FASTER: Fusion AnalyticS for public Transport Event Response

F ASTER: F usion AnalyticS for public T ransp ort Ev en t Resp onse Sebastien Blandin, Laura Wyn ter, Hasan Poonaw ala, Sean Laguna IBM Researc h Singap ore { sblandin, lwynter, hasanp, slaguna } @sg.ibm.com Basile Dura Ecole P olytechnique F rance basile.dura@polytechnique.edu Abstract Increasing urban concen tration raises op erational c hallenges that can b enefit from integrated monitor- ing and decision supp ort. Such complex systems need to lev erage the full stac k of analytical metho ds, from state estimation using multi-sensor fusion for situa- tional aw areness, to prediction and computation of optimal resp onses. The F ASTER platform that we describ e in this w ork, deploy ed at nation scale and handling 1.5 billion public transp ort trips a y ear, of- fers suc h a full stac k of tec hniques for this large-scale, real-time problem. F ASTER provides fine-grained situational aw areness and real-time decision supp ort with the ob jectiv e of improving the public transp ort comm uter exp erience. The metho ds employ ed range from statistical machine learning to agent-based sim- ulation and mixed-in teger optimization. In this w ork w e present an ov erview of the challenges and meth- o ds in volv ed, with details of the comm uter mo vemen t prediction module, as well as a discussion of op en problems. 1 In tro duction Efficien t mov ement of people in increasingly dense cities is one of the key c hallenges to wards sustain- able gro wth of urban areas throughout the world. Enabling effectiv e resp onse to incidents and unfore- seen e v en ts requires real-time monitoring of the pub- lic transp ort net work level of service, which in turn hinges on fine-grained real-time information on pas- senger mov emen ts. While real-time information on v ehicle mo vemen ts is at the heart of traditional control cen ters, high- qualit y quantitativ e information on passenger mov e- men ts is usually lacking. Indeed, while tic k eting data w ould represent the most natural source of such in- formation, it do es not generally provide destination information when a passenger en ters the netw ork, is often not a v ailable for pro cessing in real-time, and in dense net works does not indicate which route is cho- sen. Cameras p ossess v aluable information on pas- senger counts on platforms but due to computational constrain ts are seldom pro cessed to provide quanti- tativ e measures. Hence estimation of the netw ork state in terms of the current passenger mo vemen ts requires the fusion of multiple real-time data sources. In a real-world setting how ever, n umerous c hallenges arise. The dif- feren t sensing sources a v ailable hav e heterogeneous co verage, latency , and error statistics. Metho ds used to lev erage the multi-modal sources must therefore b e robust to different noise levels and time scales. Because of the real-time nature of the problem, they m ust also b e fast and scalable. The F ASTER solution is motiv ated by the con- strain ts arising when applying mainstream AI tech- 1 niques to op erational settings. Robustness in practice An imp erativ e of mission-critical applications is that a minimal level of service is required in all conditions. Because public transp ort systems are even t-based in nature, via the dynamics of train arriv als and departures, lac k of data due to failure of the sensors or IT net work is often indistinguishable from a fault of the underlying physical system being monitored. Consistency across heterogeneous use-cases A cit y-scale cyb er-ph ysical system needs to supp ort heterogeneous use-cases, from monitoring of cro wd lev els in sections of train platforms to offline anal- ysis of daily netw ork level of service. This requires that the underlying solution in tegrates a trade-off b e- t ween optimal estimation metho ds for sp ecific use- cases (real-time, offline), and global coherence of the estimates. Complexit y v ersus optimality With a goal of mo del explainabilit y and robustness, imp ortan t for instance in critical situations suc h as incident re- sp onse, it is imp ortant to con trol the complexity of the mo dels used, for instance by com bining simple linear mo dels in a multi-modal fusion framework, whose output can in turn b e used by parsimonious agen t-based engines. Con tributions The main contributions of this w ork include: • design of an end-to-end solution using machine learning, agen t-based sim ulation and mixed- in teger optimization, • nov el methodologies employ ed in sp ecific ana- lytic mo dules such as the passenger mov ement prediction mo del, • implementation and deploymen t of the solution at city-scale with constrain ts from real-time and offline settings. In Section 2 we presen t an o verview of related w ork. Section 3 pro vides a description of the system ar- c hitecture. In Section 4 we present and ev aluate a framew ork for commuter mov ements prediction. In Section 5 we outline the observed b enefits of such an in tegrated approach. W e conclude with op en prob- lems in Section 6. 