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    <p>Hi Rory,</p>
    <p><br>
    </p>
    <p>I recommend to start with the latest MobilityDB extension (docker
      image seems to be outdated) and import and partition the Berlin
      Workshop data, as mentioned in
<a class="moz-txt-link-freetext" href="https://docs.mobilitydb.com/MobilityDB-BerlinMOD/master/mobilitydb-berlinmod.pdf">https://docs.mobilitydb.com/MobilityDB-BerlinMOD/master/mobilitydb-berlinmod.pdf</a>.</p>
    <p>The query below should give a good starting point for your
      analysis - for a given period, output the average time cars remain
      in regions. <br>
    </p>
    <pre style="background-color:#ffffff;color:#080808;font-family:'JetBrains Mono',monospace;font-size:9,0pt;"><span style="color:#0033b3;">select </span><span style="color:#871094;">carid</span>,
       <span style="color:#871094;">regionid</span>,
       <span style="font-style:italic;">avg</span>(<span style="color:#00627a;font-style:italic;">duration</span>(
               (<span style="color:#00627a;font-style:italic;">atgeometry</span>((<span style="color:#00627a;font-style:italic;">atPeriod</span>(<span style="color:#000000;">T</span>.<span style="color:#871094;">Trip</span>, <span style="color:#067d17;">'[2007-05-28 00:00:00+00, 2007-05-29 00:00:00+00]'</span>::<span style="color:#0033b3;">period</span>)),
                           <span style="color:#000000;">R</span>.<span style="color:#871094;">geom</span>))::<span style="color:#0033b3;">tgeompoint</span>))
<span style="color:#0033b3;">FROM </span><span style="color:#000000;">Trips T</span>,
     <span style="color:#000000;">Regions R
</span><span style="color:#0033b3;">WHERE </span><span style="color:#000000;">T</span>.<span style="color:#871094;">Trip </span><span style="color:#000000;">&& </span><span style="color:#00627a;font-style:italic;">stbox</span>(<span style="color:#000000;">R</span>.<span style="color:#871094;">Geom</span>, <span style="color:#067d17;">'[2007-05-28 00:00:00+00, 2007-05-29 00:00:00+00]'</span>::<span style="color:#0033b3;">period</span>)
  <span style="color:#0033b3;">AND </span><span style="color:#00627a;font-style:italic;">st_intersects</span>(<span style="color:#00627a;font-style:italic;">trajectory</span>(<span style="color:#00627a;font-style:italic;">atPeriod</span>(<span style="color:#000000;">T</span>.<span style="color:#871094;">Trip</span>, <span style="color:#067d17;">'[2007-05-28 00:00:00+00, 2007-05-29 00:00:00+00]'</span>::<span style="color:#0033b3;">period</span>)),
                    <span style="color:#000000;">R</span>.<span style="color:#871094;">Geom</span>)
<span style="color:#0033b3;">group by </span><span style="color:#871094;">carid</span>, <span style="color:#871094;">regionid</span><span style="color:#871094;"></span></pre>
    <p>Just let me know if this works out for. <br>
    </p>
    <p>Florian<br>
    </p>
    <p><br>
    </p>
    <div class="moz-cite-prefix">Am 24.02.2022 um 08:53 schrieb Rory
      Meyer:<br>
    </div>
    <blockquote type="cite"
cite="mid:DB9PR05MB8026C130DCBE0AEBD0DC7A06843D9@DB9PR05MB8026.eurprd05.prod.outlook.com">
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <style type="text/css" style="display:none;">P {margin-top:0;margin-bottom:0;}</style>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">I haven't looked at MobilityDB (although I will
          now). In addition to PostGIS I'm using TimeScaleDB to build
          "continuous aggregates" of the GPS data in order to get things
          like the latest position per hour, the average speed per day
          etc. It's pretty handy for that but is unable to use more
          complex aggregates with window functions, distinct, trajectory
          creation etc. </span><br>
      </div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;"><br>
        </span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">I suppose the main part of my query would be
          portion that distributes the difference between the lead/lag
          and current event_times (time delta) over the grids that the
          lead/lag created line pass over:</span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">      sum(((st_length(st_intersection(traj.traj,
          grid.geom)) * traj.time_delta) / traj.traj_dist))<br>
        </span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">Does MobilityDB have a function that could help
          with this? </span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;"><br>
        </span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">I tried to stay away from using the trajectory
          data type since it is only (x,y,t) and what I really need is
          (x,y,t,m1,m2,m3....) so that I can distribute the
          speed/bearing/dataX over the hexagon weighted with the time
          associated with each vertex.</span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;"><br>
        </span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255,
        255, 255);">
        <span style="color: rgb(0, 0, 0); font-family: "Segoe
          UI", "Segoe UI Web (West European)",
          "Segoe UI", -apple-system, BlinkMacSystemFont,
          Roboto, "Helvetica Neue", sans-serif; font-size:
          14px; background-color: rgb(255, 255, 255); display: inline
          !important;">Regards,</span></div>
      <div style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
        255);"><span style="font-size: 14px;">Rory</span></div>
      <div style="font-family: Calibri, Arial, Helvetica, sans-serif;
        font-size: 12pt; color: rgb(0, 0, 0);">
        <br>
      </div>
      <hr tabindex="-1" style="display:inline-block; width:98%">
      <div id="divRplyFwdMsg" dir="ltr"><font style="font-size: 11pt;"
          face="Calibri, sans-serif" color="#000000"><b>From:</b>
          Florian Nadler <a class="moz-txt-link-rfc2396E" href="mailto:florian.nadler@cybertec.at"><florian.nadler@cybertec.at></a><br>
          <b>Sent:</b> 24 February 2022 07:45<br>
          <b>To:</b> PostGIS Users Discussion
          <a class="moz-txt-link-rfc2396E" href="mailto:postgis-users@lists.osgeo.org"><postgis-users@lists.osgeo.org></a>; Rory Meyer
          <a class="moz-txt-link-rfc2396E" href="mailto:rory.meyer@VLIZ.be"><rory.meyer@VLIZ.be></a><br>
          <b>Subject:</b> Re: [postgis-users] Non-linear time cost;
          please suggest a better way to structure the query</font>
        <div> </div>
      </div>
      <div>
        <p style="margin-top: 0px; margin-bottom: 0px;">Hi, <br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;"><br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;">apart from Paul
          advice did you ever take into consideration to use MobilityDB
          for this kind of spatial questions?</p>
        <p style="margin-top: 0px; margin-bottom: 0px;"><br>
          This will imply creating trajectories out of gps points too,
          but might simplify query design and processing time as this
          extension is developed for this kind of queries.
