QUANTIFYING THE CRITICALITY OF HIGHWAY INFRASTRUCTURE FOR ...docs.trb.org/prp/17-02433.pdf · 1...

QUANTIFYING THE CRITICALITY OF HIGHWAY INFRASTRUCTURE FOR 1

FREIGHT TRANSPORTATION 2 3

Zahra Ashrafi 4

MASc Candidate, Department of Civil and Environmental Engineering 5

University of Waterloo 6

200 University Avenue West, Waterloo, ON, Canada N2L 3G1 7

E-mail: [email protected] 8

9

Hamed Shahrokhi Shahraki 10

PhD Student, Department of Civil and Environmental Engineering 11




15

Chris Bachmann*, PhD 16

Assistant Professor, Department of Civil and Environmental Engineering 17




Phone: 519-888-4567 x31303 21

22

Kevin Gingerich 23

Research Associate, Cross-Border Institute (CBI) 24

PhD Candidate, Department of Civil and Environmental Engineering 25

University of Windsor 26

401 Sunset Ave., Windsor, ON N9B 3P4 27

Email: [email protected] 28

Phone: 519-253-3000 x3737 29

30

Hanna Maoh, PhD 31

Associate Director, Cross-Border Institute (CBI) 32

Associate Professor, Department of Civil and Environmental Engineering 33

University of Windsor 34

401 Sunset Avenue, Windsor, ON, Canada, N9B 3P4 35

Email: [email protected] 36

Phone: 519-253-3000 x4987 37

38

*corresponding author 39

40

Word count: 246 words abstract + 5522 words text + 463 words references + 5 tables/figures x 41

250 words (each) = 7481 words 42

43

Submission Date: November 15, 2016. 44

Transportation Research Board (TRB) 96th Annual Meeting. January 8-12, 2017. Washington, 45

D.C.46

mailto:[email protected]





Ashrafi, Shahrokhi Shahraki, Bachmann, Gingerich, Maoh 2

ABSTRACT 1 Events that disable parts of the highway transportation network, ranging from weather conditions 2

to construction closures, may affect freight travel times and ultimately degrade economic 3

productivity. While previous studies of criticality typically focus on the impacts of natural disasters 4

or terrorist attacks on system-wide travel times, they have not quantified the costs associated with 5

disruptions to the economy via the freight transportation system. This paper quantifies the 6

economic criticality of highway infrastructure in Ontario, Canada, using a new measure of 7

criticality that determines the cost of highway closures in dollar values ($) based on the value of 8

goods, the time delayed, and the associated value of time. Measured this way, criticality has some 9

correlation with truck volumes, but differs by considering the values of shipments and the physical 10

redundancy in the network, resulting in new insights to critical freight infrastructure. For example, 11

due to the high redundancy of the highway network within the Greater Toronto Area (GTA), 12

highways become more critical further away from this metropolitan area. Moreover, sections of 13

Highway 401 located west of the GTA are found to be more critical than those located east of the 14

GTA because of lower redundancy in the western portion of the network, despite carrying lower 15

truck volumes. This measure has many potential applications in freight transportation planning, 16

operations, and maintenance. Finally, with the cost of these disruptions quantified in dollars, one 17

can then calculate the monetary benefits of potential transportation improvements for comparison 18

(i.e., cost-benefit analysis). 19


INTRODUCTION 1 Efficient and reliable freight transportation is critical to a country’s economic prosperity and 2

competitive advantage. Producers rely on transportation systems to move raw materials into 3

processing facilities, intermediate goods to factories, and finished goods from factories to 4

distribution centers, stores, and export markets. In terms of both tonnage and value, trucking is a 5

common mode of transportation in North America. For example, trucks transported 68% of the 6

Province of Ontario’s export value and 84% of the province’s import value in 2006 (1). In an 7

advanced economy where many goods are expensive and needed in tightly scheduled 8

manufacturing and distribution systems, shippers and carriers require a reliable transportation 9

system. Late arrivals can have significant costs for factories waiting for parts to assemble, and for 10

carriers who miss guaranteed delivery times. Hence, events that disable parts of the highway 11

transportation network, ranging from weather conditions to construction closures, may affect 12

freight travel times and ultimately degrade economic productivity. Parts of the network that have 13

particularly severe economic impacts may be considered critical. 14

Various terminology and indicators have been proposed in the literature to assess the 15

impacts of critical links on overall transportation network performance. Jenelius et al. (2) suggest 16

using the term vulnerability, which can be divided into two parts, one containing the probability 17

of a hazardous event, and the other containing the consequences, which they call exposure. Hence, 18