2 Related w ork In the context of road net works, mo deling vehicle mo vemen ts has lev eraged techniques from sequential estimation and automatic con trol as early as the 90’s, with the seminal w ork of [32]. More recen tly , ap- plications of data assimilation and distributed plan- ning ha ve benefited from the prep onderance of smart- phones, used as sensors and instruments of feed- bac k, via guidance and incen tives [2, 44, 15]. Similar metho ds hav e subsequently been emplo yed for pub- lic transp ort netw orks [26]. F urther, the a v ailability of unstructured data has allow ed adding semantics to pure spatio-temp oral represen tation of dynamical patterns [33, 22]. Mobile traces ha ve b een used to analyze and pre- dict mov ement patterns of people [29, 19, 34, 36, 7, 13, 18, 21, 14, 35] with applications ranging from real- time congestion monitoring to land-use planning, us- ing techniques such as non-linear filtering and top o- logical graph analysis. Ho wev er, the spatial resolu- tion of GPS and cellular sensing is often a limiting factor in indo or settings. On the other hand, wifi sensing has fine-grained spatial resolution. [12] prop oses a system to estimate the num b er of passengers in public transport vehicles. In [5] users’ locations at a mass even t are trac ked us- ing prob e and other wifi requests. In [39, 24], the authors build a system to passively “sniff ” wifi sig- nals of office w orkers with an online SVM mo del to predict their length of stay . Wifi sensing finds further application in the retail sector. The authors of [28] presen t a solution to predict the next place that a user will visit based on a Hidden Mark ov Mo del (HMM) framew ork. In [20] the authors prop ose a Recurrent Neural Net work approach to classify GPS trip traces by 2 transp ortation mo de. Deep generative mo dels hav e b een explored in [25]. The authors of [8] use prob e requests to reveal underlying so cial relationships. In [1] the authors build snapshots of users at a large scale even t. These new opp ortunities to efficiently manage cities through the use of connected technol- ogy hav e led to the definition of “urban comput- ing” [42, 23, 43]. Agen t-based mo dels ha ve b enefited from develop- men ts in machine learning leading to hybrid mo d- els [41]. The problem of inferring train arriv als and hence delays of public transp ort services was ad- dressed by [16] where regional train timetables are inferred using cell phone data by detecting bursts in n umber of cell phones. How ever, their metho d would not work well on a dense urban metro system. The problem of detecting even ts of comm uters left b ehind in a subw a y system is addressed in [44]. The authors rely on offline farecard data, and estimate the most lik ely mo del assuming kno wn distributions of passen- gers walking times. Related to our goal of mo deling passenger mov e- men ts is the inference of users’ trip activities in a public transp ortation system. [11] prop oses a semi- con tinuous hidden Marko v mo del framework. Activ- ities are clustered using a Gaussian mixture that de- p ends on the start time and duration of the activit y . Similarly , [40] applies an HMM framework to activit y classification. While agen t-based simulation has historically been fo cused on infrequen t planning exercises, more recen t endea vors hav e pro v en that they are now practical for real-time applications [27, 10, 3, 17]. Progress in clas- sic problems suc h as vehicle routing [4] and the use of surrogate and hybrid models [31, 6] ha ve pushed the field forward, as well as system implementations suc h as the use of high-performance computing al- lo wing reac hing nation scale [30]. 3 System o v erview The F ASTER system is a city-scale solution pro- viding situational a wareness and decision supp ort to monitor and manage a large-scale public transport net work, in particular in terms of improving the re- sp onse during inciden ts and ev ents. 3.1 System con text The system describ ed in this work ingests sev eral het- erogeneous data sources with v arying lev els of latency in order to build a comprehensive and fine-grained view of the ground conditions, raise early warnings and alerts during unexpected even ts, and compute optimized resp onse plans to public transport inci- den ts. Data sources include structured and unstruc- tured data such as CCTV streams, tic keting informa- tion, wifi traces, system data on the train locations, and quantities deriv ed from cellular devices. One of the wa ys in which users interact with the F ASTER system is through the key p erformanc e in- dic ators (KPI) that the