56. Overall, 202407501

[0229] 23

[0230] the error is higher in value for the regions with high demand, with the highest percentage error being 10.33% and an overall forecasting error of around 6.7%. The second plot (median error vs hour) of Fig. 6 shows the median absolute error for each hour. The median hourly absolute error is around 5.31 on average for the entire network whereas the median hourly demand is around 38.12. 6) To establish if this error is sufficiently small, the error can be evaluated using the success of the rebalancing recommendations, which is measured in terms of driver confidence, fleet utilization, and overall profits.

[0231] Travel Time Prediction

[0232] Fig. 7 shows graphs illustrating probability distribution of error in travel time prediction, according to an embodiment of the invention. The figure on the left (density vs absolute error) in Fig. 7 shows the probability distribution of the error in travel time prediction. The median error is approximately 2 minutes and the 99th percentile of error is approximately 11 minutes. The error in the travel time prediction impacts the reachability of the idle-sanding taxis as defined by equation (24). Reachability is defined as the fraction of inter region trips that can be served withing planning horizon. Duration of the planning horizon plays a critical role in determining the reachability of the taxi drivers. The figure on the right (reachability vs time step duration) in Fig. 7 shows the reachability (percentage) vs planning horizon (minutes) plot. The black curve shows that a planning horizon approximately 30 minutes is sufficient to ensure that a taxi is able to reposition between any two regions within the planning horizon. Further, the red curve shows that in addition to repositioning, a taxi driver can also finish a trip if the planning horizon is further increased to 60 minutes. To achieve this, trips that are no longer than 30 minutes are considered. Such trips account for 95% of all the trips in the raw data. This helps to define the time step to be 60 minutes in duration, and the benefits are two-fold. Firstly, the planning horizon duration is sufficiently large so that the demands can be forecasted with high accuracy in terms of error percentage (small planning horizon duration lead to sparse time-series which are difficult to forecast). Secondly, it ensures that each taxi can reposition and serve a customer within the planning horizon, thus it makes it possible to discretize the simulation into time-steps, in which the sequence of operations in Algorithm 1 or Fig. 3 can be executed. 202407501

[0233] 24

[0234] Taxi Driver’s Preference to Reposition

[0235] Fig. 8 shows graphs illustrating the relationship between feature and accuracy, according to an embodiment of the invention. Specifically, the first bar chart (feature vs feature weight) of Fig. 8 illustrates the feature importance plot highlighting that search distance plays the highest role in predicting taxi driver repositioning preference, while the second graph (accuracy vs destination) shows the accuracy improvement as the number of destinations increase. To evaluate the performance of the driver preference prediction problem, a modified accuracy is used as the metric of evaluation which is defined in the context of top-k destinations. The top-k destinations for a driver are predicted by selecting the regions with the highest Lcj values. If the driver’s actual choice of destination falls within these k choices, the prediction is correct. The fraction of total number of correct predictions out of total number of predictions made for the driver is defined as the accuracy. As shown in right plot (accuracy vs destinations) in Fig. 8, the accuracy with which the proposed model can pinpoint (k = 1 ) the exact choice of driver destination is around 73%. Note that this accuracy varies from driver to driver due to a varied degree of randomness in each driver’s decision-making process and 73% is the average accuracy value for all the drivers. As the value of k increases, the accuracy increases as well, for e.g., it can be predicted that a driver will head to one of the two predicted destinations (k = 2) with an accuracy of 83%, one of three predicted destinations (k = 3) with an accuracy of 87% and one of four predicted destinations (k = 4) with an accuracy of 90%. For the repositioning recommendation system, it is unnecessary to predict the exact destination of a driver, as this is neither possible with absolute certainty due to the inherent random choices of drivers, nor desirable, as drivers are expected to remain more exploratory, i.e., has a non-zero probability of moving to more than one region. This exploratory nature will ensure that the drivers can be steered to destinations in an optimized manner avoiding over supply. Instead, a probability distribution over the regions may be required, representing a driver’s choice of the repositioning destinations, which can be used to estimate the expected supply distribution (18). A dataset can be used to extract the features for training the driver preference prediction model and Fig. 8 shows the features used for predicting the driver preference. As a first step, the unique drivers in the dataset is identified, which 202407501

