ArrivalsHeadwayGenerator.java
package org.opentrafficsim.road.gtu.generator.headway;
import org.djunits.value.vdouble.scalar.Duration;
import org.djunits.value.vdouble.scalar.Time;
import org.opentrafficsim.base.parameters.ParameterException;
import org.opentrafficsim.core.distributions.Generator;
import org.opentrafficsim.core.distributions.ProbabilityException;
import nl.tudelft.simulation.dsol.simulators.SimulatorInterface;
import nl.tudelft.simulation.jstats.distributions.DistNormal;
import nl.tudelft.simulation.jstats.streams.StreamInterface;
/**
* Headway generation based on {@code Arrivals}.
* <p>
* Copyright (c) 2013-2018 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
* BSD-style license. See <a href="http://opentrafficsim.org/node/13">OpenTrafficSim License</a>.
* <p>
* @version $Revision$, $LastChangedDate$, by $Author$, initial version 13 dec. 2017 <br>
* @author <a href="http://www.tbm.tudelft.nl/averbraeck">Alexander Verbraeck</a>
* @author <a href="http://www.tudelft.nl/pknoppers">Peter Knoppers</a>
* @author <a href="http://www.transport.citg.tudelft.nl">Wouter Schakel</a>
*/
public class ArrivalsHeadwayGenerator implements Generator<Duration>
{
/** Arrivals. */
private final Arrivals arrivals;
/** Simulator. */
private final SimulatorInterface.TimeDoubleUnit simulator;
/** Random stream to draw headway. */
private final StreamInterface stream;
/** Random headway generator. */
private final HeadwayDistribution distribution;
/** First GTU. */
private boolean first = true;
/**
* @param arrivals Arrivals; arrivals
* @param simulator SimulatorInterface.TimeDoubleUnit; simulator
* @param stream StreamInterface; random stream to draw headway
* @param distribution HeadwayDistribution; random headway distribution
*/
public ArrivalsHeadwayGenerator(final Arrivals arrivals, final SimulatorInterface.TimeDoubleUnit simulator,
final StreamInterface stream, final HeadwayDistribution distribution)
{
this.arrivals = arrivals;
this.simulator = simulator;
this.stream = stream;
this.distribution = distribution;
}
/**
* Returns a new headway {@code h} assuming that the previous vehicle arrived at the current time {@code t0}. The vehicle
* thus arrives at {@code t1 = t0 + h}. This method guarantees that no vehicle arrives during periods where demand is zero,
* while maintaining random headways based on average demand over a certain time period.<br>
* <br>
* The general method is to find {@code h} such that the integral of the demand pattern {@code D} from {@code t0} until
* {@code t1} equals {@code r}: Σ{@code D(t0 > t1) = r}. One can think of {@code r} as being 1 and representing an
* additional vehicle to arrive. The headway {@code h} that results correlates directly to the mean demand between
* {@code t0} and {@code t1}.<br>
* <br>
* The value of {@code r} always has a mean of 1, but may vary between specific vehicle arrivals depending on the headway
* distribution. When assuming constant headways for any given demand level, {@code r} always equals 1. For exponentially
* distributed headways {@code r} may range anywhere between 0 and infinity.<br>
* <br>
* This usage of {@code r} guarantees that no vehicles arrive during periods with 0 demand. For example:
* <ul>
* <li>Suppose we have 0 demand between 300s and 400s.</li>
* <li>The previous vehicle was generated at 299s.</li>
* <li>The demand at 299s equals 1800veh/h (1 veh per 2s).</li>
* <li>For both constant and exponentially distributed headways, the expected next vehicle arrival based on this demand
* value alone would be 299 + 2 = 301s. This is within the 0-demand period and should not happen. It's also not
* theoretically sound, as the demand from 299s until 301s is not 1800veh/h on average.</li>
* <li>Using integration we find that the surface of demand from 299s until 300s equals 0.5 veh for stepwise demand, and
* 0.25 veh for linear demand. Consequently, the vehicle will not arrive until later slices integrate to an additional 0.5
* veh or 0.75 veh respectively. This additional surface under the demand curve is only found after 400s.</li>
* <li>In case the exponential headway distribution would have resulted in {@code r} < 0.5 (stepwise demand) or 0.25
* (linear demand), a vehicle will simply arrive between 299s and 300s.</li>
* </ul>
* <br>
* @return Duration; new headway
* @throws ProbabilityException if the stored collection is empty
* @throws ParameterException in case of a parameter exception
*/
@Override
public Duration draw() throws ProbabilityException, ParameterException
{
Time now = this.simulator.getSimulatorTime();
// initial slice times and frequencies
Time t1 = now;
double f1 = this.arrivals.getFrequency(t1, true).si;
Time t2 = this.arrivals.nextTimeSlice(t1);
if (t2 == null)
{