system pro duces and trans- mits to the command ce n tre. The KPIs pro duced in- clude real-time quantities suc h as estimated station platform cro wd, dw ell time dela ys and long aggregate passenger w ait times. The estimates are updated ev- ery time new data b ecomes av ailable, so that users ha ve access to the most accurate information despite latency of some data sources. This set of KPIs consti- tutes the common representation mo del for all anal- ysis. Breaking with the usual situation in that planning users and command cen tre users hav e differen t, segre- gated tools and metho dologies to analyze the public transp ort system, F ASTER offers these tw o classes of users access to the same system, so that all in- formation used, estimated or observ ed, is consisten t across the real-time analyses and the planning stud- ies. Figure 1 show cases a view of the key p erformance indicators. Sim ulation and optimization functionalities are in- tegrated into the ov erall system using the stream- ing data pro cessing flow and the online KPI esti- mates. Thus the user can choose to analyze past ac- tual days based on replaying the stored (real-time) es- timates, simulate historical even ts with adjustmen ts based also on the estimated v alues from the histor- ical day , analyze “typical day” scenarios in the ag- gregate, or in vestigate more prospective hand-crafted scenarios designed from an arbitrary base-case. Users can run the estimated or simulated scenario forward 3 Figure 1: F ASTER in tegrated real-time monitoring in terface. in time, or they may trigger the mixed-in teger opti- mization routine to find an improv ed solution based on a given p o ol of resources and one or more pre- defined metrics. F or instance, the optimization mod- ule can recommend emergency bus routes and sched- ules when an incident o ccurs. 3.2 Lam b da arc hitecture The F ASTER solution relies on a lam b da architecture to ingest on the order of 1 TB of data daily and serv e all classes of users according to their requirements. Pro cessed data feeds contribute to updating the com- mon represen tation in the form of aggregate KPIs, whic h supp orts all of the applications suc h as pre- diction, alerts, pro duction of optimal response plans, and playbac k analysis. The architecture, see Figure 2, includes b oth a batc h lay er and a speed lay er with the speed lay er fo- cused on real-time monitoring and decision supp ort, while the batch lay er orchestrates heavy pro cessing, sim ulation and calibration jobs. The lo w-latency data feeds consumed include data from wifi-enabled devices, CCTV cameras, and train lo cations. 3.3 Reconciliation engine The F ASTER solution provides a full digital t win of lo cations, p eople, and vehicles using a common refer- en tial. Each of these ob ject t yp es is augmen ted with Figure 2: Lambda architecture. appropriate KPIs. The reconciliation engine thus al- leviates the intrinsic limitations of individual sources, suc h as the limited co verage of cameras, the position- ing noise of indoor traces, and the latency of tic k eting information. In order to supp ort transparen t fusion of data sources as they become av ailable, we make use of a principled framework relying on data-stream sp e- cific fundamen tals such as linear mo dels and entit y resolution metho ds, that we then combine in a com- mon reconciliation engine integrating the most lik ely curren t common representation, as well as sp ecific applications requirements. F or eac h KPI, or related group of KPIs, the recon- ciliation op erates at the level of coarse agent metrics, using methods inspired b y (prior) linear po oling from the com bination of exp erts literature. Here eac h ex- p ert is a learner task ed to maximize the accuracy of certain commuter metrics, such as p oin t-to-p oin t tra vel-time, or cro wd densit y . The estimates are then re-aligned on a common spatio-temp oral grid, and re- w eighted according to estimates of the reliability of eac h learner for this data feed and the quan tities pro- duced in previous time steps. This metho d allo ws improving estimate accuracy , and has a computational adv antage in terms of pro- viding the estimates on the quan tities of in terest. Us- ing a single com bined indirect sensing mec hanism fa- cilitates the up dates and reasoning as well as error analysis. The end result is that the F ASTER sys- tem produces accurate estimates of quantities suc h 4 as train o ccupancy or platform cro wding, which are traditionally not av ailable due to the lack of direct sensing mechanisms. 