ATWL Representation of the Recommended Workflow for Problem A

workflow bike-sharing-spatio-temporal-analysis template: loop(define-unit (places) → visualise → assess) → characterise (aggregate) → characterise (availability) → define-unit (daily episodes) → characterise (profiles) → loop(define-unit (cluster days) → characterise (cluster summaries) → contextualise (calendar) → visualise → abstract → assess) → define-unit (critical events) → visualise → abstract → define-unit (group places) → loop(abstract (cycles) → generate-knowledge (configure) → build-model → visualise → assess → characterise (residuals) → visualise → assess) → build-model (allocation) → loop(characterise (simulate) → visualise → assess) → generate-knowledge description: "Analyse spatio-temporal patterns of public bike usage at the level of places (groups of nearby docking stations), reveal patterns of bike shortage and station overcrowding related to diurnal, weekly, seasonal cycles and holidays, build predictive demand-supply models, and develop a bike allocation/relocation strategy"

# ========================================== # GIVEN ARTIFACTS # ========================================== artifact D_trips : entities origin: given internal structure: elementary embedment: {set, time} features: - id: bike_id value structure: atomic value type: reference description: "Bike identifier" - id: origin_station value structure: atomic value type: reference description: "Origin docking station" - id: origin_time value structure: atomic value type: temporal description: "Trip start time" - id: dest_station value structure: atomic value type: reference description: "Destination docking station" - id: dest_time value structure: atomic value type: temporal description: "Trip end time" description: "Individual bike trip records with origin and destination stations and timestamps" artifact D_stations : entities origin: given internal structure: elementary embedment: space features: - id: coordinates value structure: atomic value type: spatial description: "Geographic location" - id: capacity value structure: atomic value type: numeric description: "Number of docking positions" description: "Docking stations with geographic locations and docking capacities" artifact D_calendar : entities origin: given internal structure: elementary embedment: time features: - id: day_of_week value structure: atomic value type: categorical description: "Day of week" - id: month value structure: atomic value type: categorical description: "Month" - id: season value structure: atomic value type: categorical description: "Season" - id: is_holiday value structure: atomic value type: categorical description: "Holiday indicator (yes/no)" - id: day_type value structure: atomic value type: categorical description: "Working day, weekend, or public holiday" description: "Calendar structure with day-of-week, month, season, and holiday annotations" artifact K_domain : knowledge(D_trips, D_stations) origin: given representation form: "domain constraints and assumptions" description: "Domain knowledge: system operating hours, fleet size, initial bike distribution (or estimation method), known relocation operations, special event calendar"

# ========================================== # PHASE 0: PLACE DEFINITION # Adapted from 1.6 (place delineation) and 1.3 (spatial aggregation), # simplified because station locations are given. # ========================================== artifact S_station_clustering : specification origin: given representation form: "parameter settings" description: "Spatial clustering parameters: distance threshold for grouping nearby stations, minimum group size" loop L_place_definition: purpose: "Group spatially close docking stations into places that serve as analytical units for the entire workflow" until: "Places are spatially coherent, popular areas with multiple stations are properly grouped, and place granularity is appropriate for pattern analysis" body: transform T_cluster_stations : intent: define-unit manner: "spatial clustering by proximity" input: D_stations, S_station_clustering output: D_places, F_place_membership actor: machine description: "Group spatially close stations into places; compute aggregate capacity per place" artifact D_places : entities internal structure: group/cluster embedment: space features: - id: centroid value structure: atomic value type: spatial description: "Centroid location of member stations" - id: total_capacity value structure: atomic value type: numeric description: "Sum of docking capacities of members" - id: num_stations value structure: atomic value type: numeric description: "Number of member stations" description: "Groups of nearby docking stations forming place-level analytical units with aggregate capacities" artifact F_place_membership : feature(D_stations) value structure: atomic value type: categorical description: "Place assignment for each station" transform T_vis_places : intent: visualise manner: "stations and places on geographic map" input: D_stations, D_places, F_place_membership output: V_places_map actor: machine description: "Display stations colored by place membership on map with place boundaries and capacity indicators" artifact V_places_map : visualisation(D_stations, D_places, F_place_membership) layout: "geographic map" form: "colored points with cluster boundaries" encoding: "station position from coordinates; color from place membership; boundary from convex hull or buffer; place label size proportional to total capacity" description: "Map showing station grouping into places" transform T_assess_places : intent: assess manner: "evaluate spatial coherence and granularity" input: V_places_map, D_places, S_station_clustering output: K_place_assessment actor: human description: "Assess whether places are spatially coherent, popular areas are properly grouped, and granularity is appropriate" artifact K_place_assessment : knowledge(D_places) representation form: "quality judgment" description: "Assessment of place quality and whether clustering parameter adjustment is needed" if K_place_assessment indicates adjustment needed: then: transform T_adjust_station_clustering : intent: generate-knowledge manner: "adjust spatial clustering parameters" input: K_place_assessment, V_places_map, S_station_clustering output: S_station_clustering' actor: human description: "Adjust distance threshold or minimum size" artifact S_station_clustering' : specification representation form: "parameter settings" description: "Updated clustering parameters" assign: S_station_clustering := S_station_clustering' else: exit loop L_place_definition end loop L_place_definition

# ========================================== # PHASE 1: SPATIO-TEMPORAL AGGREGATION # Adapted from 1.11 (spatio-temporal aggregation) and 1.6 (place-level # aggregation with flows). # ========================================== artifact S_time_granularity : specification origin: given representation form: "parameter settings" description: "Time interval for aggregation (e.g., 1 hour)" transform T_aggregate_trips : intent: characterise manner: "spatio-temporal aggregation by places and time intervals" input: D_trips, D_places, F_place_membership, S_time_granularity output: F_take_series, F_return_series, F_flow_series actor: machine description: "Count bike takes and returns per place per time interval; compute directed flows between place pairs over time" artifact F_take_series : feature(D_places) value structure: vector value type: numeric representation form: "time series per place" description: "Time series of bike take counts per place per time interval" artifact F_return_series : feature(D_places) value structure: vector value type: numeric representation form: "time series per place" description: "Time series of bike return counts per place per time interval" artifact F_flow_series : feature(D_places) value structure: relational configuration value type: {reference, numeric} representation form: "directed flows with time series" description: "Time series of directed bike flow counts between each pair of places" transform T_compute_availability : intent: characterise manner: "compute running availability from cumulative net flow" input: D_places, F_take_series, F_return_series, K_domain output: F_net_flow, F_availability, F_occupancy_rate actor: machine description: "Compute net flow (returns minus takes), running bike availability, and occupancy rate as fraction of capacity, using initial distribution from domain knowledge" artifact F_net_flow : feature(D_places) value structure: vector value type: numeric representation form: "time series per place" description: "Time series of net bike flow (returns - takes) per place per interval" artifact F_availability : feature(D_places) value structure: vector value type: numeric representation form: "time series per place" description: "Estimated available bike count per place over time, derived from cumulative net flow and initial state" artifact F_occupancy_rate : feature(D_places) value structure: vector value type: numeric representation form: "time series per place" description: "Fraction of capacity occupied at each place over time (0 = empty, 1 = full)"

# ========================================== # PHASE 2: TEMPORAL PATTERN DISCOVERY # Adapted from 1.1 (cluster-calendar) extended with multi-place profiles, # and from 1.3 (temporal clustering with calendar view and flow thumbnails). # ========================================== transform T_partition_days : intent: define-unit manner: "time-partitioning into daily episodes" input: D_places, F_take_series, F_return_series, F_net_flow, F_availability