package org.opentrafficsim.road.od;
   
   import java.util.ArrayList;
   import java.util.Arrays;
   import java.util.Comparator;
   import java.util.LinkedHashMap;
   import java.util.LinkedHashSet;
   import java.util.List;
   import java.util.Map;
  import java.util.Map.Entry;
  import java.util.Set;
  import java.util.stream.Collectors;
  
  import org.djunits.unit.FrequencyUnit;
  import org.djunits.value.vdouble.scalar.Duration;
  import org.djunits.value.vdouble.scalar.Frequency;
  import org.djunits.value.vdouble.scalar.Length;
  import org.djunits.value.vdouble.scalar.Time;
  import org.djutils.exceptions.Throw;
  import org.opentrafficsim.base.parameters.ParameterException;
  import org.opentrafficsim.core.distributions.Generator;
  import org.opentrafficsim.core.dsol.OtsSimulatorInterface;
  import org.opentrafficsim.core.gtu.GtuException;
  import org.opentrafficsim.core.gtu.GtuType;
  import org.opentrafficsim.core.idgenerator.IdGenerator;
  import org.opentrafficsim.core.math.Draw;
  import org.opentrafficsim.core.network.Connector;
  import org.opentrafficsim.core.network.Link;
  import org.opentrafficsim.core.network.LinkType;
  import org.opentrafficsim.core.network.NetworkException;
  import org.opentrafficsim.core.network.Node;
  import org.opentrafficsim.core.object.DetectorType;
  import org.opentrafficsim.road.gtu.generator.GeneratorPositions;
  import org.opentrafficsim.road.gtu.generator.GeneratorPositions.LaneBiases;
  import org.opentrafficsim.road.gtu.generator.LaneBasedGtuGenerator;
  import org.opentrafficsim.road.gtu.generator.LaneBasedGtuGenerator.RoomChecker;
  import org.opentrafficsim.road.gtu.generator.MarkovCorrelation;
  import org.opentrafficsim.road.gtu.generator.characteristics.LaneBasedGtuCharacteristics;
  import org.opentrafficsim.road.gtu.generator.characteristics.LaneBasedGtuCharacteristicsGenerator;
  import org.opentrafficsim.road.gtu.generator.characteristics.LaneBasedGtuCharacteristicsGeneratorOd;
  import org.opentrafficsim.road.gtu.generator.headway.Arrivals;
  import org.opentrafficsim.road.gtu.generator.headway.ArrivalsHeadwayGenerator;
  import org.opentrafficsim.road.gtu.generator.headway.ArrivalsHeadwayGenerator.HeadwayDistribution;
  import org.opentrafficsim.road.gtu.generator.headway.DemandPattern;
  import org.opentrafficsim.road.network.RoadNetwork;
  import org.opentrafficsim.road.network.lane.CrossSectionLink;
  import org.opentrafficsim.road.network.lane.Lane;
  import org.opentrafficsim.road.network.lane.LanePosition;
  import org.opentrafficsim.road.network.lane.object.detector.LaneDetector;
  import org.opentrafficsim.road.network.lane.object.detector.SinkDetector;
  
  import nl.tudelft.simulation.dsol.SimRuntimeException;
  import nl.tudelft.simulation.jstats.streams.MersenneTwister;
  import nl.tudelft.simulation.jstats.streams.StreamInterface;
  
  /**
   * Utility to create vehicle generators on a network from an OD.
   * <p>
   * Copyright (c) 2013-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
   * BSD-style license. See <a href="https://opentrafficsim.org/docs/license.html">OpenTrafficSim License</a>.
   * </p>
   * @author <a href="https://github.com/averbraeck">Alexander Verbraeck</a>
   * @author <a href="https://github.com/peter-knoppers">Peter Knoppers</a>
   * @author <a href="https://github.com/wjschakel">Wouter Schakel</a>
   */
  public final class OdApplier
  {
  
      /**
       * Utility class.
       */
      private OdApplier()
      {
          //
      }
  