3.4 Example: demand-supply gap es- timation W e illustrate the system design philosoph y by de- scribing below how a complex high-lev el KPI, the demand-supply gap (DSG), is computed, based on es- timates pro vided as part of the common referen tial in the form of low-lev el KPIs. The demand-supply gap, expressed as the count of passengers unable to board a train at a given p oint in time, is a k ey metric of netw ork level of service. Ho wev er indirect metho ds suc h as netw ork simula- tion only provide low-accuracy estimates, and no sen- sor provides a complete measurement of that quan- tit y . In particular CCTV pro vides observ ations on p ortions of the platform and is notoriously difficult to use for measuring accurately the demand-supply gap. Tic keting data pro vides only the entry coun ts, reflecting the demand rather than the demand-supply gap. In order to estimate the demand-supply gap, we rely on cro wd level estimates, that are pro vided from linear mo dels learning adaptiv ely scaling parameters relating the num b er of connected device observ ations to actual crowd lev el in a sup ervised wa y . The DSG is then estimated using a discriminative classification metho d with the following feature s et: • count of commuters waiting to b oard a train, • count of commuters “missing the train”, i.e. ob- serv ed contin uing to wait for the next train once a train departs, • waiting time third quartile and standard devia- tion, • train headw ay obtained by robust sp ectral clus- tering. W e highligh t that we are estimating the macroscopic demand-supply gap, and not whether sp ecific com- m uters will b e left b ehind. W e use greedy forward feature selection to select the most relev ant features for model building. Since the datasets are highly sk ewed, the v ast ma jority of samples reflecting no DSG, we inv ok e a b o otstrapping pro cedure to obtain an unbiased classification result. Giv en the low num b er of DSG even ts, it is un- realistic to rely solely on station-sp ecific mo dels for accurate estimation. On the other hand, given the lac k of stationarity of the underlying processes across stations and times, w e cannot readily train mo dels across the entire dataset. W e thus normalize the fea- tures across the entire dataset, and build a hierarch y of models. The mo dels are trained in a top-down fashion from a netw ork-wide mo del for all stations to line sp ecific mo dels, with distinct models for each line on the net work, and finally fine-grained models for each unique station on the netw ork. 3.5 Scalable agen t-based mo deling The F ASTER simulation engine ingests the state esti- mated b y the machine learning models used to create the KPI representation and forwards them in time to offer a fully data-driven simulation. Computation time b eing an imp erativ e, the agen t- based framew ork integrates microscopic mo dels with a generic mesoscopic formulation in the form of a queuing net work, which has b een sho wn to provide a go od trade-off b etw een accuracy and efficiency . A dominan t computation cost in traditional agent- based routing b eing the computation of shortest paths, w e rely on lo w frequency shortest path up- dates com bined with even t-based re-computation to accoun t for sudden global or local c hanges. During simulation, several metrics can b e pro duced dep ending on the user’s interest. Unnecessary stor- age of simulation data is av oided b y a dynamically generated data structure con taining only the data necessary for the user-specified metric. This reduces the memory usage of the sim ulator by around 15% and results in mo derate but noticeable sp eedup. A generic incident mo del supp orting the class of faults encountered triggers the optimization engine. In the interest of scalability , w e parameterize the set of candidate resp onse lines for a given incident as il- lustrated in Figure 3. The set is parameterized b y the 5 n umber of resp onse lines, the allo wed amount of ov er- lap, the maximal lengths, and the n umber of distinct train lines they are required to co ver. This achiev es a go od trade-off b et w een qualit y of the resp onse plans, resp onsiv eness of the system, and practicality of the lines for actual real-time op erations. Figure 3: Resp onse lines; emergency train lines may “lo op” around the incident or go through av ailable trac ks. Emergency bus lines are focused on re- connecting the netw ork at a regional or connection to connection scale. In order to solve the optimal action plan problem, w e first con vert the discrete transport supply pro- vided b y individual train and bus services to a so- called contin uous flow supply , and mo del the passen- ger mov ements as flows in a time expanded trans- p ortation net work. The ob jective of the optimiza- tion routine is to pro duce emergency resp onse bus routes and train sc hedules minimizing delay to im- pacted commuters. W e mo del the netw ork using a classical time- expanded graph with a node n u,t,l represen ting a sta- tion u at time t for line l , and with arcs mo deling service runtime, passenger walking time, and waiting time. F or every group