output: D_days actor: machine description: "Partition all place-level time series into daily episodes, each containing hourly profiles for all places" artifact D_days : entities internal structure: episode embedment: time features: - id: date value structure: atomic value type: temporal description: "Calendar date" - id: take_profiles value structure: matrix value type: numeric description: "Hourly take counts: places x hours" - id: return_profiles value structure: matrix value type: numeric description: "Hourly return counts: places x hours" - id: net_flow_profiles value structure: matrix value type: numeric description: "Hourly net flow: places x hours" - id: availability_profiles value structure: matrix value type: numeric description: "Hourly availability: places x hours" description: "Daily episodes containing hourly demand-supply profiles across all places" transform T_profile_days : intent: characterise manner: "compute composite daily profiles" input: D_days output: F_day_profile actor: machine description: "Represent each day by a feature vector capturing system-wide hourly take and return patterns" artifact F_day_profile : feature(D_days) value structure: vector value type: numeric description: "Composite daily profile: system-wide hourly take and return curves, total volume, and peak-hour indicators" artifact S_day_clustering : specification origin: given representation form: "parameter settings" description: "Day clustering parameters: number of clusters, distance measure, features included" loop L_day_clustering: purpose: "Cluster days with similar demand-supply patterns to reveal diurnal, weekly, seasonal, and holiday regularities" until: "Day clusters are interpretable, well-separated, and reveal clear correspondence with weekday/weekend/holiday and seasonal structure" body: transform T_cluster_days : intent: define-unit manner: "hierarchical clustering by profile similarity" input: D_days, F_day_profile, S_day_clustering output: D_day_clusters, F_day_cluster_label actor: hybrid description: "Group days with similar system-wide demand-supply profiles" artifact D_day_clusters : entities internal structure: group/cluster embedment: set features: - id: cluster_size value structure: atomic value type: numeric description: "Number of days in cluster" description: "Groups of days with similar demand-supply patterns" artifact F_day_cluster_label : feature(D_days) value structure: atomic value type: categorical description: "Cluster membership for each day" transform T_aggregate_clusters : intent: characterise manner: "compute cluster-average profiles and flow summaries" input: D_day_clusters, F_day_profile, D_days, F_take_series, F_return_series, F_flow_series output: F_cluster_profile, F_cluster_flow actor: machine artifact F_cluster_profile : feature(D_day_clusters) value structure: vector value type: numeric description: "Cluster-average hourly profiles of takes, returns, and net flow, both system-wide and per place" artifact F_cluster_flow : feature(D_day_clusters) value structure: relational configuration value type: {reference, numeric} representation form: "average directed flows per cluster for selected hours (e.g., morning peak, evening peak)" description: "Cluster-average inter-place flow patterns" transform T_arrange_calendar : intent: contextualise manner: "calendar-based" input: D_days, D_calendar output: A_calendar actor: machine artifact A_calendar : arrangement(D_days) context: D_calendar principle: "calendar date mapping to grid position (weeks as rows, days of week as columns)" transform T_vis_calendar : intent: visualise manner: "calendar grid with color-coded clusters" input: A_calendar, F_day_cluster_label output: V_calendar actor: machine artifact V_calendar : visualisation(A_calendar, F_day_cluster_label) layout: "calendar grid (months as row groups, weekdays as columns)" form: "colored cells with holiday markers" encoding: "position from A_calendar; color from cluster label; markers for holidays" transform T_vis_profiles : intent: visualise manner: "line graphs and flow thumbnails per cluster" input: F_cluster_profile, F_cluster_flow, D_day_clusters, D_places output: V_profiles actor: machine artifact V_profiles : visualisation(F_cluster_profile, F_cluster_flow, D_day_clusters, D_places) layout: "one panel per cluster: line graphs above, flow map thumbnails below (morning/evening peaks)" form: "line graphs with confidence bands; directed flow arrows on small maps" encoding: "x: hour of day; y: average count; separate lines for takes and returns; flow arrows: width from magnitude, color from cluster" transform T_vis_place_heatmap : intent: visualise manner: "heatmap of place-level demand variation" input: F_cluster_profile, D_places, D_day_clusters output: V_place_heatmap actor: machine