If you want to animate multiple markers you will have to change the animate and startAnimation functions to handle multiple markers (probably make all the variables into arrays).

example

code snippet:

var map;
  var directionDisplay;
  var directionsService;
  var stepDisplay;
 
  var position;
  var marker = [];
  var polyline = [];
  var poly2 = [];
  var poly = null;
  var startLocation = [];
  var endLocation = [];
  var timerHandle = [];
    
  
  var speed = 0.000005, wait = 1;
  var infowindow = null;
  
  var myPano;   
  var panoClient;
  var nextPanoId;
  
  var startLoc = new Array();
  startLoc[0] = 'rio claro, trinidad';
  startLoc[1] = 'preysal, trinidad';
  startLoc[2] = 'san fernando, trinidad';
  startLoc[3] = 'couva, trinidad';

  var endLoc = new Array();
  endLoc[0] = 'princes town, trinidad';
  endLoc[1] = 'tabaquite, trinidad';
  endLoc[2] = 'mayaro, trinidad';
  endLoc[3] = 'arima, trinidad';


  var Colors = ["#FF0000", "#00FF00", "#0000FF"];


function initialize() {  

  infowindow = new google.maps.InfoWindow(
    { 
      size: new google.maps.Size(150,50)
    });

    var myOptions = {
      zoom: 10,
      mapTypeId: google.maps.MapTypeId.ROADMAP
    }
    map = new google.maps.Map(document.getElementById("map_canvas"), myOptions);

    address = 'Trinidad and Tobago'
    geocoder = new google.maps.Geocoder();
    geocoder.geocode( { 'address': address}, function(results, status) {
     map.fitBounds(results[0].geometry.viewport);

    }); 
  // setRoutes();
  } 


function createMarker(latlng, label, html) {
// alert("createMarker("+latlng+","+label+","+html+","+color+")");
    var contentString = '<b>'+label+'</b><br>'+html;
    var marker = new google.maps.Marker({
        position: latlng,
        map: map,
        title: label,
        zIndex: Math.round(latlng.lat()*-100000)<<5
        });
        marker.myname = label;


    google.maps.event.addListener(marker, 'click', function() {
        infowindow.setContent(contentString); 
        infowindow.open(map,marker);
        });
    return marker;
}  

function setRoutes(){   

    var directionsDisplay = new Array();

    for (var i=0; i< startLoc.length; i++){

    var rendererOptions = {
        map: map,
        suppressMarkers : true,
        preserveViewport: true
    }
    directionsService = new google.maps.DirectionsService();

    var travelMode = google.maps.DirectionsTravelMode.DRIVING;  

    var request = {
        origin: startLoc[i],
        destination: endLoc[i],
        travelMode: travelMode
    };  

        directionsService.route(request,makeRouteCallback(i,directionsDisplay[i]));

    }   


    function makeRouteCallback(routeNum,disp){
        if (polyline[routeNum] && (polyline[routeNum].getMap() != null)) {
         startAnimation(routeNum);
         return;
        }
        return function(response, status){
          
          if (status == google.maps.DirectionsStatus.OK){

            var bounds = new google.maps.LatLngBounds();
            var route = response.routes[0];
            startLocation[routeNum] = new Object();
            endLocation[routeNum] = new Object();


            polyline[routeNum] = new google.maps.Polyline({
            path: [],
            strokeColor: '#FFFF00',
            strokeWeight: 3
            });

            poly2[routeNum] = new google.maps.Polyline({
            path: [],
            strokeColor: '#FFFF00',
            strokeWeight: 3
            });     


            // For each route, display summary information.
            var path = response.routes[0].overview_path;
            var legs = response.routes[0].legs;


            disp = new google.maps.DirectionsRenderer(rendererOptions);     
            disp.setMap(map);
            disp.setDirections(response);