of v p passengers with same origin and start time, we add a commo dit y p from a no de n o p ,s p (corresp onding to origin station o p and start time s p ), to a destination node z d p (corresp ond- ing to station d p ), with demand v p . T aking the num- b er of services n l on a line l as a v ariable we get a mixed in teger program solving the optimal action plan problem: min X p ∈ P, a ∈ A f p,a h a s.t. (1) X n 0 ∈ N f p,n 0 n = X n 0 ∈ N f p,nn 0 ∀ n 6 = n o p ,s p , z d p , p ∈ P (2) X n 0 ∈ N f p,n 0 n = v p for n = n o p ,s p ∀ p ∈ P (3) X n 0 ∈ N f p,nn 0 = − v p for n = z d p ∀ p ∈ P (4) X p ∈ P f p,a ≤ c l n l /τ l ∀ arc a = − − − − − − − − → n u,t,l n v ,t + r ,l ∈ A. (5) with flow v ariables f p,a , and where service capacities and headw a ys are denoted c l and τ l , resp ectiv ely , and with a ∈ A the set of arcs. Equations (2)-(3)-(4) are the flow conserv ation constrain ts, and (5) contains the service capacit y constraints. The ob jectiv e (1) is the total trav el time of the passengers, v arious ob jec- tiv e functions are supp orted in the system. Observ e that a passenger uses a w aiting arc a = − − − − − − − − → n v ,t,l n v ,t +1 ,l only if line l leaving from no de n v ,t,l is full. The mixed-in teger program (MIP) is solved on m ultiple cores using CPLEX, and is follow ed b y a lo cal searc h step. If demand is well-met based on the result of the MIP optimization, relative to the train and bus av ailability , the lo cal search simply fine-tunes the result b y either adjusting the rate of trains on existing lines or swapping out less-used lines for oth- ers. If the demand is not w ell-met or the num b er of a v ailable trains or buses is large, new train and bus lines are generated using a vehicle routing formula- tion, based on the residual demand from the output of the optimization, to replace or supplement lines in the current resp onse plan. A work queue is used to parallelize the simulation runs during the lo cal search step. The simulation runs are assigned to threads in an asynchronously streaming manner suc h that minimal w aiting is re- quired by individual threads. The parallelism is de- signed such that eac h thread runs entirely indep en- den tly from the other threads. These tw o features of the implementation allo w for a v ery straigh tforward implemen tation of a distributed parallelism v ariation of the lo cal search step, which generalizes to an API 6 for running multiple simulations across hardw are re- sources ov er the netw ork. 4 Mo deling comm uter dynam- ics In this section we describ e commuter mov ement mo d- els in a HMM framew ork, fo cusing on handling a con- tin uous state-space, and scalabilit y ov er large n umber of users. 4.1 CHMM Figure 4: Contin uous HMM. The c ontinuous hidden Markov mo del (CHMM) [11] is a HMM extension whic h con- siders clusters of hidden states, see Figure 4. In our form ulation, the index t is the trip and the hidden v ariable x t is the exit station of the t trip. W e denote A the transition matrix, so that A = { a i,j } where a i,j = P ( x t +1 = j | x t = i ). Eac h state emits to a hidden cluster, according to a sto c hastic emission matrix G = { g i,k } where g i,k = P ( m t = k | x t = i ). Eac h cluster emits a contin uous observ ation, ac- cording to a Gaussian distribution o t ∼ N ( µ k , Σ k ). The CHMM mo del is thus fully parameterized b y λ = { A , G , { µ k , Σ k }} . In our setting the mo del is trained on the observ a- tions given as a tuple including the time of en try in the netw ork, duration of the activity , i.e. the time out of the netw ork, and the position of the exit station. W e p erform the parameter estimation via a v ariant of the Baum-W elch algorithm [9]. 4.2 Aggregate mo del The scalability of the CHMM approach can b e sub- stan tially improv ed by clustering similar users and building an aggregate model for each cluster. A naiv e approach and one that we use as a baseline is to compute a histogram representation of spatio- temp oral frequency ov er a discretized domain for the relev ant spatial and temp oral features. Sp ecifically , in our baseline representation, the following spatio- temp oral features are employ ed: • frequency of presence, o ver a discretized spatial domain, • frequency of tra vel by time p erio d, ov er a dis- cretized temp oral domain, • spatial entrop y , ov er a discretized spatial do- main, where the spatial entrop y of user u is defined as: en tropy( u ) = − X s ∈ S u f s log f s , S u is the set of stations visited b y the user and f s is the frequency with which the user visited station s . The resulting adjacency matrix for a subset of 8000 users using a euclidean distance metric is illustrated in Figure 5. Figure 5: Adjacency matrix for euclidean distance in spatio-temp oral histogram-based feature space. The b est av ailable clustering of the