[0236] 25

[0237] can be done by filtering out the drivers whose “medallion” matches with the “hack license”. A unique driver is the one for whom a trail of pick-ups and drop-offs which is coherent with time can be established. This means that every pickup is later than the previous drop-off. This information has been provided because in the dataset, multiple drivers can have same “hack license” at the same time. Since the dataset contains only the pick-up and drop-off data, a driver’s repositioning choice is defined as the next region of pickup after a drop-off. Each driver’s preference is learned by training a separate logistic regression model. The drivers whose choice can be predicted with the highest accuracy are selected. In this case the top 100 drivers are selected. These drivers are chosen to be representative drivers, and a group of drivers are assumed to have the same preference as that of the representative driver in the group, e.g., if there are 1000 drivers in the simulation, then groups of 10 drivers will have same preference distribution as their representative driver. This assumption is taken because of practical limitation of data availability, e.g., in a dataset there are only 925 unique drivers and not all of them have a predictable preference. Each driver preference model is trained using the features shown in the left plot in Fig. 8. It was found that the topmost feature to predict if a driver will move to the destination or not was the distance between the two regions. It is obvious that a driver will not go very far away in search of the passengers. Second influential feature is the median trip distance at the destination. This is because longer trip distance translates to higher profits. Note that the labels or targets in the logistic regression model are {1,0}, where 1 implies that the driver will go the destination. Since, raw data only contains the data points corresponding to the selected destinations (label=1), the training data is augmented with label=0 for all the other destinations.

[0238] The corresponding features such as search distance, median trip distance etc, can be easily extracted from the raw data. So, for each label=1 data point, there are 65 data points each with the label=0, since there are 66 regions in total. Once the logistic regression model is trained, its performance can be evaluated using accuracy evaluation, which measures how often the model correctly predicts {0,1}. However, this may not be a good metric due to the significant imbalance between the label=0 and label=1 data points. The abundance of label=0 data points makes it 202407501

[0239] 26

[0240] easier to reject a potential destination, leading to misleadingly high accuracy values — around 99% for almost all drivers. So, a modified accuracy is chosen as a metric of evaluation as detailed previously and shown in Fig. 8.

[0241] Fig. 9 shows graphs illustrating the impact of individual factors on driver’s repositioning choice, according to an embodiment of the invention. The first plot (probability density vs distance of destination region) shows the distribution of distance of destination region for two decisions, i.e., to reposition or to wait in the same station. The red plot shows the distribution of the distance that the driver is ready to travel in search of passengers. The blue plot shows the distribution of the distance that the driver will not travel in search of passengers. As seen in the plot, the driver rarely travels more than 5 km in search of passengers. The second plot (probability density vs pickups in region) shows how the distribution of the pickups in a region impacts a driver’s decision to stay in the same region or move to another region. As seen in the plot the drivers are aware of the upcoming demands in the region they are standing because the driver repositions himself if the demand falls below a certain threshold. The red plot is the distribution of the pickups for which the driver chooses to move to another region. The blue plot shows the distribution of the pickups in the region for which the driver stays in the same region. As seen in the third plot (probability density vs median trip distance of destination) the drivers are aware of the median trip distance at the destination. This can be seen as a spike in the probability distribution (blue plot) in which the drivers don’t move to the regions where median trip distance is almost zero. Finally, with respect to the hour of the day (see graph of probability density vs hour), there is a slight preference to stay in same region during evenings even though there is no clear preferred hour.

[0242] Taxi Driver’s Confidence on Recommender System

[0243] As the driver keeps following the system recommendations, the driver’s belief is updated using (Eq. (9)). Three scenarios are created based on the values of the weights eO, e1: 1) Neutral eO = e1: In this scenario, a neutral impact of successful and failed recommendation on the driver’s confidence is assumed. 2) Pessimistic eO < e1: In this scenario there is a more impact of failed recommendations as compared to the successful recommendations on the driver’s confidence. 3) 202407501

[0244] 27

[0245] Optimistic eO > e1: In this scenario there is a more impact of successful recommendations as compared to the failed recommendations on the driver’s confidence.

[0246] Fig. 10 shows graphs illustrating relationship between driver classes and confidence level, according to an embodiment of the invention. In particular, one graph shows the dynamics of the confidence level of three classes of drivers namely optimistic, pessimistic, and neutral while the other graph shows the expected rewards associated with driver following their own preference or following the recommender system. As seen in the graph (average confidence vs hour) in Fig. 10, the confidence of the drivers that are defined as optimistic grows the fastest, followed by the neutral drivers, and slowest by the pessimistic drivers. Note that for the pessimistic drivers, the confidence level doesn’t converge to 1, rather it converges to 0.9. The other graph (probability density vs expected reward) shows the probability distribution of the expected allocation probabilities associated with each of the two choices, i.e, following own preference, or following the recommender system. The distribution in blue is that of the expected allocation probability 9c of the driver when he follows his own preference. It can be seen that the expected value of the expected allocation probability is close to 0.4 which means that there is a 42% chance (on average) of allocation within the planning horizon, if the driver follows his own preference. On contrary the distribution in red is that of the driver always following the repositioning recommender system. It can be seen that the expected value of the expected allocation probability 9r is close to 90%, which means that if the diver follows the repositioning recommendation from the recommender system, there is a 90% chance (on average) of allocation within the planning horizon. The black dotted line represents the belief of the driver regarding the recommender system at the beginning of the simulation. Flat prior ensures uniform distribution of a driver’s belief at the beginning of simulation.