      /**
       * Applies the OD to the network by creating vehicle generators. The map returned contains objects created for vehicle
       * generation. These are bundled in a {@code GeneratorObjects} and mapped to the vehicle generator id. Vehicle generator id
       * is equal to the origin node id. For lane-based generators the id's are appended with an ordered number (e.g. A1), where
       * the ordering is first by link id, and then right to left concerning the lateral lane position at the start of the lane.
       * For node "A" this would for example be:<br>
       * <table >
       * <caption>&nbsp;</caption>
       * <tr>
       * <th>Generator id</th>
       * <th>Link</th>
       * <th>Lateral start offset</th>
       * </tr>
       * <tr>
       * <th>A1</th>
       * <th>AB</th>
       * <th>-1.75m</th>
       * </tr>
       * <tr>
       * <th>A2</th>
       * <th>AB</th>
       * <th>1.75m</th>
       * </tr>
      * <tr>
      * <th>A3</th>
      * <th>AC</th>
      * <th>-3.5m</th>
      * </tr>
      * <tr>
      * <th>A4</th>
      * <th>AC</th>
      * <th>0.0m</th>
      * </tr>
      * </table>
      * If the GTU generation is lane-based (i.e. {@code Lane} in the {@code Categorization}) this method creates a
      * {@code LaneBasedGtuGenerator} per lane. It will have a single source of demand data, specifying demand towards all
      * relevant destinations, and with a unique {@code MarkovChain} for the GTU type if {@code MarkovCorrelation} is defined.
      * For zone GTU generation one {@code LaneBasedGtuGenerator} is created, with one single source of demand data, specifying
      * demand towards all destinations. A single {@code MarkovChain} may be used. Traffic is distributed over possible
      * {@code Connectors} based on their link-weight, or the number of lanes of the connected links if no weight is given.
      * @param network network
      * @param od OD matrix
      * @param odOptions options for vehicle generation
      * @param detectorType detector type.
      * @return Map&lt;String, GeneratorObjects&gt; map of generator id's and created generator objects mainly for testing
      * @throws ParameterException if a parameter is missing
      * @throws SimRuntimeException if this method is called after simulation time 0
      */
     @SuppressWarnings("checkstyle:methodlength")
     public static Map<String, GeneratorObjects> applyOd(final RoadNetwork network, final OdMatrix od, final OdOptions odOptions,
             final DetectorType detectorType) throws ParameterException, SimRuntimeException
     {
         Throw.whenNull(network, "Network may not be null.");
         Throw.whenNull(od, "OD matrix may not be null.");
         Throw.whenNull(odOptions, "OD options may not be null.");
         OtsSimulatorInterface simulator = network.getSimulator();
         Throw.when(!simulator.getSimulatorTime().eq0(), SimRuntimeException.class,
                 "Method OdApplier.applyOd() should be invoked at simulation time 0.");
 
         // TODO sinks? white extension links?
         for (Node destination : od.getDestinations())
         {
             createSensorsAtDestination(destination, detectorType);
         }
 
         // TODO clean up stream acquiring code after task OTS-315 has been completed
         StreamInterface stream = getStream(simulator);
 
         boolean laneBased = od.getCategorization().entails(Lane.class);
         Map<String, GeneratorObjects> output = new LinkedHashMap<>();
         for (Node origin : od.getOrigins())
         {
             Map<Lane, DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>> originNodePerLane = new LinkedHashMap<>();
             DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>> originNodeZone =
                     buildDemandNodeTree(od, odOptions, stream, origin, originNodePerLane);
             Map<DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>, Set<LanePosition>> initialPositions =
                     new LinkedHashMap<>();
             Map<CrossSectionLink, Double> linkWeights = new LinkedHashMap<>();
             Map<CrossSectionLink, Node> viaNodes = new LinkedHashMap<>();
             if (laneBased)
             {
                 gatherPositionsLaneBased(originNodePerLane, initialPositions);
             }
             else
             {
                 initialPositions.put(originNodeZone, gatherPositionsZone(origin, linkWeights, viaNodes));
             }
             if (linkWeights.isEmpty())
             {
                 linkWeights = null;
                 viaNodes = null;
             }
             initialPositions = sortByValue(initialPositions); // sorts by lateral position at link start
             createGenerators(network, odOptions, simulator, laneBased, stream, output, initialPositions, linkWeights, viaNodes);
         }
         return output;
     }
 