adjacency ma- trix derived from the histogram distance, obtained 7 using sp ectral clustering, is shown in Figure 6. K- means and DBSCAN (not visualized here) pro duce significan tly inferior clustering results on this dataset. Figure 6: Re-organized matrix after sp ectral cluster- ing using euclidean distance on histogram-based fea- ture space. Note furthermore that the histogram representa- tion of trips suffers from the drawbac k of not b eing able to distinguish trips with similar spatial patterns but differing temp oral patterns; consider for example a user regularly making the trip from A to B to C and one who trav els from C to B to A. The histograms of suc h users will b e identical in spite of v astly different temp oral patterns. W e thus define a representation that describ es the spatial and temp oral patterns of users jointly . Sp ecif- ically , we use the history of the user trips and the most lik ely CHMM corresp onding to those trips. These CHMM are group ed into trip groups. Th us eac h user is represented by a Gaussian mixture. P erforming a new clustering on this CHMM-based represen tation of the users requires a new distance metric. The appropriate metric in this case is the Kullbac k-Leibler (KL) divergence. Ho wev er, comput- ing the KL div ergence is computationally costly due to the lack of an analytical solution and as such, in the interest of scalabilit y , w e employ an approxima- tion of the KL div ergence in the form of the quadratic form distance. Defining the signature of a Gaussian mixture as: S q = {h c q i , w q i i , i = 1 ..n } , the Quadratic F orm Distance (QFD) b e- t ween t wo distributions reads QF D ( S q , S o ) = p ( w q − w o ) · A f · ( w q − w o ) > , where A f is the similarity matrix giv en b y a ij = f ( c i , c j ), and f is a pairwise distance suc h as f − ( c i , c j ) = − d ( c i , c j ) or f g ( c i , c j ) = e − αd ( c i ,c j ) 2 . Figure 7 shows the adjacency matrix resulting from sp ectral clustering p erformed on the pairwise gaus- sian quadratic form distance. Note that the clusters are far more homogeneous in size and with far fewer outliers than that obtained using sp ectral clustering on the histogram-based represen tation, shown in Fig- ure 6. Figure 7: Adjacency matrix obtained with sp ectral clustering using pairwise QFD. 4.3 CHMM mo del numerical results W e consider a dataset of 900 million trips ov er a four months p erio d, across 5 train lines and 300 bus routes. The Gauss ian mixture clustering of the activities in the CHMM is calibrated b y maximizing the lik eli- ho od. On this dataset, when the num b er of Gaussian clusters increases ab ov e ten, the log-likelihoo d drops substan tially , due to o verfitting of the model on the training set. The hyper-parameters, namely the num- b er of hidden clusters, i.e. trip groups, optimized via a grid search, w as set to 8. 8 Figure 8 shows the b o xplots of the mo del p erfor- mance without clustering users; the b o x plots illus- trate a baseline CHMM in which only information from the previous trip t is used for the t + 1 predic- tion, the CHMM tw o stage-mo del, in which we aug- men t the observ ations from the previous trip with the time of entry into the netw ork and duration of the activit y (in principle considered observ ations of the t + 1 trip), and finally the tw o-stage mo del in its online version, in whic h the entry station, is also included as observ ation. A prediction is considered accurate if the station is within a range of 1 km. The b o xes show the median accuracy (middle red line), and the accuracy at the upp er and lo wer quartiles (Q1=25% and Q3=75%). The inter-quartile range (IQR), defined as the accuracy range b etw een Q3- Q1, is used to define the upp er and low er horizontal lines as Q1-1.5(IQR) and Q3+1.5(IQR). Dots outside the horizontal lines represen t the outliers. A measurable impro v ement is observed when using the tw o-stage mo del compared to the CHMM base- line. (a) F ull p opulation (b) Users ha ving en tropy ≤ 3 (54.8% of the p opulation) Figure 8: Accuracy of the prop osed mo dels, boxplots. 4.4 Comparison of aggregate mo dels p erformance T able 1 compares the prediction performance of the 2-stage mo del (middle b o xplot in Figure 8) us- ing the (symmetric) Kullbac k-Leibler and Quadratic F orm Distances for the clustering. As exp ected, the KL QFD Mean 35.5% 33.2% Median 35.0% 30.0% T able 1: Comparison of cluster-level prediction ac- curacy for KL and QFD with sp ectral clustering, on 100 clusters. metho d using KL distance p erforms slightly b etter, but the loss of accuracy from the QFD approxima- tion is v ery small, while the QFD approximation is obtained at a fraction of the computational cost. 5 F ASTER system ev aluation The F ASTER solution describ ed in this w ork has b een implemented, deplo yed, and ev aluated b oth in terms of accuracy metrics for quantities of in terest es- timated by the system, as well as in terms of b enefits obtained from the op erational improv ements enabled b y the system. In this section we illustrate this v ali- dation pro cess using an exemplary set of ev aluations. 