[0247] Evaluation Metrics

[0248] To evaluate the performance of the proposed algorithm, a simulation over 10 days is performed. Since each time step is 60 minutes in duration, the total number of time steps in the simulation is 240. For each time step, the information related to the 202407501

[0249] 28

[0250] performance of the repositioning recommender system is recorded. The metrics to evaluate the performance of the repositioning recommender system are as follows: 1) Fleet Utilization: Fleet Utilization is defined as the fraction of drivers that got allocated in a time step. If a driver is allocated in the time k e K the reward yc(k) is defined in (8). The fleet utilization is evaluated using the following expression:

[0251] . \ ‘ \ j

[0252]

[0253] 2) Average Driver Profit: Driver profit for each driver c e C is defined as the difference between the earnings made by the driver in time step k e H and the rebalancing cost. Let the recommendation decision variable in time step k be denoted as xcj (k), and the earning of the driver c be Pcj (k) and Qcj (k). The average driver profit as a metric is used, which is evaluated as:

[0254] J__£ I"" BMW)

[0255]

[0256] 3) Driver Confidence: Average driver confidence at the end of the simulation is used as a measure to evaluate the impact of the performance of the repositioning recommender system on a driver’s confidence which is evaluated as follows:

[0257]

[0258] 4) Unmet Demand: Unmet demand is the fraction of unfulfilled passenger requests which is evaluated using the difference between the actual demands in a time step and the served demands in a time step. The served demands is also same the number of allocated taxis. So the unmet demand is evaluated as follows:

[0259]

[0260] 5) Rebalancing Efficiency: The rebalancing efficiency is evaluated as a fraction of recommendations that were successful, i.e., out of all the recommendations that the system gave to the driver’s, how many recommendations were effectively adhered by the drivers. The rebalancing efficiency is evaluated as: 202407501

[0261] 29

[0262] — I—— |

[0263]

[0264] 6) Computation Cost: The computation time is critical to ensure that the model can generate a rebalancing recommendation within the time step duration. The decision variables scale with increase in fleet size and the number of regions. The regions are assumed to remain the same and evaluate the computation time as a function of the fleet size.

[0265] Baseline Models

[0266] The model (30) can be formulated as a Linear program, by relaxing the decision variable xcj e [0, 1], and using an auxiliary variable qjj that replaces tjj in objective function Eq. (29) and two new constraints are introduced:

[0267]

[0268] • ■ 2,.! R. <, W. 5 ( leu

[0269] In an embodiment, the baseline models were formulated by altering the expected supply equation (18) in Model 30. Starting from a model that is agnostic to the driver confidence-level as well as preferences, the model is incrementally improve by adding more information with regards to the state of the drivers. The objective of creating these models is to evaluate the improvement in the recommender system in terms of the evaluation metrics as defined in the previous subsection.

[0270] 1) Agnostic Recommender Model: This model is agnostic to the state of the driver, i.e., the recommender system doesn’t take the driver’s confidence as well as preferences into consideration while generating the repositioning recommendations. Most of the models in the existing literature are agnostic model. Agnostic model is same as (30), except that the expected supply (18) is now defined as:

[0271] *v"ll' '1

[0272]

[0273] ■

[0274] This implies that the agnostic models assume that a recommendation given to an idle standing driver shall be adhered with absolute certainty. 202407501

[0275] 30

[0276] 2) Confidence-Aware Recommender Model: This model incorporates driver confidence into the recommendation process. The objective is to adjust the recommender system based on the likelihood of a driver rejecting a recommendation. In the case of rejection, the model assumes that the driver remains in the same region. An alternative assumption where the driver chooses a random destination is considered impractical, as rational drivers are unlikely to act randomly. To represent whether the driver stays in the region, an indicator function I used, which is 1 if the driver remains in region j after rejection, and 0 otherwise. Equation (18) is defined as follows:

[0277]

[0278] 3) Confidence & Preference Aware Recommender Model:

[0279] The confidence and Preference aware model is same as the model (30) with linearization using Eq. (36). So this model is aware of the driver confidence as well as preference.