     /**
      * Builds nested demand node structure (i.e. tree) for demand and GTU characteristics generation. If
      * {@code MarkovCorrelation} is specified, in case of zone GTU generation, a single {@code MarkovChain} is used for the
      * selection of GTU type and the relevant lane. In case of lane-based GTU generation, one {@code MarkovChain} is used for
      * each lane, even when multiple {@code Category}'s contain the same lane. This method loops over all destinations for the
      * given origin, and then over all categories. For lane-based GTU generation, at that level the appropriate origin node is
      * taken from the input map, or it is created in to it, and the destination demand-node coupled to that for the looped
      * destination is obtained or created, with possible {@code MarkovChain}. For zone GTU generation, the looping is a more
      * straight-forward creation of nodes from origin, and for destination and category. The result of lane-based GTU generation
      * is given in the input map, for zone GTU generation the single origin demand node is returned by the method.
      * @param od OD matrix.
      * @param odOptions OD options.
      * @param stream random number stream.
      * @param origin origin node.
      * @param originNodePerLane map of origin demand node per lane, populated for lane-based GTU generation.
      * @return demand node structure for the entire generator in case of zone GTU generation.
      */
     private static DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>> buildDemandNodeTree(final OdMatrix od,
             final OdOptions odOptions, final StreamInterface stream, final Node origin,
             final Map<Lane, DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>> originNodePerLane)
     {
         boolean laneBased = od.getCategorization().entails(Lane.class);
         boolean markovian = od.getCategorization().entails(GtuType.class);
         DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>> demandNode = null; // for each generator, flexibly used
         MarkovChain markovChain = null;
         if (!laneBased)
         {
             demandNode = new DemandNode<>(origin, stream, null);
             LinkType linkType = getLinkTypeFromNode(origin);
             if (markovian)
             {
                 MarkovCorrelation<GtuType, Frequency> correlation = odOptions.get(OdOptions.MARKOV, null, origin, linkType);
                 if (correlation != null)
                 {
                     Throw.when(!od.getCategorization().entails(GtuType.class), IllegalArgumentException.class,
                             "Markov correlation can only be used on OD categorization entailing GTU type.");
                     markovChain = new MarkovChain(correlation);
                 }
             }
         }
         for (Node destination : od.getDestinations())
         {
             Set<Category> categories = od.getCategories(origin, destination);
             if (!categories.isEmpty())
             {
                 DemandNode<Node, DemandNode<Category, ?>> destinationNode = null;
                 if (!laneBased)
                 {
                     destinationNode = new DemandNode<>(destination, stream, markovChain);
                     demandNode.addChild(destinationNode);
                 }
                 for (Category category : categories)
                 {
                     if (laneBased)
                     {
                         // obtain or create root and destination nodes
                         Lane lane = category.get(Lane.class);
                         demandNode = originNodePerLane.get(lane);
                         if (demandNode == null)
                         {
                             demandNode = new DemandNode<>(origin, stream, null);
                             originNodePerLane.put(lane, demandNode);
                         }
                         destinationNode = demandNode.getChild(destination);
                         if (destinationNode == null)
                         {
                             markovChain = null;
                             if (markovian)
                             {
                                 MarkovCorrelation<GtuType, Frequency> correlation =
                                         odOptions.get(OdOptions.MARKOV, lane, origin, lane.getLink().getType());
                                 if (correlation != null)
                                 {
                                     Throw.when(!od.getCategorization().entails(GtuType.class), IllegalArgumentException.class,
                                             "Markov correlation can only be used on OD categorization entailing GTU type.");
                                     markovChain = new MarkovChain(correlation); // 1 for each generator per lane
                                 }
                             }
                             destinationNode = new DemandNode<>(destination, stream, markovChain);
                             demandNode.addChild(destinationNode);
                         }
                     }
                     DemandNode<Category, ?> categoryNode =
                             new DemandNode<>(category, od.getDemandPattern(origin, destination, category));
                     if (markovian)
                     {
                         destinationNode.addLeaf(categoryNode, category.get(GtuType.class));
                     }
                     else
                     {
                         destinationNode.addChild(categoryNode);
                     }
                 }
             }
         }
         return demandNode;
     }
 
     /**
      * Returns a set of positions for GTU generation from each lane defined in demand. Stores the positions with the coupled
      * demand node.
      * @param originNodePerLane map with a demand node per lane.
      * @param initialPositions Map&lt;DemandNode&lt;Node, DemandNode&lt;Node, DemandNode&lt;Category, ?&gt;&gt;&gt;,
      *            Set&lt;LanePosition&gt;&gt;; map with positions per demand node.
      */
     private static void gatherPositionsLaneBased(
             final Map<Lane, DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>> originNodePerLane,
             final Map<DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>, Set<LanePosition>> initialPositions)
     {
         for (Lane lane : originNodePerLane.keySet())
         {
             DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>> demandNode = originNodePerLane.get(lane);
             Set<LanePosition> initialPosition = new LinkedHashSet<>();
             initialPosition.add(lane.getLink().getStartNode().equals(demandNode.getObject())
                     ? new LanePosition(lane, Length.ZERO) : new LanePosition(lane, lane.getLength()));
             initialPositions.put(demandNode, initialPosition);
         }
     }
 