𝑉𝑢𝑙𝑒𝑟𝑛𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 × 𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒. Moreover, they define criticality similarly to 19

vulnerability, where weakness and importance are used instead of probability and exposure, 20

respectively (i.e., 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑖𝑡𝑦 = 𝑊𝑒𝑎𝑘𝑛𝑒𝑠𝑠 × 𝐼𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒.). Jenelius et al. (2) propose two 21

measures for the importance of a link: 1) the system-wide increase in travel time as a result of the 22

link being disrupted or closed; and 2) the amount of unsatisfied demand as a result of any 23

disconnected parts in the network. Taylor and D’Este (3) and Scott et al. (4) also use the system-24

wide increase in travel time as a result of a link being disrupted or closed to measure its importance, 25

the latter (4) defining it as the “Network Robustness Index”. Snelder et al. (5) suggest robustness 26

and vulnerability have a strong relation, but they are each other’s opposites: vulnerability describes 27

the weakness of a network and robustness describes the strength of a network. 28

Sohn (6) proposes an accessibility index and compares two cases: 1) when the increases in 29

travel costs from a link being disrupted or closed are measured in distance only; and 2) when these 30

increases in travel costs measured in distance are weighed by traffic volumes, similar to Jenelius 31

et al. (2), Taylor and D’Este (3), and Scott et al. (4). Jenelius (7) focuses on the inequity 32

implications of link closures and suggests to additionally use the coefficient of variation (CV) to 33

measure how unevenly the increased travel time will be distributed among travelers. More 34

recently, others have begun using the term resiliency to describe essentially the same concepts as 35

vulnerability and criticality (8, 9). A common theme in the analysis and evaluation of network-36

based critical infrastructure is interdiction - where network elements (nodes or arcs) are disabled 37

in a model, disrupting flow through the network (10). Studies of transportation vulnerability, 38

criticality, robustness, resiliency, and so on, typically focus on the impacts of natural disasters or 39

terrorist attacks on system-wide total travel times (11, 12, 6, 13, 2, 10, 8, 3). 40

Previous measures of criticality do not capture the costs associated with disruptions to the 41

economy via the freight transportation system. For example, shippers and carriers may assign a 42

value to increases in travel time, ranging from $25 to almost $200 per hour, depending on the 43

commodity carried (14). In that sense, a closed link that causes longer delays or delays to higher-44

value goods is more economically critical than a closed link that causes shorter delays or delays to 45

lower-value goods. By measuring the volume-weighted increases in network travel times, previous 46


studies implicitly assume all vehicles in the network have the same value of time. This assumption 1

is questionable for passenger trips, since work-trips may have a higher value of time than 2

discretionary travel such as shopping trips. In the case of truck trips, this assumption is invalid 3

since the freight carried by trucks plays a central role in determining the associated values of time. 4

The objective of this research is to study the economic criticality of Ontario’s highway 5

infrastructure (i.e., those roads where disruptions would have particularly severe economic 6

consequences). This objective is achieved by: 7

Proposing a new measure of criticality for freight transportation systems that determines 8

the cost of highway closures ($) based on the value of goods, the time delayed, and the 9

associated value of time; 10

Demonstrating the applicability of the proposed measure through a theoretical example (in 11

the method section) and by applying the measure to an Ontario highway network model 12

(in the results section). 13

The remainder of this paper is organized as follows. The next section introduces a new measure of 14

criticality, specifically aimed at capturing costly disruptions to the freight transportation system, 15

including a theoretical example of how this measure differs from earlier approaches. The data used 16

to develop an Ontario highway network model are described next, followed by the results of 17

applying the proposed criticality measure to this model. In the section that follows, results are 18

discussed in the context of freight transportation planning in Ontario, and recommendations are 19

made where this measure may be most useful. The final section outlines limitations of the proposed 20

approach before providing a brief agenda for future research. 21

22

METHOD 23 In this paper, criticality is measured by removing or closing a highway segment and measuring the 24

cost of delays ($) associated with all freight shipments in the network. For a single shipment (𝑖), 25

the cost of delay (𝑞𝑖) is: 26

𝑞𝑖 = 𝑑𝑖 × 𝑡𝑖 × 𝛼 (1) 27

where 𝑑𝑖 is the dollar value ($) of shipment 𝑖, 𝑡𝑖 is the time delay (minutes) experienced by 28

shipment 𝑖, and 𝛼 is the value of time as a percentage of the shipment value (% per minute). 29

Equation 1 represents a short-term measure of economic criticality, since it captures the immediate 30

costs of shipment delays, all else being equal. In the long-run, all else is not equal, since major 31

changes to the highway network will influence long-run decisions such as firm location choices. 32

In this light, Equation 1 can be used to determine the “short-term economic criticality”, or “trade 33

criticality”, of transportation networks. For the remainder of the paper, this measure is referred to 34

as trade criticality. The values of shipments (𝑑𝑖) depend on the commodities shipped, while the 35

values of delays (𝑡𝑖) depend on the properties of the transportation network. The value of time (𝛼) 36

is a parameter that must be estimated exogenously or taken from the literature. For example, 37

