LARGE-SCALE PARALLEL GRAPH-BASED SIMULATIONS - MATSim

Algorithm 5 for Vehicle Movement through Intersections:
for all nodes do
if node visited for the first time then
Choose first incoming link randomly according to capacity
end if
for i = 1..(the number of incoming links) do
Choose next incoming link via Metropolis sampling
if link buffer is empty then
Mark link as non-eligible
else
Take first vehicle in the buffer
if destination link for vehicle has space then
Move that vehicle from buffer to destination link
else
Mark link as non-eligible
end if
end if
end for
end for
Figure 2.7: Handling intersections according to the modified Metropolis sampling.
Finally, Algorithm-5 is similar to Algorithm-4 except that if a node is visited for the first
time, the first incoming link is selected according to the flow capacity. The algorithm is given
in Figure 2.7.
The queue model reads flow capacities, free speeds and link lengths, from the input files
and accordingly calculates free flow link travel times. The free flow link travel time defines
the minimum time that vehicles on that particular link must spend. Whilst the lower-bound is
known, the upper-bound for a vehicle being on a link before moving to the next link depends on
how long the vehicle waits at the end of the link. If the randomized selection is not in favor of
a link on which a vehicle is ready to move to the next link (Figure 2.3), the travel time related
to the link increases.
There is a remark to be made about flow capacities. When several of very short links (such
as links with a buffer size 1) exist, they reduce the number of vehicles discharge from the longer
links as the available space is reduced by the short links 2 .
2.2.3 Graph Data as Input for Queue Simulation
The traffic flow simulation is fed by the graph data (the street network) and the plans of vehicles
to be executed. Plans are explained in Section 2.2.4. Before the execution of plans, the
simulation reads nodes and links of the street network. The street network is defined in the
XML [97] format and a rough example is shown in Figure 2.8. XML is explained in detail in
2 The problem can be seen as follows: Assume a short link with a given non-integer capacity (per second), with
long links of the same capacity both upstream and downstream. Then, according to standard queuing theory, the
queue length on the short link follows a random walk. However, when that random walk makes the short link
completely full, then the upstream link is no longer allowed to discharge into the short link. Since this happens
fairly often with short links, this means that short links reduce the effective capacity. Note that the effective
capacity reduction is felt for the upstream link. This phenomenon has little effect with the long links of the Swiss
street network defined in Section 2.5, but became apparent with validation studies with the Navtec network of the
Zurich area, which has many short links.
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