[0280] 4) Proposed Recommender Model:

[0281] Model (30) in it’s original form suffers from the over saturation problem, i.e., there is no upper limit on how many drivers must be recommended to the destination. To overcome this, over saturation is prevented by using a parameter that controls the total number of recommendations to be less than a constant multiple of the expected demand.

[0282]

[0283] So, the only difference between the proposed model and the confidence and parameter aware recommender model is the usage of over-saturation parameter.

[0284] Model Performance Analysis

[0285] To evaluate the performance of the proposed recommender model, each driver is initiated with a flat prior distribution over the expected reward. The simulation in run for a period of 10 days after which the driver confidence converges as shown in Fig 10. At each time step, the evaluation metrics is extracted: fleet utilization (31), 202407501

[0286] 31

[0287] average driver profit (32), driver confidence (33), unmet demand (34), rebalancing efficiency (35), and computation time.

[0288] Fig. 11A shows a table illustrating a model performance analysis while Fig. 11 B shows graphs illustrating a comparison of a proposed model with the baseline models in terms of evaluation metric, according to an embodiment of the invention. Specifically, Fig. 11 A shows the performance of the proposed model. In each plot, four models are compared namely the agnostic recommender model, confidence aware recommender model, confidence and preference aware recommender model, and the proposed model, for three classes of drivers, i.e., neutral, pessimistic and optimistic. As seen in the table, the proposed model outperforms all the baseline models for all the classes of drivers thus signifying that incorporating the driver confidence as well as preference can lead to significant improvements in terms of the defined evaluation metrics. The graphs of Fig. 11 B show a fraction of the fleet allocated in each hour on average, profit that a driver earns in each hour on average, average confidence of the drivers at the end of the simulation, fraction of demand that remains unmet in each hour on average, fraction of recommendations that led to a driver getting reward and computation time to solve the optimization model.

[0289] It was found that the fleet utilization (see Fig. 11 B) using the proposed model improved by 9.8% in the case of neutral drivers, 6.8% in the case optimistic drivers, and 40% for the pessimistic drivers, which is approximately 19% average improvement as compared to the agnostic model. This highlights the importance of giving effective recommendations to the drivers, because in the pessimistic case if a driver experiences an incorrect recommendation, then his / her confidence in the recommender system declines substantially, the result leads to lower confidence in the recommender system in the future and hence lower fleet utilization. The rebalancing efficiency graph (see Fig. 11B) shows the effectiveness of the recommendations given by the proposed model. The proposed model leads to 85% higher efficiency in terms of rebalancing recommendations in the case of neutral drivers, 78% higher efficiency for the case of optimistic drivers, and 135% higher efficiency for the case of pessimistic drivers, which leads to 99% higher rebalancing 202407501

[0290] 32

[0291] efficiency for the proposed model. Due to effective recommendations, the driver confidence (see Fig. 11 B) is 4% higher for the proposed model for the case of optimistic drivers, 10% for the case of neutral drivers, and 106% for the pessimistic drivers, which leads to 40% higher average confidence level of the drivers. The sharp contrast in the confidence level of the drivers is because of the higher penalty (9) for ineffective recommendations in the case of the pessimistic drivers. Further, the proposed model leads to 51 % less unmet demand (see Fig. 11 B) in case of the optimistic drivers, 79% lesser unmet demand in case of neutral drivers, and 60% lower unmet demand in the case of the pessimistic drives, which leads to 63% lesser unmet demand on average as compared to the agnostic model. The proposed model also leads to the highest hourly profits with profit (see Fig. 11 B) for the proposed model being 19% higher for the case of the optimistic drivers, 20% for the case of neutral drivers, and 44% higher driver profits for the case of the pessimistic model, which leads to an overall 27.67% higher driver profits. Finally, as shown in Fig. 11 B, the time it takes to solve the proposed model is 27.75 secs for the fleet size of 7000 taxis, which is higher than the agnostic model which takes 6.53 secs. However, the computation time is well within the tolerance limit because the time step for the proposed model is for 60 minutes. Overall, an improvement trend can be seen as the Agnostic model moves to the Proposed model. The intermediate models that have a partial information about the driver state also show an improvement in the performance metrics. Another important finding is that the difference in the performance is more prominent in case of the pessimistic drivers. This is because the confidence of the drivers in the case falls more rapidly when an incorrect recommendation is given by the recommender system.