Hummels and Schaur (15) estimate that each day in transit is worth 0.6 to 2.1 percent of the value 38

of the shipment. Note that the absolute value of this parameter is not important when making 39

comparisons of trade criticality between highway segments in the network since it scales all 40

shipment values by the same percentage (Equation 1). 41

Figure 1 shows a hypothetical network model to illustrate the unique property of the 42

proposed measure. The network shows truck volumes (𝑉), capacities (𝐶), and dollar value of 43

shipments (𝐷) on Link 1 and 2 (𝐷 = ∑ 𝑑𝑖𝑖 ). Volumes (𝑉) represent the observed flow of trucks 44

(veh/hour), capacity (𝐶) represents the maximum allowable flow of vehicles (veh/hour), and the 45

dollar value of shipments (D) represents the actual flow of dollars ($/hour) carried by the trucks. 46


Without loss of generality, assume the volume-delay curves (or link-performance functions) of 1

Links 1 and 2 are the same, and that there is a relatively long travel time on Link 3, such that the 2

network as illustrated is in User Equilibrium (UE). Now consider the criticality of Links 1 and 2 3

by four measures: 1) volume; 2) volume/capacity (i.e., roadway demand/supply); 3) increase in 4

total travel time when the link is closed; and 4) increase in the cost of shipment delays when the 5

link is closed. By inspection, both truck volume and the volume/capacity ratio suggest Link 2 is 6

more critical than Link 1. That is, 5 trucks are observed on Link 2 compared to only 3 trucks on 7

Link 1, and since their capacities are the same (10 veh/hour), Link 2 has a V/C ratio of 0.5 8

compared to a V/C ratio of only 0.3 on Link 1. Similarly, the increase in total travel time is highest 9

when Link 2 is closed, since 5 trucks must additionally traverse Link 3, instead of only 3 trucks 10

additionally traversing Link 3 when Link 1 is closed (recall that links 1 and 2 have the same 11

volume-delay curves, so that the travel time on Link 1 when Link 2 is closed, is equal to the travel 12

time on Link 2 when Link 1 is closed). However, the 3 trucks on Link 1 are carrying higher-value 13

goods (averaging $30/truck), whereas the trucks on Link 2 are carrying lower-value goods 14

(averaging $8/truck). Hence, the increase in the cost of shipment delays is highest when Link 1 is 15

closed, since $90 of shipments must additionally traverse Link 3, instead of only $50 of shipments 16

additionally traversing Link 3 when Link 1 is closed. In this example, the first three measures 17

suggest Link 2 is most critical, but the fourth measure identifies Link 1 as most critical by explicitly 18

taking into account the value of shipments. In any network, these four measures might produce the 19

same or different results, which are functions of the network properties, truck volumes, and 20

shipment values. While all four measures capture an aspect of criticality, only the fourth measure 21

(trade criticality) captures the short-term economic costs associated with disruptions to the freight 22

transportation system. 23

24

25 26

FIGURE 1 Example illustrating trade criticality. 27 28

Similar to previous approaches (e.g., Scott et al. (4)), the trade criticality of each highway segment 29

in a network model can be determined using multiple traffic assignments equal to the number of 30

links in the network. Let 𝑣𝑎, 𝑡𝑎 and 𝑑𝑎 represent the traffic flow (vehicles/hour), travel time 31

(minutes), and dollar value of goods ($/hour) on link 𝑎 of the network model, respectively. Each 32

link will have a link performance function such that 𝑡𝑎 = 𝑓(𝑣𝑎); that is, travel time is a function 33

Node

1

Node

3

Node

2

V= 3, C=10, V/C=0.3, D=90

V= 5, C=10, V/C=0.5, D=40

Link 1

Link 2

Link 3


of traffic flow. Each link’s traffic flow (𝑣𝑎) will have an associated value of goods (𝑑𝑎) based on 1

its composition of shipments. For a one hour traffic assignment, the system-wide travel times 2

multiplied by the value of shipments ($·minutes) in the network when all links are present (i.e., 3

the base case) is calculated from a UE assignment as: 4

𝑐0 = ∑ 𝑡𝑎𝑑𝑎𝑎 (2) 5

Second, system-wide travel times multiplied by value of shipments ($·minutes) for each scenario 6

is calculated from a UE assignment on a modified network model with link k removed as: 7

𝑐𝑘 = ∑ 𝑡𝑎𝑑𝑎𝛿𝑎𝑎 , (3) 8

where 9

𝛿𝑎 = {1, 𝑖𝑓 𝑙𝑖𝑛𝑘 𝑎 𝑖𝑠 𝑛𝑜𝑡 𝑡ℎ𝑒 𝑙𝑖𝑛𝑘 𝑟𝑒𝑚𝑜𝑣𝑒𝑑 (𝑘 ≠ 𝑎),0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (𝑘 = 𝑎).