     /**
      * Returns a set of positions for GTU generation from a zone. All links connected to the origin node are considered. In case
      * a link is a {@code Connector}, a link weight and via-node over that link are stored in the provided maps, for later use
      * in constructing weighted generator positions. For each {@code CrossSectionLink} attached to the via-node, or to the first
      * link if there was no {@code Connector}, positions are generated.
      * @param origin origin node for the zone.
      * @param linkWeights link weight map to place link weights in.
      * @param viaNodes via node map to place via nodes in.
      * @return gathered lane positions.
      */
     private static Set<LanePosition> gatherPositionsZone(final Node origin, final Map<CrossSectionLink, Double> linkWeights,
             final Map<CrossSectionLink, Node> viaNodes)
     {
         Set<LanePosition> positionSet = new LinkedHashSet<>();
         for (Link link : origin.getLinks())
         {
             if (link instanceof Connector)
             {
                 Connector connector = (Connector) link;
                 if (connector.getStartNode().equals(origin))
                 {
                     Node connectedNode = connector.getEndNode();
                     // count number of served links
                     int served = 0;
                     for (Link connectedLink : connectedNode.getLinks())
                     {
                         if (connectedLink instanceof CrossSectionLink)
                         {
                             served++;
                         }
                     }
                     for (Link connectedLink : connectedNode.getLinks())
                     {
                         if (connectedLink instanceof CrossSectionLink)
                         {
                             if (connector.getDemandWeight() > 0.0)
                             {
                                 // store weight under connected link, as this
                                 linkWeights.put(((CrossSectionLink) connectedLink), connector.getDemandWeight() / served);
                             }
                             else
                             {
                                 // negative weight results in number of lanes being used
                                 linkWeights.put(((CrossSectionLink) connectedLink), -1.0);
                             }
                             viaNodes.put((CrossSectionLink) connectedLink, connectedNode);
                             setLanePosition((CrossSectionLink) connectedLink, connectedNode, positionSet);
                         }
                     }
                 }
             }
             else if (link instanceof CrossSectionLink)
             {
                 setLanePosition((CrossSectionLink) link, origin, positionSet);
             }
         }
         return positionSet;
     }
 
     /**
      * Creates GTU generators. For lane-based GTU generation (i.e. {@code Lane} in the {@code Categorization}), the generators
      * will obtain an ID with the node id plus a counter. For this the initial positions need to be sorted. The link weights and
      * via nodes should be {@code null} for lane-based GTU generation. Furthermore, the lane is then used to obtain OD option
      * values possibly specified at the lane level. Other than that, for either lane-based or zone GTU generation, a
      * {@code LaneBasedGtuGenerator} is created for each initial position given.
      * @param network network.
      * @param odOptions od options.
      * @param simulator simulator.
      * @param laneBased lane in category.
      * @param stream random number stream.
      * @param output map that output elements will be stored in.
      * @param initialPositions Map&lt;DemandNode&lt;Node, DemandNode&lt;Node, DemandNode&lt;Category, ?&gt;&gt;&gt;,
      *            Set&lt;LanePosition&gt;&gt;; sorted initial positions.
      * @param linkWeights weights per link, may be {@code null}.
      * @param viaNodes nodes to select from for zone, may be {@code null}.
      * @throws ParameterException if drawing from the inter-arrival generator fails
      */
     @SuppressWarnings("checkstyle:parameternumber")
     private static void createGenerators(final RoadNetwork network, final OdOptions odOptions,
             final OtsSimulatorInterface simulator, final boolean laneBased, final StreamInterface stream,
             final Map<String, GeneratorObjects> output,
             final Map<DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>, Set<LanePosition>> initialPositions,
             final Map<CrossSectionLink, Double> linkWeights, final Map<CrossSectionLink, Node> viaNodes)
             throws ParameterException
     {
         Map<Node, Integer> laneGeneratorCounterForUniqueId = new LinkedHashMap<>();
         for (DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>> root : initialPositions.keySet())
         {
             Set<LanePosition> initialPosition = initialPositions.get(root);
             // id
             Node o = root.getObject();
             String id = o.getId();
             if (laneBased)
             {
                 Integer count = laneGeneratorCounterForUniqueId.get(o);
                 if (count == null)
                 {
                     count = 0;
                 }
                 count++;
                 id += count;
                 laneGeneratorCounterForUniqueId.put(o, count);
             }
             // functional generation elements
             Lane lane;
             LinkType linkType;
             if (laneBased)
             {
                 lane = initialPosition.iterator().next().lane();
                 linkType = lane.getLink().getType();
             }
             else
             {
                 lane = null;
                 linkType = getLinkTypeFromNode(o);
             }
             HeadwayDistribution randomization = odOptions.get(OdOptions.HEADWAY_DIST, lane, o, linkType);
             ArrivalsHeadwayGenerator headwayGenerator = new ArrivalsHeadwayGenerator(root, simulator, stream, randomization);
             LaneBasedGtuCharacteristicsGeneratorOd characteristicsGeneratorOd =
                     odOptions.get(OdOptions.GTU_TYPE, lane, o, linkType);
             LaneBasedGtuCharacteristicsGenerator characteristicsGenerator = new LaneBasedGtuCharacteristicsGenerator()
             {
                 @Override
                 public LaneBasedGtuCharacteristics draw() throws ParameterException, GtuException
                 {
                     Time time = simulator.getSimulatorAbsTime();
                     Node origin = root.getObject();
                     DemandNode<Node, DemandNode<Category, ?>> destinationNode = root.draw(time);
                     Node destination = destinationNode.getObject();
                     Category category = destinationNode.draw(time).getObject();
                     return characteristicsGeneratorOd.draw(origin, destination, category, stream);
                 }
             };
 