artifact V_place_heatmap : visualisation(F_cluster_profile, D_places, D_day_clusters) layout: "matrix: places as rows, hours as columns, one panel per cluster" form: "colored cells" encoding: "color intensity from net flow value; blue for net bike gain, red for net bike loss" transform T_interpret_patterns : intent: abstract manner: "identify temporal pattern types and associations" input: V_calendar, V_profiles, V_place_heatmap, D_day_clusters output: P_temporal_patterns actor: human artifact P_temporal_patterns : pattern(D_day_clusters, D_places) representation form: "labeled pattern types with descriptions" description: "Named demand-supply pattern types (e.g., 'regular weekday', 'weekend', 'summer weekday', 'public holiday') with diurnal shape descriptions and place-specific variations" transform T_assess_day_clusters : intent: assess input: V_calendar, V_profiles, V_place_heatmap, P_temporal_patterns, D_day_clusters output: K_cluster_assessment actor: human artifact K_cluster_assessment : knowledge(D_day_clusters) representation form: "quality judgment" if K_cluster_assessment indicates refinement needed: then: transform T_adjust_day_clustering : intent: generate-knowledge manner: "adjust clustering parameters" input: K_cluster_assessment, V_calendar, V_profiles, S_day_clustering output: S_day_clustering' actor: human artifact S_day_clustering' : specification representation form: "parameter settings" assign: S_day_clustering := S_day_clustering' else: exit loop L_day_clustering end loop L_day_clustering

# ========================================== # PHASE 3: CRITICAL EVENT ANALYSIS # Adapted from 1.6 (event extraction and characterisation) with # new critical-state definitions. # ========================================== artifact S_critical_thresholds : specification origin: given representation form: "parameter settings" description: "Thresholds for critical states: minimum available bikes for shortage (e.g., <10% capacity), minimum free docks for overcrowding (e.g., <10% remaining capacity)" transform T_identify_critical : intent: define-unit manner: "extract episodes where availability crosses thresholds" input: D_places, F_availability, F_occupancy_rate, S_critical_thresholds output: D_critical_events actor: machine artifact D_critical_events : entities internal structure: episode embedment: {space, time} features: - id: place_ref value structure: atomic value type: reference description: "Place where critical event occurs" - id: event_type value structure: atomic value type: categorical description: "'shortage' or 'overcrowding'" - id: duration value structure: atomic value type: temporal description: "Duration of critical state" - id: severity value structure: atomic value type: numeric description: "Depth of critical state" description: "Episodes of bike shortage or dock overcrowding at specific places and times" transform T_characterise_critical : intent: characterise manner: "aggregate critical events by place, day type, and time of day" input: D_critical_events, D_places, F_day_cluster_label, D_days output: F_critical_frequency actor: machine artifact F_critical_frequency : feature(D_places) value structure: matrix value type: numeric representation form: "critical event frequency matrix (place x hour x day-type)" transform T_vis_critical : intent: visualise manner: "geographic map with temporal diagrams and calendar heatmap" input: D_places, F_critical_frequency, A_calendar, F_day_cluster_label, D_critical_events output: V_critical actor: machine artifact V_critical : visualisation(D_places, F_critical_frequency, A_calendar) layout: "geographic map with embedded hourly bar diagrams; calendar heatmap panel" form: "sized bicolored glyphs on map with bar diagrams; colored calendar cells" encoding: "map: glyph size from total critical frequency; red for shortage, blue for overcrowding; bar diagram shows hourly profile. Calendar: cell color intensity from critical event count per day" transform T_interpret_critical : intent: abstract manner: "identify critical spatio-temporal patterns" input: V_critical, P_temporal_patterns, F_critical_frequency, V_place_heatmap output: P_critical_patterns actor: human artifact P_critical_patterns : pattern(D_places, D_critical_events) representation form: "categorised critical patterns with descriptions" description: "Identified critical patterns: places prone to shortage vs. overcrowding, time-of-day and day-type concentrations, spatial complementarity (e.g., morning shortage in residential areas paired with overcrowding in business areas), seasonal variation"

# ========================================== # PHASE 4: PREDICTIVE MODEL BUILDING # Adapted from 1.11 (time series clustering, representative derivation, # model fitting, and residual-based evaluation). # ========================================== transform