[0292] In an embodiment, driver preference and confidence aware taxi rebalancing model are formulated that can effectively provide the repositioning recommendations to the taxi drivers. The proposed model also provides a quantitative way to study the dynamics of the driver’s confidence-level on the recommender system, and how incorporating driver preferences and confidence levels can enhance the performance in terms of the driver profits, and fleet utilization. Extensive experiments show that the proposed model performs better than the model that is 202407501

[0293] 33

[0294] agnostic to these attributes of the taxi driver, and hence can be used to provide better repositioning recommendations.

[0295] Fig. 12 shows a schematic diagram illustrating a system for routing transportation, according to an embodiment of the invention. As shown in the figure, the system can be a Driver State Aware Repositioning Recommender System (DSRS) where an allocated taxi picks up a passenger and drops him to his destination. The idle taxi needs to know where hould he go next to get his next ride as quickly as possible and the DSRS provides the destination recommendation.

[0296] Fig. 13 shows a schematic diagram illustrating an example mobile application of the system of Fig. 12, according to an embodiment of the invention. In this example embodiment, the DSRS system can be a mobile application or a dashboard embedded in the taxi.

[0297] Fig. 14 shows a schematic diagram illustrating an architecture of the system of Fig.

[0298] 12, according to an embodiment of the invention. In this example embodiment, the system architecture can include the components of data management, data preprocessing, feature extraction, demand forecasting, supply forecasting, optimization and model explanation. The system can further include traffic health screening, driver behaviour analysis, III buffer, III backend and a dashboard web portal.

[0299] The foregoing description shall be interpreted as illustrative and not be limited thereto. One of ordinary skill in the art would understand that certain modifications may come within the scope of this disclosure. Although the different non-limiting embodiments are illustrated as having specific components or steps, the embodiments of this disclosure are not limited to those combinations. Some of the components or features from any of the non-limiting embodiments may be used in combination with features or components from any of the other non-limiting embodiments. For these reasons, the appended claims should be studied to determine the true scope and content of this disclosure.

Claims

20240750134Claims1. A system for routing a fleet of transportation, the system comprising:a fleet management server;a fleet of transportations, each of the transportation in the fleet comprises at least one user’s client device;a communication network in wireless communication with the fleet management server and the at least one user’s client device;characterised in that the fleet management server comprises:a routing recommendation model having at least one processor having a memory and a set of instructions stored thereon, the routing recommendation model operable to:determine at least one transportation in the fleet of transportation in a state of idle;andgenerate a recommendation notice for transmitting to the at least one user’s client device of the at least one transportation in the fleet determined to be in a state of idle, the recommendation notice comprising:at least one route destination;an estimated time of travel to each of the at least one route destination;an amount of power consumption rate required for the at least one transportation in the fleet of transportation determined to be in a state of idle to travel from a current location to each of the at least one route destination,or combination thereof.

2. The system according to claim 1, the system comprising:a data fetching model operable to receive at least one class of data from a database.

3. The system according to claim 2, characterised in that the at least one class of data receivable by the data fetching model is an adherence data20240750135comprising a record of historic adherence to the notification generated by the a user.

4. The system according to claim 2, characterised in that the at least one class of data receivable by the data fetching model is a preference data comprising a feature vector to store an information to generate a user’s preference to execute recommendation notice.

5. The system according to claim 2, characterised in that the at least one class of data receivable by the data fetching model is a demand data comprising a feature vector to store an information to generate a forecast for a route destination in demand of transportation.

6. The system according to claims 1 - 5, characterised in that the system comprises:a confidence model operable to generate a probability of the user accepting and executing the recommended notice.

7. A method for routing a fleet of transportation, the method comprising:determining, by way of a global positioning system (GPS), at least one transport in a fleet of transportation in a state of idle; andgenerating, by way of a route recommendation model, a recommendation notice for transmitting to at least one user’s client device of the at least one transportation in the fleet determined to be in a state of idle via a communication network,characterised by that the recommendation notice comprises:at least one route destination;an estimated time of travel to each of the at least one route destination;an amount of power consumption rate required for the at least one transportation in the fleet of transportation determined to be in a state of idle to travel from a current location to each of the at least one route destination,20240750136or combination thereof.

8. A processor program product comprising instructions stored thereon to cause the apparatus as disclosed in claims 1 - 6 to execute the steps of claim 7.

9. A computer readable medium having stored thereon the processor program product of claim 8.

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