             RoomChecker roomChecker = odOptions.get(OdOptions.ROOM_CHECKER, lane, o, linkType);
             IdGenerator idGenerator = odOptions.get(OdOptions.GTU_ID, lane, o, linkType);
             LaneBiases biases = odOptions.get(OdOptions.LANE_BIAS, lane, o, linkType);
             // and finally, the generator
             try
             {
                 LaneBasedGtuGenerator generator = new LaneBasedGtuGenerator(id, headwayGenerator, characteristicsGenerator,
                         GeneratorPositions.create(initialPosition, stream, biases, linkWeights, viaNodes), network, simulator,
                         roomChecker, idGenerator);
                 generator.setNoLaneChangeDistance(odOptions.get(OdOptions.NO_LC_DIST, lane, o, linkType));
                 generator.setInstantaneousLaneChange(odOptions.get(OdOptions.INSTANT_LC, lane, o, linkType));
                 generator.setErrorHandler(odOptions.get(OdOptions.ERROR_HANDLER, lane, o, linkType));
                 output.put(id, new GeneratorObjects(generator, headwayGenerator, characteristicsGenerator));
             }
             catch (SimRuntimeException exception)
             {
                 // should not happen, we check that time is 0
                 simulator.getLogger().always().error(exception);
                 throw new RuntimeException(exception);
             }
             catch (NetworkException exception)
             {
                 // should not happen, as unique ids are guaranteed by UUID
                 simulator.getLogger().always().error(exception);
                 throw new RuntimeException(exception);
             }
         }
     }
 
     /**
      * Obtains a stream for vehicle generation.
      * @param simulator simulator.
      * @return stream for vehicle generation.
      */
     private static StreamInterface getStream(final OtsSimulatorInterface simulator)
     {
         StreamInterface stream = simulator.getModel().getStream("generation");
         if (stream == null)
         {
             stream = simulator.getModel().getStream("default");
             if (stream == null)
             {
                 System.out
                         .println("Using locally created stream (not from the simulator) for vehicle generation, with seed 1.");
                 stream = new MersenneTwister(1L);
             }
             else
             {
                 System.out.println("Using stream 'default' for vehicle generation.");
             }
         }
         return stream;
     }
 
     /**
      * Create destination sensors at all lanes connected to a destination node. This method considers connectors too.
      * @param destination destination node
      * @param detectorType detector type.
      */
     private static void createSensorsAtDestination(final Node destination, final DetectorType detectorType)
     {
         for (Link link : destination.getLinks())
         {
             if (link.isConnector() && !link.getStartNode().equals(destination))
             {
                 createSensorsAtDestinationNode(link.getStartNode(), detectorType);
             }
             else
             {
                 createSensorsAtDestinationNode(destination, detectorType);
             }
         }
     }
 