(4) 10

Finally, the trade criticality of link 𝑘, defined as the increase in the cost of delays to all shipments 11

in the network as a consequence of removing link 𝑘, is calculated as: 12

𝑞𝑘 = 𝛼(𝑐𝑘 − 𝑐0) (5) 13

where 𝑞𝑘 is trade criticality of link k measured in dollars ($), and 𝛼 is the value of time as a 14

percentage of shipment values (% per minute). 15

16

DATA 17 This paper studies the trade criticality of Ontario’s highway infrastructure using a newly developed 18

inter-regional travel demand model. The network model was developed in the INRO Emme 4.2 19

software suite. The network includes 74 zones, representing Ontario’s 49 Census Divisions (CDs) 20

and 25 external zones representing border crossings. The external zones include: 10 border 21

crossings with Quebec, 1 with Manitoba, 3 with Minnesota, 5 with Michigan, and 6 with New 22

York. Roads are classified based on their speeds: 40-70 km/h, 70–80 km/h, 80–90 km/h, and 90- 23

100 km/h. In total, the network is comprised of 35,254 links and 14,444 nodes. For any given 24

network link, the link performance function, which is a mathematical representation of the relation 25

between traffic volume and travel time, follows the formula suggested by the Bureau of Public 26

Roads (BPR): 27

𝑡 = 𝑡𝑓 [1 + 𝛼 (𝑉

𝐶)

𝛽

] (6) 28

29

where 𝑡 is congested link travel time, 𝑡𝑓 is link free-flow travel time, 𝑉 is link volume, 𝐶 is link 30

design capacity, and 𝛼 and 𝛽 are calibration parameters. 31

Regional origin-destination (OD) daily truck flows were taken directly from the 2012 32

Ministry of Transportation of Ontario (MTO) Commercial Vehicle Survey (CVS). Each record in 33

the MTO CVS was multiplied by the National Weight for Expansion (NW) determined by the 34

MTO as “The value for national expansion weight, taking into account trips passing each Data 35

Collection Site (DCS) and not site-specific but suitable for global analysis of the data” (16). Since 36

this factor is used to estimate equivalent total weekly truck trips in Ontario, it was divided by 7 to 37


determine equivalent daily trips. For internal zones, the estimation of hourly truck trips was based 1

on traffic count data from the MTO. Hourly truck factors per CD were derived from hourly truck 2

traffic count information collected at a number of stations distributed throughout the Province. 3

Each CD was assigned one or more traffic count stations based on their locations. If a CD did not 4

have a station located in it, the closest station was assigned to it. Using the collected data, an hourly 5

distribution per CD was generated based on averaging the hourly truck trips of all the stations 6

located with the CD. The hourly factor for each hour of the day was then applied to the daily truck 7

OD matrix to create hourly matrices for the CDs. External zones rely on the hourly factor for the 8

CD in which they are located. For example, the border crossing to Quebec via Highway 401 9

corresponds to the Stormont, Dundas, and Glengarry, CD. Finally, the value of goods carried by 10

each truck was determined from the cargo value in the MTO CVS record. 11

While not the focus of this study, it is important to include passenger demands in the model 12

to create realistic congestion effects. Trip generation and trip distribution models were estimated 13

using passenger trip data for the Greater Toronto Area (GTA), from the last available year (2011) 14

of the Transportation Tomorrow Survey (TTS) (17). The TTS data include 14 CDs for model 15

estimation, after which total trips and corresponding OD flows for all 49 CDs were modelled. The 16

assumed variables for the trip generation models included: population, number of workers, and 17

number of jobs per CD, all obtained from the 2011 Canadian Census and the 2011 National 18

Household Survey. Trip generation results show both trip production and attraction correlate to 19

population and the number of workers and/or jobs, respectively. For trip distribution, a gravity 20

model based on inter-census distance was used to distribute the trips between origins and 21

destinations. The Iterative Proportion Fitting (IPF) method was used to balance the resulting matrix 22

of estimated trips from the gravity model to match the totals from the trip generation models. 23

Comparing the observed (2011 TTS) inter-OD trips with the predicted (modelled) inter-OD trips 24

for the available 14 CDs results in a correlation coefficient of 0.95 for all 168 (14 × 14) 25

observations. According to the 2011 Canadian Census, the average percentage of auto work trips 26

was 87.5%. Removing the outlier cases (i.e., Toronto and Ottawa with 52.9% and 66.7% auto 27

shares, respectively) resulted in an average percentage of 88.6% (i.e. 0.89) in automobile work 28

trips. This mode share was used to scale the estimated trips for the 49 census divisions. Hourly 29

factors were derived from hourly traffic count data from the MTO, as described for freight 30

demands above. 31

To validate the model, a comparison between the simulated and observed traffic counts 32

and travel times from external data was conducted. The quality of the model fit was assessed by 33

correlation coefficients, which range between −1 and 1. The correlation coefficient for 74 travel 34

time observations from combined truck and car traffic throughout all highways in the network are 35

0.82 and 0.64 for the AM and PM peak hours, respectively. The only notable exception is Highway 36