return null; // no new vehicle
}
double f2 = this.arrivals.getFrequency(t2, false).si;
// next vehicle's random factor
double rem = this.distribution.draw(this.stream);
if (this.first)
{
// first headway may be partially in the past, take a random factor
rem *= this.stream.nextDouble();
this.first = false;
}
// integrate until rem (by reducing it to 0.0, possibly in steps per slice)
while (rem > 0.0)
{
// extrapolate to find 'integration = rem' in this slice giving demand slope, this may beyond the slice length
double dt = t2.si - t1.si;
double t;
double slope = (f2 - f1) / dt;
if (Math.abs(slope) < 1e-12) // no slope
{
if (f1 > 0.0)
{
t = rem / f1; // rem = t * f1, t = rem / f1
}
else
{
t = Double.POSITIVE_INFINITY; // no demand in this slice
}
}
else
{
// reverse of trapezoidal rule: rem = t * (f1 + (f1 + t * slope)) / 2
double sqrt = 2 * slope * rem + f1 * f1;
if (sqrt >= 0.0)
{
t = (-f1 + Math.sqrt(sqrt)) / slope;
}
else
{
t = Double.POSITIVE_INFINITY; // not sufficient demand in this slice, with negative slope
}
}
if (t > dt)
{
// next slice
rem -= dt * (f1 + f2) / 2; // subtract integral of this slice using trapezoidal rule
t1 = t2;
t2 = this.arrivals.nextTimeSlice(t1);
if (t2 == null)
{
return null; // no new vehicle
}
f1 = this.arrivals.getFrequency(t1, true).si; // we can't use f1 = f2 due to possible steps in demand
f2 = this.arrivals.getFrequency(t2, false).si;
}
else
{
// return resulting integration times
return Duration.createSI(t1.si + t - now.si);
}
}
throw new RuntimeException("Exception while determining headway from Arrivals.");
}
/**
* Headway distribution.
* <p>
* Copyright (c) 2013-2018 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
* <br>
* BSD-style license. See <a href="http://opentrafficsim.org/node/13">OpenTrafficSim License</a>.
* <p>
* @version $Revision$, $LastChangedDate$, by $Author$, initial version 5 dec. 2017 <br>
* @author <a href="http://www.tbm.tudelft.nl/averbraeck">Alexander Verbraeck</a>
* @author <a href="http://www.tudelft.nl/pknoppers">Peter Knoppers</a>
* @author <a href="http://www.transport.citg.tudelft.nl">Wouter Schakel</a>
*/
public interface HeadwayDistribution
{
/** Constant headway. */
HeadwayDistribution CONSTANT = new HeadwayDistribution()
{
@Override
public double draw(final StreamInterface randomStream)
{
return 1.0;
}
@Override
public String getName()
{
return "CONSTANT";
}
};
/** Exponential headway distribution. */
HeadwayDistribution EXPONENTIAL = new HeadwayDistribution()
{
@Override
public double draw(final StreamInterface randomStream)
{
return -Math.log(randomStream.nextDouble());
}
@Override
public String getName()
{
return "EXPONENTIAL";
}
};
/** Uniform headway distribution. */
HeadwayDistribution UNIFORM = new HeadwayDistribution()
{
@Override
public double draw(final StreamInterface randomStream)
{
return 2.0 * randomStream.nextDouble();
}
@Override
public String getName()
{
return "UNIFORM";
}
};
/** Triangular headway distribution. */
HeadwayDistribution TRIANGULAR = new HeadwayDistribution()
{
@Override
public double draw(final StreamInterface randomStream)
{
double r = randomStream.nextDouble();
if (r < .5)
{
return Math.sqrt(r * 2.0);
}
return 2.0 - Math.sqrt((1.0 - r) * 2.0);
}
@Override
public String getName()
{
return "TRIANGULAR";
}
};
/** Triangular (left side, mean 2/3) and exponential (right side, mean 4/3) headway distribution. */
HeadwayDistribution TRI_EXP = new HeadwayDistribution()
{
@Override
public double draw(final StreamInterface randomStream)
{
double r = randomStream.nextDouble();
if (r < .5)
{
return Math.sqrt(r * 2.0); // left-hand side of triangular distribution, with mean 2/3
}
return 1.0 - Math.log((1.0 - r) * 2.0) / 3.0; // 1 + 1/3, where 1/3 is mean of exponential right-hand side
// note: 50% with mean 2/3 and 50% with mean 1 + 1/3 gives a mean of 1
}
@Override
public String getName()
{
return "TRI_EXP";
}
};
/** Log-normal headway distribution (variance = 1.0). */
HeadwayDistribution LOGNORMAL = new HeadwayDistribution()
{
/** Mu. */
private final double mu = Math.log(1.0 / Math.sqrt(2.0));
/** Sigma. */
private final double sigma = Math.sqrt(Math.log(2.0));
@Override
public double draw(final StreamInterface randomStream)
{
return Math.exp(new DistNormal(randomStream, this.mu, this.sigma).draw());
}
@Override
public String getName()
{
return "LOGNORMAL";
}
};
/**
* Draws a randomized headway factor. The average value returned is always 1.0. The returned value is applied on the
* demand pattern by (reversed) integration to derive actual headways.
* @param randomStream StreamInterface; random number stream
* @return randomized headway factor
*/
double draw(StreamInterface randomStream);
/**
* Returns the distribution name.
* @return distribution name
*/
String getName();
}
}