     /**
      * Create sensors at all lanes connected to this node. This method does not handle connectors.
      * @param destination the destination node
      * @param detectorType detector type.
      */
     private static void createSensorsAtDestinationNode(final Node destination, final DetectorType detectorType)
     {
         for (Link link : destination.getLinks())
         {
             if (link instanceof CrossSectionLink)
             {
                 for (Lane lane : ((CrossSectionLink) link).getLanes())
                 {
                     try
                     {
                         // if the lane already contains a SinkDetector, skip creating a new one
                         boolean destinationDetectorExists = false;
                         for (LaneDetector detector : lane.getDetectors())
                         {
                             if (detector instanceof SinkDetector)
                             {
                                 destinationDetectorExists = true;
                             }
                         }
                         if (!destinationDetectorExists)
                         {
                             new SinkDetector(lane, lane.getLength(), detectorType, SinkDetector.DESTINATION);
                         }
                     }
                     catch (NetworkException exception)
                     {
                         // can not happen, we use Length.ZERO and lane.getLength()
                         destination.getNetwork().getSimulator().getLogger().always().error(exception);
                         throw new RuntimeException(exception);
                     }
                 }
             }
         }
     }
 
     /**
      * Returns the common ancestor {@code LinkType} of all links connected to the node, moving through connectors.
      * @param node origin node
      * @return common ancestor {@code LinkType} of all links connected to the node, moving through connectors
      */
     private static LinkType getLinkTypeFromNode(final Node node)
     {
         return getLinkTypeFromNode0(node, false);
     }
 
     /**
      * Returns the common ancestor {@code LinkType} of all links connected to the node, moving through connectors.
      * @param node origin node
      * @param ignoreConnectors ignore connectors
      * @return common ancestor {@code LinkType} of all links connected to the node, moving through connectors
      */
     private static LinkType getLinkTypeFromNode0(final Node node, final boolean ignoreConnectors)
     {
         LinkType linkType = null;
         for (Link link : node.getLinks())
         {
             LinkType next = link.getType();
             if (!ignoreConnectors && link.isConnector())
             {
                 Node otherNode = link.getStartNode().equals(node) ? link.getEndNode() : link.getStartNode();
                 next = getLinkTypeFromNode0(otherNode, true);
             }
             if (next != null && !link.isConnector())
             {
                 if (linkType == null)
                 {
                     linkType = next;
                 }
                 else
                 {
                     linkType = linkType.commonAncestor(next);
                     if (linkType == null)
                     {
                         // incompatible link types
                         return null;
                     }
                 }
             }
         }
         return linkType;
     }
 
     /**
      * Returns a sorted map.
      * @param map input map
      * @param <K> key type (implemented for cleaner code only)
      * @param <V> value type (implemented for cleaner code only)
      * @return sorted map
      */
     private static <K, V extends Set<LanePosition>> Map<K, V> sortByValue(final Map<K, V> map)
     {
         return map.entrySet().stream().sorted(new Comparator<Map.Entry<K, V>>()
         {
             @Override
             public int compare(final Entry<K, V> o1, final Entry<K, V> o2)
             {
                 LanePosition lanePos1 = o1.getValue().iterator().next();
                 String linkId1 = lanePos1.lane().getLink().getId();
                 LanePosition lanePos2 = o2.getValue().iterator().next();
                 String linkId2 = lanePos2.lane().getLink().getId();
                 int c = linkId1.compareToIgnoreCase(linkId2);
                 if (c == 0)
                 {
                     Length pos1 = Length.ZERO;
                     Length lat1 = lanePos1.lane().getLateralCenterPosition(pos1);
                     Length pos2 = Length.ZERO;
                     Length lat2 = lanePos2.lane().getLateralCenterPosition(pos2);
                     return lat1.compareTo(lat2);
                 }
                 return c;
             }
         }).collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue, (e1, e2) -> e1, LinkedHashMap::new));
     }
 
     /**
      * Adds {@code LanePosition}s to the input set, for {@code Lane}s on the given link, starting at the given {@code Node}.
      * @param link link with lanes to add positions for
      * @param node node on the side where positions should be placed
      * @param positionSet set to add position to
      */
     private static void setLanePosition(final CrossSectionLink link, final Node node, final Set<LanePosition> positionSet)
     {
         for (Lane lane : link.getLanes())
         {
             // TODO should be GTU type dependent.
             if (lane.getLink().getStartNode().equals(node))
             {
                 positionSet.add(new LanePosition(lane, Length.ZERO));
             }
         }
     }
 