          <br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;"><br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;">Checkout <a
            class="x_moz-txt-link-freetext moz-txt-link-freetext"
href="https://docs.mobilitydb.com/MobilityDB-BerlinMOD/master/mobilitydb-berlinmod.pdf"
            moz-do-not-send="true">
https://docs.mobilitydb.com/MobilityDB-BerlinMOD/master/mobilitydb-berlinmod.pdf</a>,
          chapter 3.3 which deals with quite simliar analysis.<br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;"><br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;">Florian<br>
        </p>
        <p style="margin-top: 0px; margin-bottom: 0px;"><br>
        </p>
        <div class="x_moz-cite-prefix">Am 23.02.2022 um 15:14 schrieb
          Rory Meyer:<br>
        </div>
        <blockquote type="cite">
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            Afternoon all,</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            I've got a database full of GPS points (along with
            associated data like speed, bearing, time, GPS_ID, class
            etc) and I'm trying to do complex aggregations with the
            data. I'm trying to build up a "heatmap" of the data by
            first creating a grid of polygons using ST_HexagonGrid and
            then using a window function to overlay the lines (created
            from a lead/lag window of each GPS point and the next one
            from the same GPS_ID) over the grid. I'd like to get the the
            number of seconds that gps carrying vehicles spend in each
            hex cell, grouped by class, speed, date, direction etc etc.
            The end goal would be to query a lon/lat and get a bunch of
            aggregated data for different classes, speed/bearing
            distributions. </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            Here's a simplified look at the SQL (sorry, it's not really
            simple...):</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            '''</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            SELECT
            <div>    grid.gid,</div>
            <div>    grid.geom,</div>
            <div>    avg(traj.bearing, 511.0) AS avg_bearing,</div>
            <div>    avg(traj.time_delta) AS avg_time_delta,</div>
            <div>    sum(((st_length(st_intersection(traj.traj,
              grid.geom)) * traj.time_delta) / traj.traj_dist)) AS
              cum_time_in_grid</div>
            <div>FROM (</div>
            <div>(my_hex_grid AS grid LEFT JOIN ( SELECT</div>
            <div>                                                       
               subquery.gps_id,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>subquery.event_date,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>subquery.bearing,
            </div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>subquery.time_delta,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>st_makeline(subquery.pos,
              subquery.pos2) AS traj,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>st_distance(subquery.pos,
              subquery.pos2) AS traj_dist</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>FROM
              ( </div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>SELECT </div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>gps.mmsi,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>date_part('epoch'::text,
              (lead(gps.event_time) OVER time_order - gps.event_time))
              AS
              <span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">
                                                                       
                       </span>time_delta,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>gps.geom,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>gps.bearing,</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>lead(gps.geom)
              OVER time_order AS geom2</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span> FROM
              gps</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>WHERE
              ((gps.event_time >= '<Start Time>') AND
              (gps.event_time <= '<End Time>'))</div>
            <div><span style="color: rgb(0, 0, 0); background-color:
                rgb(255, 255, 255); display: inline !important;">       
                                                                 </span>WINDOW
              time_order AS (PARTITION BY gps.gps_id ORDER BY
              gps.event_time)) as subquery</div>
            <div>                                  ON
              (st_intersects(gps.traj, grid.geom)))</div>
              GROUP BY grid.gid, grid.geom</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            '''</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            My issue is that I've got a non-linear increase in time that
            the query takes to complete. If <Start Time> to
            <End Time> is a couple of hours then it's takes a
            couple of seconds to run. If it's for a day, it takes a
            couple minutes to run. If it's for a week it takes a couple
            of hours. </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            I'd like to run this for over a year of data but that won't
            be feasible at this rate. </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            Is there some way to avoid this non-linear increase in time
            or would it be best to just write some python code to loop
            through smaller chunks of data and write the results
            somewhere?</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            <br>
          </div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            Regards,</div>
          <div style="font-family: Calibri, Arial, Helvetica,
            sans-serif; font-size: 12pt; color: rgb(0, 0, 0);
            background-color: rgb(255, 255, 255);">
            Rory</div>
          <br>
          <fieldset class="x_moz-mime-attachment-header"></fieldset>
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    <pre class="moz-signature" cols="72">-- 
CYBERTEC PostgreSQL International GmbH
Römerstraße 19, A-2752 Wöllersdorf
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