401 West Bound (WB), which brings these correlation coefficients down by having a negative 37

correlation coefficient for its 9 observations. The correlation coefficient for 49 truck count 38

observations throughout all highways in the network are 0.76 and 0.73 for the AM and PM peak 39

hours, respectively. Excluding Highway 401, the correlation coefficient for the 37 truck count 40

observations throughout the remainder of the network are 0.78 and 0.87 for the AM and PM peak 41

hours, respectively, again indicating a lower model fit for Highway 401. Finally, the correlation 42

coefficient for 49 car count observations throughout all highways in the network are 0.48 and 0.52 43

for the AM and PM peak hours, respectively. Due to the large zonal aggregation scheme, intra-CD 44

flows are absent from model, which is likely responsible for a large part of the difference in 45

observed and predicted car counts, especially on Highway 401. In sum, the model represents travel 46


times and truck flows well, but passenger flows would benefit from further calibration. For the 1

purposes of this study, the model is a good representation of Ontario’s highway freight flows, and 2

can be used for a preliminary assessment of trade criticality, especially in relative terms. Ongoing 3

and future work to improve this model is noted in the discussion section. 4

Finally, the value of time as a percentage of the shipment value (i.e., % per hour) in 5

Equation 5 was taken from Hummels and Schaur (15), who estimate that each day in transit is 6

worth as much as 2.1 percent of the value of the shipment. For validation, this value of time (2.1% 7

per day) was applied to the truck cargo values in the MTO CVS, resulting in an average value of 8

time of $75/hour, which falls within the range of $25 to almost $200 per hour estimated previously 9

by the Federal Highway Administration (FHWA) (14). 10

11

RESULTS 12 Figure 2 shows the trade criticality of Ontario’s highways during the AM peak hour. Thicker and 13

thinner bars illustrate the most critical and least critical highways in Figure 2, respectively. During 14

the AM peak hour, sections of Highway 401 (officially named Mac Donald-Cartier Freeway) and 15

Highway 400 have the most critical highway segments. The sections of Highway 401 which are 16

most critical are located west of the GTA. These include: Mill St. to Norwich Ave. (with trade 17

criticality of $1978); between Oxford Road 3 and Cedar Creek Rd. ($1850); from Oxford 2 to 18

Drumbo Rd. ($1662); from Foldens Line to Mill St. ($1623); between Cedar Creek Rd. and Oxford 19

Road 3 ($1605); and from Drumbo Rd. to Oxford 2 ($1568). There is also unsatisfied demand (i.e., 20

disconnected OD pairs) when two segments of Highway 401 are removed (from East Puce Rd. to 21

Manning Rd. and vice-versa) in Lakeshore Ontario. The section of Highway 400 which is most 22

critical is from Rankin Lake Rd. to J. R. Drive ($2546) in the town of Parry Sound. 23

There are 14 critical border crossings comprising highways and bridges to external zones, 24

which result in unsatisfied demand as a result of their closure. Six of these critical border crossings 25

are to Quebec: two of them are Autoroute 20 (Autoroute du Souvenir) in both directions, two of 26

them are Autoroute 40 (Autoroute Felix-Lecierc) in both directions, and the last two are 27

MacDonald Cartier Bridge in both directions. The other eight critical border crossings are with the 28

United States (US), including through Blue Water Bridge (Highway 402) in Sarnia, the Queenston-29

Lewiston Bridge in Niagara Falls, the Thousand Island International Bridge near Kingston, and 30

the Peace Bridge in Fort Erie, which are all critical in both directions.31


1 FIGURE 2 Trade criticality of Ontario’s highway infrastructure during the AM peak. IDs of most critical segments are listed 2

in Table 1.3


Figure 3 shows the trade criticality of Ontario’s highway infrastructure during PM peak hour. As 1

in Figure 2, thicker and thinner bars illustrate the most critical and least critical highways, 2

respectively. Notably, some of the most critical highway segments including those resulting in 3

unsatisfied demand during the AM peak and PM peak are the same. The results suggest that a 4

number of segments on Highway 401 located west of the GTA are highly critical. These include: 5

Oxford Rd. 3 to Cedar Creek Rd. (with trade criticality of $2172), from Oxford 2 to Drumbo Rd. 6

($2008), from Northumberland St. to Cedar Creek Rd. ($1917), from Mill St. to Norwich Ave. 7

($1907), from Highbury Ave. South to Veterans Memorial Pkwy ($1826), from Foldens Line to 8

Mill St. ($1821), and from Westchester Bourne to Dorchester Rd. ($1806). There are also 9

unsatisfied demands when three segments of Highway 401 are removed: from Concession Rd. 11 10

to Provincial Rd., from Manning Rd. to Concession Rd. 11, and from East Puce Rd. to Manning 11

Rd., all in Lakeshore Ontario. 12

There are 16 critical border crossings resulting in unsatisfied demand during the PM peak, 13

8 of which are to Quebec: Autoroute 20 (Autoroute du Souvenir), Trans-Canada Highway, 14

Autoroute 40 (Autoroute Felix-Lecierc) and MacDonald Cartier Bridge, all in both directions. The 15

other eight critical border crossings are with the USA, including through Blue Water Bridge 16

(Highway 402) in Sarnia, the Queenston-Lewiston Bridge in Niagara Falls, the Thousand Island 17