     /**
      * Node for demand tree. Based on two constructors there are 2 types of nodes:<br>
      * <ul>
      * <li>Branch nodes; with an object and a stream for randomly drawing a child node.</li>
      * <li>Leaf nodes; with an object and demand data (time, frequency, interpolation).</li>
      * </ul>
      * To accomplish a branching of Node (origin) &gt; Node (destination) &gt; Category, the following generics types can be
      * used:<br>
      * <br>
      * {@code DemandNode<Node, DemandNode<Node, DemandNode<Category, ?>>>}
      * <p>
      * Copyright (c) 2013-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
      * <br>
      * BSD-style license. See <a href="https://opentrafficsim.org/docs/license.html">OpenTrafficSim License</a>.
      * </p>
      * @author <a href="https://github.com/averbraeck">Alexander Verbraeck</a>
      * @author <a href="https://github.com/peter-knoppers">Peter Knoppers</a>
      * @author <a href="https://github.com/wjschakel">Wouter Schakel</a>
      * @param <T> type of contained object
      * @param <K> type of child nodes
      */
     private static class DemandNode<T, K extends DemandNode<?, ?>> implements Arrivals
     {
 
         /** Node object. */
         private final T object;
 
         /** Random stream to draw child node. */
         private final StreamInterface stream;
 
         /** Children. */
         private final List<K> children = new ArrayList<>();
 
         /** Demand data. */
         private final DemandPattern demandPattern;
 
         /** Unique GTU types of leaf nodes. */
         private final List<GtuType> gtuTypes = new ArrayList<>();
 
         /** Number of leaf nodes for the unique GTU types. */
         private final List<Integer> gtuTypeCounts = new ArrayList<>();
 
         /** GTU type of leaf nodes. */
         private final Map<K, GtuType> gtuTypesPerChild = new LinkedHashMap<>();
 
         /** Markov chain for GTU type selection. */
         private final MarkovChain markov;
 
         /**
          * Constructor for branching node, with Markov selection.
          * @param object node object
          * @param stream random stream to draw child node
          * @param markov Markov chain
          */
         DemandNode(final T object, final StreamInterface stream, final MarkovChain markov)
         {
             this.object = object;
             this.stream = stream;
             this.demandPattern = null;
             this.markov = markov;
         }
 
         /**
          * Constructor for leaf node, without Markov selection.
          * @param object node object
          * @param demandPattern demand data
          */
         DemandNode(final T object, final DemandPattern demandPattern)
         {
             this.object = object;
             this.stream = null;
             this.demandPattern = demandPattern;
             this.markov = null;
         }
 
         /**
          * Adds child to a branching node.
          * @param child child node
          */
         public void addChild(final K child)
         {
             this.children.add(child);
         }
 
         /**
          * Adds child to a branching node.
          * @param child child node
          * @param gtuType gtu type for Markov chain
          */
         public void addLeaf(final K child, final GtuType gtuType)
         {
             Throw.when(this.gtuTypes == null, IllegalStateException.class,
                     "Adding leaf with GtuType in not possible on a non-Markov node.");
             addChild(child);
             this.gtuTypesPerChild.put(child, gtuType);
             if (!this.gtuTypes.contains(gtuType))
             {
                 this.gtuTypes.add(gtuType);
                 this.gtuTypeCounts.add(1);
             }
             else
             {
                 int index = this.gtuTypes.indexOf(gtuType);
                 this.gtuTypeCounts.set(index, this.gtuTypeCounts.get(index) + 1);
             }
         }
 
         /**
          * Randomly draws a child node.
          * @param time simulation time
          * @return randomly drawn child node
          */
         public K draw(final Time time)
         {
             Throw.when(this.children.isEmpty(), RuntimeException.class, "Calling draw on a leaf node in the demand tree.");
             Map<K, Double> weightMap = new LinkedHashMap<>();
             if (this.markov == null)
             {
                 // regular draw, loop children and collect their frequencies
                 for (K child : this.children)
                 {
                     double f = child.getFrequency(time, true).si; // sliceStart = true is arbitrary
                     weightMap.put(child, f);
                 }
             }
             else
             {
                 // markov chain draw, the markov chain only selects a GTU type, not a child node
                 GtuType[] gtuTypeArray = new GtuType[this.gtuTypes.size()];
                 gtuTypeArray = this.gtuTypes.toArray(gtuTypeArray);
                 Frequency[] steadyState = new Frequency[this.gtuTypes.size()];
                 Arrays.fill(steadyState, Frequency.ZERO);
                 Map<K, Frequency> frequencies = new LinkedHashMap<>(); // stored, saves us from calculating them twice
                 for (K child : this.children)
                 {
                     GtuType gtuType = this.gtuTypesPerChild.get(child);
                     int index = this.gtuTypes.indexOf(gtuType);
                     Frequency f = child.getFrequency(time, true); // sliceStart = true is arbitrary
                     frequencies.put(child, f);
                     steadyState[index] = steadyState[index].plus(f);
                 }
                 GtuType nextGtuType = this.markov.draw(gtuTypeArray, steadyState, this.stream);
                 // select only child nodes registered to the next GTU type
                 for (K child : this.children)
                 {
                     if (this.gtuTypesPerChild.get(child).equals(nextGtuType))
                     {
                         double f = frequencies.get(child).si;
                         weightMap.put(child, f);
                     }
                 }
             }
             return Draw.drawWeighted(weightMap, this.stream);
         }
 