5.1 Early w arnings for real-time mon- itoring Real-time estimation of netw ork conditions allows anomaly detection metho ds to raise alerts regarding situations that the control center should pay closer atten tion to. In Figure 9 w e illustrate such a case of in terruption of train services rep orted from 19:53pm to 20:23pm. The KPI illustrates clearly that the ser- vice was impacted as early as 19:30pm, more than 20 min utes before the incident rep ort was created. Suc h early warnings hav e b een prov en useful to mitigate the comp ounded impact of the incident as 9 Figure 9: An anomalous trend in commuter crowd- ing (solid black line) exceeding the medium (dotted blue line) and severe (dotted green line) alert levels is detected b efore manual incident rep orts (vertical blue lines). time progresses. W e highlight that, as in most real- w orld implementations, the priority of anomaly de- tection metho ds is to maintain the num b er of false p ositiv e under a certain v alue, and maximize the n umber of true p ositiv e under this constrain t. 5.2 Daily estimation of demand- supply gap A k ey quantit y in the monitoring of the quality of the transp ort service level is the demand-supply gap (DSG). The DSG measures the prop ortion of com- m uters intending to trav el who are unable to b oard a train b ecause it is full. Due to the difficulty of col- lecting fine-grained ground-truth DSG estimates (i.e. ho w many trains commuters are forced to miss b e- fore boarding a train), we p erform v alidation on the binary DSG detection problem (i.e. existence during a time p erio d of a DSG even t or not). W e use d 100K ground-truth DSG even t lab els (p os- itiv e and negative instances) collected ov er a p eriod of 8 months at ab out 60 stations, where a DSG even t is declared if an y passenger is forcedly left behind due to lac k of capacity . In T able 2 we present Precision, Recall, and Accuracy , for detecting DSG for a family of mo dels, running at the station, line, or netw ork lev el. Category #Mo dels Precision Recall Accuracy Net work 1 75 72 98 Line 1 to 10 77 72 98 Station 10 to 100 85 75 99 T able 2: Performance of different mo del categories. The statistical impro vemen t in mo del accuracy ob- tained with more fine-grained mo dels has to b e bal- anced with the complexity asso ciated with the main- tenance of 100 times more mo del instances and data streams. As these algorithms form the basis of an op erational system, the imp ortance of mo del main te- nance is not to b e neglected. W e refer the interested reader to [37] for more details on this mo del. 5.3 Long-term analysis of level of ser- vice The system includes a long-term demand mo del whic h can b e inv oked in particular for the manage- men t of planned even ts. This parsimonious long-term predictiv e mo del, used for one-da y ahead to one-y ear ahead, was sho wn to p erform well across a n umber of sp ecial ev ents, with less than 20% error 90% of the time. W e illustrate here the p erformance on the case of a yearly ev ent in Figure 10. The mo del includes a hierarch y of calendar dep en- dencies. The first level includes weekda y/week end classes, the second lev el includes the day of w eek, and the third level includes whether the day is a sp ecial ev ent or not (National Day , New Y ear’s Eve, etc.). Additiv e terms are then calibrated based on the full history , typically inv olving multiple years of data, to learn level-specific harmonics, considered as additive to the mo del from the previous lev el. 5.4 Data-driv en resp onse plans Our agent-based implemen tation leads to a serial sim- ulation of sev eral millions of passengers and trains 10 (a) Offline prediction of crowding (green) at train station neigh b oring the even t, at a 10 min resolution, compared to actual situation (red), and typical day (black). (b) Offline prediction of crowding (green) at the train station closest to the even t, at a 10 min resolution, com- pared to actual situation (red), and typical da y (black). Ev ening crowding is visible on the tw o days. Figure 10: P erformance of the predictive mo del, able to capture spatial distinctions in rare temp oral v ari- ations due to recurrent even ts. across 5 lines at 5000x sp eed sequen tially . The sys- tem allo ws for meaningful explorations of alternatives during incidents and even ts based on the data-driven estimates of the current situation on the ground. T a- ble 3 gives the accuracy for a 6 months p eriod, in terms of the mean a verage error (MAE), the mean relativ e error (MRE) and the Bhattac haryya co