            //Markers               
            for (i=0;i<legs.length;i++) {
              if (i == 0) { 
                startLocation[routeNum].latlng = legs[i].start_location;
                startLocation[routeNum].address = legs[i].start_address;
                // marker = google.maps.Marker({map:map,position: startLocation.latlng});
                marker[routeNum] = createMarker(legs[i].start_location,"start",legs[i].start_address,"green");
              }
              endLocation[routeNum].latlng = legs[i].end_location;
              endLocation[routeNum].address = legs[i].end_address;
              var steps = legs[i].steps;

              for (j=0;j<steps.length;j++) {
                var nextSegment = steps[j].path;                
                var nextSegment = steps[j].path;

                for (k=0;k<nextSegment.length;k++) {
                    polyline[routeNum].getPath().push(nextSegment[k]);
                    //bounds.extend(nextSegment[k]);
                }

              }
            }

         }       

         polyline[routeNum].setMap(map);
         //map.fitBounds(bounds);
         startAnimation(routeNum);  

    } // else alert("Directions request failed: "+status);

  }

}

    var lastVertex = 1;
    var stepnum=0;
    var step = 50; // 5; // metres
    var tick = 100; // milliseconds
    var eol= [];
//----------------------------------------------------------------------                
 function updatePoly(i,d) {
 // Spawn a new polyline every 20 vertices, because updating a 100-vertex poly is too slow
    if (poly2[i].getPath().getLength() > 20) {
          poly2[i]=new google.maps.Polyline([polyline[i].getPath().getAt(lastVertex-1)]);
          // map.addOverlay(poly2)
        }

    if (polyline[i].GetIndexAtDistance(d) < lastVertex+2) {
        if (poly2[i].getPath().getLength()>1) {
            poly2[i].getPath().removeAt(poly2[i].getPath().getLength()-1)
        }
            poly2[i].getPath().insertAt(poly2[i].getPath().getLength(),polyline[i].GetPointAtDistance(d));
    } else {
        poly2[i].getPath().insertAt(poly2[i].getPath().getLength(),endLocation[i].latlng);
    }
 }
//----------------------------------------------------------------------------

function animate(index,d) {
   if (d>eol[index]) {

      marker[index].setPosition(endLocation[index].latlng);
      return;
   }
    var p = polyline[index].GetPointAtDistance(d);

    //map.panTo(p);
    marker[index].setPosition(p);
    updatePoly(index,d);
    timerHandle[index] = setTimeout("animate("+index+","+(d+step)+")", tick);
}

//-------------------------------------------------------------------------

function startAnimation(index) {
        if (timerHandle[index]) clearTimeout(timerHandle[index]);
        eol[index]=polyline[index].Distance();
        map.setCenter(polyline[index].getPath().getAt(0));

        poly2[index] = new google.maps.Polyline({path: [polyline[index].getPath().getAt(0)], strokeColor:"#FFFF00", strokeWeight:3});

        timerHandle[index] = setTimeout("animate("+index+",50)",2000);  // Allow time for the initial map display
}

//----------------------------------------------------------------------------    
google.maps.event.addDomListener(window,'load',initialize);

//src="http://www.geocodezip.com/scripts/v3_epoly.js"
/*********************************************************************\
*                                                                     *
* epolys.js                                          by Mike Williams *
* updated to API v3                                  by Larry Ross    *
*                                                                     *
* A Google Maps API Extension                                         *
*                                                                     *
* Adds various Methods to google.maps.Polygon and google.maps.Polyline *
* .Distance()       returns the length of the poly path               *
*                                                                     *
* .GetPointAtDistance() returns a GLatLng at the specified distance   *
*                   along the path.                                   *
*                   The distance is specified in metres               *
*                   Reurns null if the path is shorter than that      *
*                                                                     *
* .GetPointsAtDistance() returns an array of GLatLngs at the          *
*                   specified interval along the path.                *
*                   The distance is specified in metres               *
*                                                                     *
\*********************************************************************/
// === first support methods that don't (yet) exist in v3
google.maps.LatLng.prototype.distanceFrom = function(newLatLng) {
  var EarthRadiusMeters = 6378137.0; // meters
  var lat1 = this.lat();
  var lon1 = this.lng();
  var lat2 = newLatLng.lat();
  var lon2 = newLatLng.lng();
  var dLat = (lat2-lat1) * Math.PI / 180;
  var dLon = (lon2-lon1) * Math.PI / 180;
  var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
    Math.cos(lat1 * Math.PI / 180 ) * Math.cos(lat2 * Math.PI / 180 ) *
    Math.sin(dLon/2) * Math.sin(dLon/2);
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
  var d = EarthRadiusMeters * c;
  return d;
}

