Scenario Performance Data and Histograms

SimPy probes monitor and collect performance metrics experienced by individual entities in the simulation. By plotting several of these metrics as histograms, we can gain some deeper insight into what the system is doing over time.

We present a set of example histograms in Figures 5.8 through 5.12. This data was taken from one of the 1D rail networks with linear sequential routing serving a moderate load of passengers.

Passenger Performance Metrics

Improving system performance perceived by passengers of the system often comes at the expense of vehicle fleet operating costs. Improving passenger service goals typically increases the number of vehicles operating and the distance they must travel during the course of a schedule. Since our optimization goal favors the fulfillment of passenger goals first, we expect to see some fairly straightforward trends.

Histograms in red pertain to the transit system performance from the point of view of the passengers.

Transit Time: In Figure 5.8, we see the total number of passengers served by the system, and time they were delivered to their final station. Thus, we can view this graph as the system response to the demand impulse at time $t=0$. Each time segment takes 2 units of time. Therefore the width of each histogram bin is 2 time units long, and we don't see our first arrivals until $t=4$, since passengers must travel through 2 segments via a waypoint before arriving. Large groups of passengers continue to get dropped off at their destinations after roughly every other time segment, since all stations are separated by one waypoint. The quantity of passengers delivered diminishes with time, as fewer combinations of station pairs are that number of segments apart. We do notice that some deliveries are also made on the ``odd'' time steps in between the ``even'' peaks, where the scheduler has shuffled some of the overflow passengers to take advantage of unused station capacity.

Figure 5.8: Passenger Transit Time

Departure Latency: Figure 5.9 shows us the amount of time most passengers spend waiting at their station of departure. Most passengers can board vehicles right away, whereas a small number of passengers must wait for the next time step. This helps shed light on the ``even'' peaks and ``odd'' valleys we saw in the passenger transit time histogram of Figure 5.8.

Figure 5.9: Passenger Departure Time
Figure 5.10: Passenger Stops / Transfers

Number of Stops / Transfers: Finally, Figure 5.10 shows us how many stops passengers had to endure to get to their destinations. Since we only had 7 stations in our linear network that passengers must visit in sequence, we get a very predictable ramp down to 6 stops for passengers that traversed the entire line from one end to the other.

Vehicle Fleet Performance Metrics

Histograms in blue relate to vehicle fleet activity.

Segments Traveled: Figure 5.11 shows the system response of vehicles to the demand impulse. Again, we see a gradual ramp down, as fewer passengers remain in the system as time passes. In our scenarios, the second bin tends to have the most traffic. The first bin likely is lower because the initial location of the vehicles is free, so vehicles can essentially be created anywhere. Therefore, the difference in the first bin and the second bin might be attributed to the advantage vehicles receive from the ability to magically appear exactly where they are needed for these scenarios.

A more difficult feature to explain is the valley right after the first peak of activity (and to some extent the less pronounced valleys following subsequent peaks). The system appears to operate in fits and starts, and it actually appears to rest between surges of activity. This is observed in all of the linear sequential routing scenarios. The optimization function attempts to deliver passengers as early as possible, so we would expect the system to push deliveries to the left and not waste time ``resting''. Perhaps the system is maxing out its capacity in a highly coordinated fashion during a delivery peak, and then uses the ebb of the rest period to do some ``housekeeping'', moving a small number of vehicles out of the way for the next coordinated surge. In this fashion, the system could deliver large numbers of people faster in two pulses with a gap between them as opposed to spreading the deliveries out evenly, especially if these coordinated pulses were necessary to allow passengers to make transfers.

Figure 5.11: Vehicles In Transit
Figure 5.12: Vehicle Fleet Utilization

Utilization per Time Step: Finally, we look at how full the vehicles were as they traveled their routes in Figure 5.12. Since minimizing vehicle travel is the lowest priority goal, the vast majority of vehicles operate nearly empty. In this scenario, the empty vehicles are likely moving out of their way of the ones with passengers. Also, some empty vehicles may move to restore the fleet's initial state at the end of the scenario, which offsets some of the advantage gained by their ``magical'' initial positioning discussed in Section 5.4.3.

Gains in vehicle utilization and thus efficiency could be achieved by cutting back on the number of vehicles in the fleet and performing a new optimization. This would allow us to still emphasize passenger performance over vehicle efficiency. Otherwise, the scheduler would likely present passengers with unreasonable wait times and transfers in order to fill its vehicles up to capacity.