T_group_places : intent: define-unit manner: "cluster by temporal demand-supply similarity" input: D_places, F_take_series, F_return_series output: D_place_groups, F_place_group_label actor: hybrid artifact D_place_groups : entities internal structure: group/cluster embedment: set description: "Groups of places with similar temporal demand-supply patterns" artifact F_place_group_label : feature(D_places) value structure: atomic value type: categorical description: "Place group membership" artifact S_model_config : specification origin: given representation form: "model configuration" description: "Initial model configuration: model type, cycle lengths (diurnal=24h, weekly=168h), seasonal component, holiday effect handling" artifact K_modelling_strategy : knowledge origin: given representation form: "refinement strategy" description: "Modelling guidance from prior residual analysis; initially neutral" loop L_modelling: purpose: "Build and refine predictive models of bike demand and supply per place group until models capture diurnal, weekly, seasonal, and holiday effects" until: "Model residuals show no systematic temporal or spatial patterns; predictions capture demand-supply dynamics across all day types" body: transform T_identify_cycles : intent: abstract manner: "identify periodic and trend components" input: V_profiles, P_temporal_patterns, D_place_groups output: P_temporal_chars actor: human artifact P_temporal_chars : pattern(D_place_groups) representation form: "identified temporal characteristics" transform T_configure_model : intent: generate-knowledge manner: "specify model structure from identified cycles" input: P_temporal_chars, K_modelling_strategy, S_model_config output: S_model_config' actor: human artifact S_model_config' : specification representation form: "model configuration" assign: S_model_config := S_model_config' transform T_derive_representative : intent: characterise manner: "compute group-representative demand-supply series" input: D_place_groups, F_take_series, F_return_series output: F_representative actor: machine artifact F_representative : feature(D_place_groups) value structure: vector value type: numeric description: "Representative demand-supply time series per place group" transform T_build_demand_model : intent: build-model manner: "fit time series model with multiple seasonal components and holiday effects" input: F_representative, S_model_config, D_calendar output: M_demand_supply actor: machine artifact M_demand_supply : model(F_representative, S_model_config) model type: "seasonal time series model" representation form: "fitted parametric model with multiple seasonal components and calendar effects" transform T_vis_model : intent: visualise manner: "model curves overlaid on data" input: M_demand_supply, F_representative, F_take_series, F_return_series output: V_model actor: machine artifact V_model : visualisation(M_demand_supply, F_representative) layout: "temporal axis, one panel per place group" form: "line graphs with confidence bands" encoding: "x: time; y: count; solid lines for model; dashed lines for data; bands for prediction interval" transform T_assess_model : intent: assess input: V_model, M_demand_supply output: K_model_assessment actor: human artifact K_model_assessment : knowledge(M_demand_supply) representation form: "quality judgment" if K_model_assessment indicates refinement needed: then: transform T_compute_residuals : intent: characterise manner: "compute prediction residuals per place" input: M_demand_supply, D_places, F_take_series, F_return_series, D_place_groups output: F_residuals actor: machine artifact F_residuals : feature(D_places) value structure: vector value type: numeric transform T_vis_residuals : intent: visualise manner: "residuals over time and space" input: F_residuals, D_places, D_calendar, D_place_groups output: V_residuals actor: machine artifact V_residuals : visualisation(F_residuals, D_places) layout: "temporal panel with quintile bands; geographic map panel" form: "summary bands and colored areas" transform T_assess_residuals : intent: assess input: V_residuals, D_place_groups output: K_residual_quality actor: human artifact K_residual_quality : knowledge(M_demand_supply) representation form: "quality judgment" transform T_decide_refinement : intent: generate-knowledge manner: "diagnose residual patterns and formulate refinement strategy" input: K_residual_quality, V_residuals, K_model_assessment, S_model_config output: K_modelling_strategy', S_model_config_r actor: human assign: K_modelling_strategy := K_modelling_strategy' S_model_config := S_model_config_r else: exit loop L_modelling end loop L_modelling

# ========================================== # PHASE 5: ALLOCATION / RELOCATION MODEL # Inspired by 1.5 (EventAction prescriptive