google.maps.LatLng.prototype.latRadians = function() {
  return this.lat() * Math.PI/180;
}

google.maps.LatLng.prototype.lngRadians = function() {
  return this.lng() * Math.PI/180;
}

// === A method which returns the length of a path in metres ===
google.maps.Polyline.prototype.Distance = function() {
  var dist = 0;
  for (var i=1; i < this.getPath().getLength(); i++) {
    dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i-1));
  }
  return dist;
}
// === A method which returns a GLatLng of a point a given distance along the path ===
// === Returns null if the path is shorter than the specified distance ===
google.maps.Polyline.prototype.GetPointAtDistance = function(metres) {
  // some awkward special cases
  if (metres == 0) return this.getPath().getAt(0);
  if (metres < 0) return null;
  if (this.getPath().getLength() < 2) return null;
  var dist=0;
  var olddist=0;
  for (var i=1; (i < this.getPath().getLength() && dist < metres); i++) {
    olddist = dist;
    dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i-1));
  }
  if (dist < metres) {
    return null;
  }
  var p1= this.getPath().getAt(i-2);
  var p2= this.getPath().getAt(i-1);
  var m = (metres-olddist)/(dist-olddist);
  return new google.maps.LatLng( p1.lat() + (p2.lat()-p1.lat())*m, p1.lng() + (p2.lng()-p1.lng())*m);
}

// === A method which returns an array of GLatLngs of points a given interval along the path ===
google.maps.Polyline.prototype.GetPointsAtDistance = function(metres) {
  var next = metres;
  var points = [];
  // some awkward special cases
  if (metres <= 0) return points;
  var dist=0;
  var olddist=0;
  for (var i=1; (i < this.getPath().getLength()); i++) {
    olddist = dist;
    dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i-1));
    while (dist > next) {
      var p1= this.getPath().getAt(i-1);
      var p2= this.getPath().getAt(i);
      var m = (next-olddist)/(dist-olddist);
      points.push(new google.maps.LatLng( p1.lat() + (p2.lat()-p1.lat())*m, p1.lng() + (p2.lng()-p1.lng())*m));
      next += metres;    
    }
  }
  return points;
}

// === A method which returns the Vertex number at a given distance along the path ===
// === Returns null if the path is shorter than the specified distance ===
google.maps.Polyline.prototype.GetIndexAtDistance = function(metres) {
  // some awkward special cases
  if (metres == 0) return this.getPath().getAt(0);
  if (metres < 0) return null;
  var dist=0;
  var olddist=0;
  for (var i=1; (i < this.getPath().getLength() && dist < metres); i++) {
    olddist = dist;
    dist += this.getPath().getAt(i).distanceFrom(this.getPath().getAt(i-1));
  }
  if (dist < metres) {return null;}
  return i;
}
html{height:100%;}
body{height:100%;margin:0px;font-family: Helvetica,Arial;}
<script type="text/javascript" src="https://maps.google.com/maps/api/js?key=AIzaSyCkUOdZ5y7hMm0yrcCQoCvLwzdM6M8s5qk"></script>


<div id="tools">

    <button onclick="setRoutes();">Start</button>

</div>

<div id="map_canvas" style="width:100%;height:100%;"></div>