International Bridge near Kingston, and Peace Bridge in Fort Erie, all of which are critical in both 18

directions.19


1 FIGURE 3 Trade criticality of Ontario’s highway infrastructure during the PM peak. IDs of most critical segments are listed 2

in Table 1. 3


Figure 4 shows the frequencies and cumulative percentages of trade criticality values for the AM 1

and PM peak hours. In this application, frequency represents the number of links in the network 2

that have a trade criticality within a specified range. For example, 971 links have a trade criticality 3

between $1 and $99 in the PM peak (tallest bar on Figure 4). Recall that the trade criticality of a 4

link represents the increase in the cost of delays to all shipments in the network as a consequence 5

of closing the link. Trade criticalities generally range from $0-$2999. As illustrated in Figure 4, 6

the histogram of trade criticalities for the Ontario highway network resembles a Gamma 7

distribution for both AM and PM peak hours. The maximum frequencies of trade criticality for the 8

two periods are between $1 and $99 with frequencies of 634 and 971, respectively. Combining 9

these least critical segments with segments having a trade criticality of zero, results in 44% and 10

54% of the highway network in the AM and PM peak hours, respectively, having a trade criticality 11

of less than $100 (i.e., no or low criticality). As trade criticality increases, the frequency of 12

occurrence decreases. For example, segments within the range of $900 to $999 have frequencies 13

of 50 and 42 for the AM peak and PM peak hour, respectively. 14

There are also cases where trade criticality is negative or where the highway closure results 15

in unsatisfied demand. Thirty-one links, representing 1.02% of total highway links in the network, 16

result in unsatisfied demand for both the AM and PM peaks. 266 and 281 links result in a negative 17

trade criticality value for the AM and PM peak hours respectively (representing 8.76% and 9.26% 18

of total highway links). These links indicate the network is better off as a result of their removal. 19

In a real-world terms, this means that the removal of the link did not result in shipment delay costs, 20

but rather shipment time improvements resulting in cost savings. Braess’s Paradox states that 21

adding a new road to a congested traffic network can increase the network-wide total travel time, 22

and hence the removal of an existing road can decrease the network-wide total travel time. 23

Similarly, it is seen in these cases that trade criticality is negative by removing these links. These 24

cases represent either Braess’s Paradox (network-wide total travel times decrease), or cases where 25

high-value trucks benefit at the expense of low-value trucks (since travel times are additionally 26

weighted by the value of goods in Equation 2 and 3). 27

28

29 FIGURE 4 Frequency-distribution plot of trade criticality in the Ontario highway network. 30

0.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%

0

200

400

600

800

1000

1200

Fre

qu

en

cy

Trade Criticality ($)

Frequency (AM) Frequency (PM) Cumulative % (AM) Cumulative % (PM)


1

Table 1 shows the comparison of top ranked highway segments by trade criticality and 2

corresponding rank in truck volume and vice-versa, for the AM and PM peak hours. Many of the 3

most critical highway segments by trade criticality are on Highway 401 in locations west of the 4

GTA near Woodstock, Ayr, Brant, and Beachville. On the other hand, many of the most critical 5

highway segments by truck volume are on Highway 401 in locations east of the GTA near Ajax, 6

Whitby, Putnam, and Oshawa. Overall, the correlation coefficients of the most critical highway 7

segments by trade criticality ranking and corresponding ranking for truck volume for the AM and 8

PM peak hours are 0.55 and 0.59, respectively. The value of the correlation coefficient for the AM 9

and PM peak hours shows the ranking based on trade criticality has correlation with corresponding 10

ranking by truck volume, but the measures are not perfectly correlated as trade criticality 11

additionally considers the truck’s value of goods and the surrounding highway network 12

characteristics. 13


TABLE 1 Comparison of Top Ranked Highway Segments by Truck Volume and by Trade Criticality 1 2

AM PM

Top Ten Most Critical Highway Segments by Trade Criticality Top Ten Most Critical Highway Segments by Trade Criticality

Id: Highway Segment Name Trade

Criticalit

y ($)

Trade

Criticality

Rank

Truck

Volume

Rank

Id: Highway Segment Name Trade

Criticalit

y ($)

Trade

Criticalit

y Rank

Truck

Volume

Rank

1: 401 from E Puce Rd to Manning Rd 10533 1 281 1: 401 from E Puce Rd to Manning Rd 13125 1 339

2: 401 from E Puce Rd to Manning Rd 10304 2 282 2: 401 from E Puce Rd to Manning Rd 12891 2 338

3: 400 from Rankin Lake Rd to J. R. Dr 2546 3 2294 3: 401 from Oxford Rd 3 to Cedar Creek Rd 2172 3 93

4: 401 from Mill St to Norwich Ave 1978 4 152 4: 401 from Oxford 2 to Drumbo Rd 2008 4 94

5: 401 from Mill St to Norwich Ave 1978 5 154 5: 401 from Northumberland St to Cedar