loop): # specify allocation → simulate → assess → refine. # ========================================== artifact S_allocation_criteria : specification origin: given representation form: "constraints and objectives" description: "Allocation objectives: minimise expected shortage and overcrowding; constraints: total fleet size, place capacities, logistical relocation limits" transform T_build_allocation_model : intent: build-model manner: "formulate optimisation model for bike distribution" input: M_demand_supply, D_places, S_allocation_criteria, D_calendar output: M_allocation actor: hybrid artifact M_allocation : model(M_demand_supply, D_places, S_allocation_criteria) model type: "constrained optimisation model" representation form: "objective function with demand predictions, capacity constraints, and logistics constraints" loop L_allocation_validation: purpose: "Validate and refine the allocation model by simulating recommendations on historical data and assessing effectiveness at reducing critical events" until: "Allocation recommendations effectively reduce shortage and overcrowding across all day types and places to acceptable levels" body: transform T_simulate_allocation : intent: characterise manner: "simulate availability under recommended allocation across sample historical dates" input: M_allocation, M_demand_supply, D_days, D_places, D_calendar, F_availability output: F_simulated_availability, F_simulated_critical actor: machine artifact F_simulated_availability : feature(D_places) value structure: matrix value type: numeric description: "Simulated hourly availability per place under recommended allocation for sample dates" artifact F_simulated_critical : feature(D_places) value structure: matrix value type: numeric description: "Predicted critical event counts per place under recommended allocation vs. actual historical allocation" transform T_vis_allocation : intent: visualise manner: "comparison of actual vs. recommended outcomes" input: F_simulated_critical, F_critical_frequency, D_places, D_day_clusters output: V_allocation actor: machine artifact V_allocation : visualisation(F_simulated_critical, F_critical_frequency, D_places) layout: "geographic map with paired bar diagrams; summary table by day type" form: "paired bars on map; tabular summary" encoding: "paired bars showing actual vs. recommended critical event frequency; red for shortage, blue for overcrowding; table: rows by day type, columns by total critical events, percentage reduction" transform T_assess_allocation : intent: assess input: V_allocation, F_simulated_critical, S_allocation_criteria output: K_allocation_assessment actor: human artifact K_allocation_assessment : knowledge(M_allocation) representation form: "quality judgment" if K_allocation_assessment indicates refinement needed: then: transform T_refine_allocation : intent: generate-knowledge manner: "adjust allocation criteria or model" input: K_allocation_assessment, V_allocation, S_allocation_criteria, P_critical_patterns output: S_allocation_criteria' actor: human artifact S_allocation_criteria' : specification representation form: "constraints and objectives" description: "Revised allocation criteria" assign: S_allocation_criteria := S_allocation_criteria' transform T_rebuild_allocation : intent: build-model manner: "re-optimise with revised criteria" input: M_demand_supply, D_places, S_allocation_criteria, D_calendar output: M_allocation' actor: machine artifact M_allocation' : model(M_demand_supply, D_places, S_allocation_criteria) model type: "constrained optimisation model" assign: M_allocation := M_allocation' else: exit loop L_allocation_validation end loop L_allocation_validation

# ========================================== # PHASE 6: KNOWLEDGE SYNTHESIS # ========================================== transform T_synthesize : intent: generate-knowledge manner: "integrate patterns, models, and recommendations" input: P_temporal_patterns, P_critical_patterns, M_demand_supply, M_allocation, K_allocation_assessment, K_domain output: K_final actor: human description: "Synthesize comprehensive understanding of bike sharing dynamics and formulate operational recommendations" artifact K_final : knowledge(M_demand_supply, M_allocation, P_temporal_patterns, P_critical_patterns) representation form: "statements, model descriptions, and operational recommendations" description: "Comprehensive findings: (1) identified demand-supply pattern types and their weekly, seasonal, and holiday distribution; (2) places and times prone to shortage or overcrowding with causal flow explanations; (3) predictive models of demand and supply per place for any date and time; (4) validated allocation/relocation recommendations with expected reduction in critical events; (5) operational guidance for bike redistribution logistics"