         /**
          * Returns the node object.
          * @return node object
          */
         public T getObject()
         {
             return this.object;
         }
 
         /**
          * Returns the child that pertains to specified object or {@code null} if no such child is present.
          * @param obj child object
          * @return child that pertains to specified object or {@code null} if no such child is present
          */
         public K getChild(final Object obj)
         {
             for (K child : this.children)
             {
                 if (child.getObject().equals(obj))
                 {
                     return child;
                 }
             }
             return null;
         }
 
         @Override
         public Frequency getFrequency(final Time time, final boolean sliceStart)
         {
             if (this.demandPattern != null)
             {
                 return this.demandPattern.getFrequency(time, sliceStart);
             }
             Frequency f = new Frequency(0.0, FrequencyUnit.PER_HOUR);
             for (K child : this.children)
             {
                 f = f.plus(child.getFrequency(time, sliceStart));
             }
             return f;
         }
 
         @Override
         public Time nextTimeSlice(final Time time)
         {
             if (this.demandPattern != null)
             {
                 return this.demandPattern.nextTimeSlice(time);
             }
             Time out = null;
             for (K child : this.children)
             {
                 Time childSlice = child.nextTimeSlice(time);
                 out = out == null || (childSlice != null && childSlice.lt(out)) ? childSlice : out;
             }
             return out;
         }
 
         @Override
         public String toString()
         {
             return "DemandNode [object=" + this.object + ", stream=" + this.stream + ", children=" + this.children
                     + ", demandPattern=" + this.demandPattern + ", gtuTypes=" + this.gtuTypes + ", gtuTypeCounts="
                     + this.gtuTypeCounts + ", gtuTypesPerChild=" + this.gtuTypesPerChild + ", markov=" + this.markov + "]";
         }
 
     }
 
     /**
      * Wrapper class around a {@code MarkovCorrelation}, including the last type. One of these should be used for each vehicle
      * generator.
      */
     private static class MarkovChain
     {
         /** Markov correlation for GTU type selection. */
         private final MarkovCorrelation<GtuType, Frequency> markov;
 
         /** Previously returned GTU type. */
         private GtuType previousGtuType = null;
 
         /**
          * Constructor.
          * @param markov Markov correlation for GTU type selection
          */
         MarkovChain(final MarkovCorrelation<GtuType, Frequency> markov)
         {
             this.markov = markov;
         }
 
         /**
          * Returns a next GTU type drawn using a Markov chain.
          * @param gtuTypes GtuTypes to consider
          * @param intensities frequency for each GTU type, i.e. the steady-state
          * @param stream stream for random numbers
          * @return next GTU type drawn using a Markov chain
          */
         public GtuType draw(final GtuType[] gtuTypes, final Frequency[] intensities, final StreamInterface stream)
         {
             this.previousGtuType = this.markov.drawState(this.previousGtuType, gtuTypes, intensities, stream);
             return this.previousGtuType;
         }
     }
 
     /**
      * Class to contain created generator objects.
      * <p>
      * Copyright (c) 2013-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
      * <br>
      * BSD-style license. See <a href="https://opentrafficsim.org/docs/license.html">OpenTrafficSim License</a>.
      * </p>
      * @author <a href="https://github.com/averbraeck">Alexander Verbraeck</a>
      * @author <a href="https://github.com/peter-knoppers">Peter Knoppers</a>
      * @author <a href="https://github.com/wjschakel">Wouter Schakel</a>
      * @param generator main generator for GTU's
      * @param headwayGenerator generator of headways
      * @param characteristicsGenerator generator of GTU characteristics
      */
     public static record GeneratorObjects(LaneBasedGtuGenerator generator, Generator<Duration> headwayGenerator,
             LaneBasedGtuCharacteristicsGenerator characteristicsGenerator)
     {
     }
 
 }