Creek Rd

1917 5 96

6: 401 from Oxford Rd 3 to Cedar Creek Rd 1850 6 294 6: 401 from Mill St to Norwich Ave 1907 6 23

7: 401 from Oxford 2 to Drumbo Rd 1662 7 296 7: 401 from Mill St to Norwich Ave 1907 7 25

8: 401 from Foldens Line to Mill St 1623 8 86 8: 401 from Highbury Ave S to Veterans

Memorial Pkwy

1826 8 27

9: 401 from Cedar Creek Rd to Oxford Rd 3 1605 9 163 9: 401 from Foldens Line to Mill St 1821 9 6

10: 401 from Drumbo Rd to Oxford 2 1568 10 165 10: 401 from Westchester Bourne to

Derchester Rd

1806 10 17

Top Ten Most Critical Highway Segments by Truck Volume Top Ten Most Critical Highway Segments by Truck Volume

Highway segment Truck

Volume

(veh/hr)

Truck

Volume

Rank

Trade

Criticalit

y Rank

Highway segment Truck

Volume

(veh/hr)

Truck

Volume

Rank

Trade

Criticalit

y Rank

401 from Brock Rd to Westney Rd S 354 1 120 401 from Elgin Rd to Putnam Rd 318 1 35

401 from Brock St S to Thickson Rd 352 2 133 401 from Culloden Line to Harris St 317 2 62

401 from Brock St S to Thickson Rd 352 3 236 401 from Putnam Rd to Culloden Line 317 3 88

401 from Westney Rd to Brock St S 352 4 179 401 from Putnam Rd to Culloden Line 317 4 64

401 from Church St to Harwood Ave S 352 5 209 401 from Elgin Rd to Putnam Rd 317 5 180

401 from Towerline Rd to Norwich Ave 349 6 115 401 from Foldens Line to Sweaburg Rd 317 6 9

401 from Thickson Rd to Stevenson Rd S 347 7 374 401 from Plank Line to Foldens Line 317 7 28

401 from Brock St South to Stevenson Rd S 347 8 312 401 from Plank Line to Foldens Line 317 8 17

401 from Putnam Rd to Elgin Rd 345 9 328 401 from Plank Line to Foldens Line 317 9 130

401 from Putnam Rd to Elgin Rd 345 10 422 401 from Plank Line to Foldens Line 317 10 53

3


DISCUSSION 1 Results in the preceding section point to a number of key findings. First, trade criticality has some 2

correlation with truck volume, but differs by considering the values of shipments and the physical 3

redundancy in the network (Table 1). For this reason, areas with high truck volumes are not 4

necessarily critical. For example, due to the high redundancy of the highway network within the 5

GTA, highways become more critical further away (Figures 2 and 3). Moreover, sections of 6

Highway 401 located west of the GTA are more critical than those located east of the GTA because 7

of the lower redundancy in the western portion of the network, despite carrying lower truck 8

volumes. Second, trade criticalities are widely distributed and resemble a gamma distribution, with 9

approximately half of the Ontario highway network being non-critical (trade criticality of zero) or 10

having very low criticality (less than $100). As the magnitude of trade criticality increases, the 11

frequency of occurrence decreases (Figure 4). Therefore, efforts aimed at improving the resiliency 12

of the Ontario highway network can focus on the Most Critical Links (MCLs), of which there are 13

few: 2.67% with a trade criticality greater than $1000 and 1.02% that result in unsatisfied demand 14

(Figure 4). Note that segments resulting in unsatisfied demand are the result of boundary effects 15

of the model (where external zones are connected by only one highway segment), but nonetheless 16

represent critical borders for Ontario’s imports and exports that lack nearby redundancy. Finally, 17

trade criticality varies by time of day (compare Figures 2 and 3, or review Table 1), and therefore 18

the timing of closures plays a large role in the associated costs. Hence, for real-world closures that 19

may last multiple hours or days, a more comprehensive trade criticality measure should be 20

computed by summing the results of specific hourly traffic assignments, rather than generalizing 21

the results of a one hour assignment to other time periods. 22

Measuring the trade criticality of transportation networks and identifying the MCLs has 23

many practical implications. First and foremost, this measure is tailored for freight transportation 24

planning. For example, physical redundancy can be planned for the MCLs to reduce overall 25

economic vulnerability. Design efforts can be focused towards reducing the likelihood and 26

consequence of disruptions or closures on these links. And as Hummels (15) notes, with value of 27

time saved, one can then calculate the monetary benefits of these initiatives (transportation 28

improvements in this context) and how they compare to the costs incurred (i.e., cost-benefit 29

analysis). Second, this measure can be used for highway maintenance and operations. Maintenance 30

and reconstruction efforts can be coordinated to avoid scenarios involving combinations of links 31

that have high criticality. Prioritisation for road maintenance and repair should also consider 32

economic criticality, including winter road maintenance programs. MCLs could also be considered 33

for greater surveillance through more highway patrols by policing organizations. These examples 34

demonstrate the many practical applications of determining the trade criticality of highway 35

infrastructure. 36

One of the limitations of the results determined in this paper is that commodity types are 37

not considered, only commodity values. In other words, it is assumed that each day in transit is 38

worth 2.1 percent of the value of the good, as determined by econometric estimates in Hummels 39

et al. (15). However, the study from where the value of time (𝛼) is taken also finds substantially 40

higher time values for automotive goods (4.3 percent) and for foods and beverages (3.1 percent). 41

