There will always be uncertainties associated with risk and delay cost elements that are difficult to accurately determine. Analyses in previous sections are based on a simplification of risk and delay cost estimation. That is, only the costs of an evacuation and a single train delayed were incorporated. In addition, artificial speed restrictions on route segments were assumed. As mentioned earlier, the objective is not to provide the best estimates but to test and illustrate various possible applications of the train speed management model developed in this chapter. In this section, I discuss some opportunities for improving the cost estimates that may be necessary for a more accurate analysis of the cost-effectiveness of train-speed reduction as a means of reducing risk. λ = 0.9 λ = 0.1 900 925 950 975 1,000 0 50 100 150 200 800 850 900 950 1,000 T ot al C os t ( $) D el ay C os t ( $) Risk Cost ($) λ = 0.9 λ = 0.1 15 mph reduction 5 mph reduction 10 mph reduction
Risk vs. Delay Cost (5 mph reduction) Risk vs. Delay Cost (10 mph reduction) Risk vs. Delay Cost (15 mph reduction)
Risk vs. Total Cost (5 mph Reduction) Risk vs. Total Cost (10 mph reduction) Risk vs. Total Cost (15 mph reduction) Risk vs. Total Cost (5 mph reduction) Risk vs. Total Cost (10 mph reduction) Risk vs. Total Cost (15 mph reduction)
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6.5.1 Consequence Costs of Hazardous Material Release Incident
Apart from the evacuation cost per person affected in a hazardous material release incident, one may consider incorporating other costs into the mathematical model. Depending on the
information available, these costs may include: remedial cleanup, track property and equipment damage, and material loss. The U.S. Department of Transportation (DOT) Pipeline and
Hazardous Materials Safety Administration (PHMSA) maintains a database of hazardous material incidents. The database is available online at
https://hazmatonline.phmsa.dot.gov/IncidentReportsSearch/ (PHMSA, 2010). One may look up the incident statistics involving the hazardous materials of interest. I analyzed the PHMSA incident database for hazardous material tank car derailments in transit during the years 1998 to 2009. Only incidents involving materials of hazard classes 3 and 4, transported in non-pressure cars, which involved fire were analyzed (Table 6.4).
Table 6.4. Consequence costs from PHMSA incident reports database.
Notes: 1) Incident data from 1998 – 2009, accessed January 2010
2) Incidents involved hazardous materials with DOT hazard classes 3 and 4 transported in non-pressure cars that were derailed in transit resulting in fire
Saat (2009) used the Hazardous Materials Transportation Environmental Consequence Model to estimate the chemical-specific expected cleanup costs of a spill, representing the nationwide average and accounting for different hydrogeological conditions along the rail lines. The expected costs of spills for a group of Light Non-Aqueous-Phase Liquids (LNAPL)
hydrocarbon compounds ranged from approximately $400,000 to $900,000.
Liu et al. (2010) developed track-class-specific consequence cost using FRA-reportable accident data. The average consequence cost, accounting for track and equipment damage due to a derailment on a mainline, is $375,000 per accident. Their estimates would include costs
unrelated to hazardous materials and exclude some hazardous-material-specific costs.
Cost ($) Material Loss Carrier Damage Property Damage Response Cost Remediation Cleanup Cost Total Amount of Damages Min 3,000 4,500 5,000 8,100 1,500 53,000 Max 849,236 2,500,000 2,300,000 350,000 950,000 3,015,000 Average 178,903 624,985 226,750 101,950 299,089 1,433,998
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The costs described here provide insight into the order of magnitude that risk cost should be. In general, the consequence cost may comprise both fixed (average) cost and variable (unit) cost. The average cost may comprise carrier and property damage costs that are independent of accident speed and severity, rolling stock, and infrastructure condition. The unit cost may comprise material loss and cleanup costs, which could be a function of spill size or volume, and emergency response or evacuation costs, which vary with the number of persons affected. The train speed management model developed in this chapter can be modified to accommodate these additional cost elements. For example, the risk cost objective function below incorporates the evacuation cost per person affected and the average consequence cost per release incident.
Where:
Em = average consequence cost per release incident for material m ($)
6.5.2 Multiple Train-delay Costs
Rail Traffic Controller (RTC) may be used to determine train delay for all possible magnitudes of speed change applied to each segment, but this can be quite time consuming. Previous studies using RTC often considered an average or a maximum speed for each train type to compute the delay on the network (Dingler et al., 2009) and, therefore, may not be suitable for analyses regarding speed changes that require more detail at the segment-specific level. The case studies in Section 6.4 consider the delay cost of one single train, i.e. the train carrying the hazardous material that is subject to the speed reduction. In this section, I revisit the estimation of delay cost using the relationship developed by Schafer (2008) to investigate if it is applicable for multiple-train delay in the speed management problems considered.
First, I determined traffic density for the route considered using the data provided by the Bureau of Transportation Statistics (BTS, 2007). For simplicity, I calculated a weighted-average traffic density instead of segment-specific density. The average density on the route considered is 86 million gross tons. I assumed a fixed speed reduction of 10 mph.
m m m m m ik i i ik ij i j ij i I j J k K m M Minimize S V L Z f(W )(P D A Y E ) (6.21) ∈ ∈ ∈ ∈ ′ =
∑∑ ∑ ∑
+170
For each segment, I computed the delay (in hours) after a 10 mph speed reduction was applied using Eq. (6.4). Here, the headway is t = 53.33/MGT = 53.33/86 = 0.62 hours. The maximum delay due to speed decrease on segments Timax is 0.15 hours. For each segment, the
number of subsequent trains delayed is less than one (B = T/t = 0.15/0.62), so the delay cost corresponding to each segment is TiO + (Ti – 0.62 )O. The second term of the summation is
negative because the segments in the route are not long enough for the multiple-train delay cost equation to have an effect. Therefore, I neglected the multiple-train delay cost when computing the total-train delay cost in the case studies in Section 6.4.
Another observation is about a difference in the order of magnitude of the risk and delay costs. Suppose all consequence cost elements in Table 6.4 were incorporated into the risk cost equation. The risk cost could outweigh the delay cost and thereby reduce the optimization problem to the single objective problem of minimizing risk. Although weighting factors or normalization can be applied to risk and delay costs as desired, there remain challenges to develop a more accurate, realistic estimation of both risk and delay costs.