ef- ficien ts (BC) b et w een the sim ulated and the smart card based trav el-times of the passengers. P assenger Set MAE (min.) MRE (%) Avg. BC All 4.9 18 0.93 Within one line 2.5 19 0.95 T able 3: Agent-based simulation av erage trav el time error. Simulated passengers trav elling within a line are not sub ject to uncertaint y at a transfers, hence the higher accuracy . During op erations, the simulation - optimization engine ev aluates on the order of 1000 responses p er inciden t, each b eing automatically generated based on the incident properties and av ailable public trans- p ort resources. F or simplicity , prop erties of the de- mand, i.e. the time-v arying structure of the origin- destination matrix and the current station cro wd den- sities, do not in tervene in the a priori design of the resp onse plans, but only in their ev aluation via sim- ulation. Figure 11: Incident b et ween station B and C in b oth directions, from 8am to 8:10am. F or the inciden t illustrated in Figure 11 o ccurring during the morning p eak, with the dominant direc- tion of traffic b eing tow ards cit y center, the opti- mization engine proposes three div erse response plans with v arying train headwa y , and standard emergency bus routes of v arying headw ays, see T able 4. In this example, giv en the hea vy anisotropic demand and the lo calized spatio-temp oral nature of the incident, the optimizer improv es the situation b y increasing the capacit y to wards city cen ter. Giv en the heavy demand, the emergency bus lines, ev en op erating at a v ery low headwa y of 1 minute, are unable to accommo date the en tire passenger flow. Hence even for short inciden ts (10 minutes here) it is imp ortan t to manage the p ost-inciden t effects, suc h as by maintaining additional trains in service when the incident is ov er. Plan 3 from T able 4 results in the best ov erall p erformance, reducing large delays as well as ov ercrowding. This is done b y deploying t wo interlea ving shuttle lines, one each from station C and D to and from the city center. In other less constrained settings, the F ASTER system has b een able to produce non-standard re- sp onse lines directly connecting the incident neigh- b orhoo d with clusters of intended commuters desti- nations. W e refer the interested reader to [38] for 11 Plan 1 Plan 2 Plan 3 T rain service C ↔ X ϕ = 4 C ↔ X ϕ = 4 C ↔ X ϕ = 4 D ↔ X ϕ = 8 # additional trains 0 0 10 Sh uttle bus ser- vice B ↔ C ϕ = 2 B ↔ C ϕ = 1 B ↔ C ϕ = 2 Av erage dela y (min) 7 7 7 Dela y ≥ 20 min (#) 300 280 200 Ov ercrowding (min) 20 19 10 T able 4: 3 plans produced b y the sim ulation opti- mization engine. Headwa y is denoted by the symbol ϕ . more details on the mo del. 6 Conclusions and op en prob- lems In the context of the F ASTER pro ject, a num b er of imp ortan t, yet often o verlooked, c hallenges were en- coun tered. Here we provide a succinct list of such problem statements, which, if addressed, will help facilitate more wide-spread adoption of agent-based tec hniques in large-scale op erational systems. Non-indep enden t statistics Many sub-systems in applications consume data pro duced by other sub- systems. This results in a deviation from traditional assumptions of statistical theory for the existence and conv ergence of estimators. A related prop ert y of a v ailable data is that the statistics of input data are often non-stationary . Real-world applications would b enefit from more principled researc h on such statis- tical challenges. Real-time dominance One consequence of real- time indep enden t sub-system interactions is that there is no opp ortunity to formally correct or up date an estimate, since it is consumed as so on as it is pro- duced. While multiple estimators differing by an al- lo wed latency can be implemen ted, their significance decreases with the latency to the fastest estimator. F urthermore, high-latency estimators hav e to b e ei- ther consisten t with lo w-latency estimators, or in dis- agreemen t with transparent and sufficien t evidence. In that con text, efficient simulation - optimization of agen t-based systems in real-time settings is of great v alue in the emerging area of digital twins and their use in op erational control. Scarcit y of significant ev ents A significant is- sue arising in large-scale real-world applications is that the situations of highest interest to users con- cern relatively rare circumstances. In contrast, while data-driv en metho ds are obviously hindered by data scarcit y , agent-based tec hniques hav e been consid- ered relatively agnostic to the frequency of o ccur- rence of the scenario considered. A significant gap remains b et w een extreme data-driven metho ds p er- forming v ery well in ideal conditions, and principled metho ds with stable av erage p erformance. 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