These results are sensible in the contexts of just-in-time manufacturing and spoilage, respectively. 42

However, due to the reduced number of observations used to estimate these coefficients, it is 43

unclear whether coefficient heterogeneity reflects true variation or noise. As such, further 44

investigation into the heterogeneity of the value of time by commodity would be useful. Another 45

limitation is that these results exclude the additional operating costs incurred by carriers due to 46


rerouting (e.g., fuel costs). However, these costs can easily be added to trade criticality if desired 1

by taking into account the increase in route distances and travel times and the corresponding costs 2

per units of travel. Remaining limitations of the results stem from the newly-developed Ontario 3

highway network model. Correlation coefficients (discussed in the data section) indicate the model 4

is a good representation of truck trips throughout Ontario, with fairly accurate travel times. But 5

congestion effects (incorporated into trade criticality through delays) could be improved further 6

by refining passenger demand estimates, especially those using Highway 401. Research is 7

currently underway to improve passenger demand estimates by: including intra-CD trips in the 8

traffic assignment, including external-external passenger trips; and ensuring long-distance 9

passenger trips are gravitating towards highways (i.e., not “rat-running” throughout the network). 10

11

CONCLUSION 12 Events that disable parts of the highway transportation network may affect travel times and 13

ultimately threaten economic productivity. While previous studies of criticality typically focus on 14

the impacts of natural disasters or terrorist attacks on system-wide travel times, they have not 15

quantified the costs associated with disruptions to the economy via the freight transportation 16

system. This paper quantified the economic criticality of Ontario’s highway infrastructure using a 17

new measure of criticality that determines the cost of highway closures in dollar values ($) based 18

on the value of goods, the time delayed, and the associated value of time. We contend that this 19

measure reflects a short-term economic criticality or trade criticality, since it captures the 20

immediate costs of shipment delays, all else being equal. This measure differs theoretically from 21

previous criticality measures (revisit Figure 1) and provides new insights to critical freight 22

infrastructure, as demonstrated by examining provincial highways in Ontario. This measure has 23

many potential applications in freight transportation planning, operations and maintenance. 24

This paper leaves ample room for future work in transportation research including three 25

directions which are largely unexplored to date. First, only networks with a single mode 26

(automobile/truck) have been considered thus far. Extending trade criticality to look at other 27

modes, such as rail, and key trade infrastructure, such as ports and intermodal facilities, would be 28

useful to gain a more comprehensive understanding of trade criticality. Second, the interdiction of 29

links in isolation have been studied. However, real-world transportation networks may have 30

multiple links disrupted or closed at the same time due to various circumstances (e.g., incidents, 31

construction operations, extreme weather events, etc.). Moreover, the combined impact of 32

interdicting two links is not simply the sum of their impacts when interdicted individually 33

(reconsider Figure 1). A complete theoretical analysis of transportation network criticality might 34

consider interdicting all elements in the power set of links: that is, the set of all subsets of links in 35

the network. Third, short term impacts of link interdictions (e.g., increases in travel costs) have 36

been studied, but the long-term economic criticality of infrastructure differs because of longer-37

term decisions (such as firm and household location choices). Extending trade criticality, which 38

we suggest represents a short-term economic criticality, to a longer-term measure, which includes 39

land use and economic impacts (e.g., through a Computable General Equilibrium (CGE) model), 40

would be useful in understanding another dimension of economic criticality. These and other 41

directions would only expand the vast array of criticality applications discussed previously. 42

Finally, engaging various stakeholders such as shippers, carriers, and government agencies, 43

in a discussion about criticality and prioritization is an area of future work that would benefit 44

practical applications. For example, while prioritizing highway infrastructure by truck volumes 45

may seem impartial, it may not be immediately clear why road segments with trucks carrying 46


higher-value shipments (or more time sensitive commodities) are deemed more critical to the 1

economy than road segments with trucks carrying lower-value shipments (or less time sensitive 2

commodities). Public participation and stakeholder engagement are key ingredients to effective 3

transportation planning. 4


ACKNOWLEDGEMENTS 1 Portions of this paper are based upon work funded by the Ministry of Transportation of Ontario 2

(MTO) under the Highway Innovation Infrastructure Funding Program (HIIFP), for the project 3

titled “Economic Criticality of Ontario’s Highway Infrastructure”. The authors are grateful to 4

Chris Pascos, Rob Tardif, and Arthur Tai, from the MTO for facilitating this research project. 5

6

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http://dmg.utoronto.ca/transportation-tomorrow-survey/tts-introduction

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