PRIORITY SCHEDULING OF URBAN REHABILITATION STREETS TO MINIMIZE CONGESTION, DELAYS, AND ACCIDENTS

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1 PRIORITY SCHEDULING OF URBAN REHABILITATION STREETS TO MINIMIZE CONGESTION, DELAYS, AND ACCIDENTS ABSTRACT Wesley C. Zech 1, and Satish Mohan 2 This paper describes the framework of a priority scheduling algorithm that minimizes traffic congestion, travel delays, and accidents that occur during the rehabilitation of urban streets. The process utilizes: (i) GIS technology for storing and visualizing the necessary data of streets, and for applying traffic assignment, (ii) previous research on the costs of congestion, travel delays, and accident rates, and (iii) utility theory for combining the values of the qualitative and quantitative attributes associated with road rehabilitation. The priority scheduling framework, developed in the research, has been applied to an example town with a population of 116,000, in which 10 street links were selected for repaving in 3 time phases, each of two months, during one construction season. By comparing the multi-attribute utilities of the three attributes using the proposed priority schedule, against the average multi-attribute utilities of 10 random time-schedules of the 10 streets (standard practice), the proposed construction scheduling algorithm yields a saving of 13 veh-hrs/hr in network travel time, $127/hr in the cost of comfort and convenience, and 11 accidents per year. Further research is required for coding the proposed algorithm into an expert system that practitioners can easily learn to use and draw priority schedules for their road rehabilitation programs. KEY WORDS GIS, Highway Rehabilitation, Multiple Objective Analysis, Utility Theory 1. INTRODUCTION The U.S. urban and suburban street infrastructure has experienced very heavy traffic growth by both passenger cars and heavy trucks over the past 20 years. This situation has necessitated more frequent pavement rehabilitation, and geometric improvements along with regular maintenance activity. This increase in street rehabilitation has resulted in increasing traffic congestion, traffic delays, and accidents. A potential solution, suggested in this paper, lies in priority time scheduling of streets selected for rehabilitation in a construction season, such that the overall traffic congestion, travel delays, and accidents are minimized. Usually, a transportation agency such as a city, selects several streets to be rehabilitated in a construction season, or in a budget year. For example, the Town of 1 Assistant Professor., Department of Civil Engineering., Auburn University, 233 Harbert Engineering Center, Auburn University, AL , Phone: 334/ , Fax: 334/ , zechwes@eng.auburn.edu 2 Associate Professor, Dept. of Civil, Structural, and Environmental Engineering, SUNY at Buffalo, 223 Ketter Hall, Buffalo, NY 14260, Phone: 716/ x 2412, Fax: 716/ , smohan@eng.buffalo.edu

2 Amherst, located in Western New York, during their construction season of six months, selected 10 streets for repaving in The working season was divided into 3 phases, each phase having a duration of 2 months. According to their plan, 3 of the streets were to be completed in the first 2 months - Phase I, another 3 were to be completed in the next 2 months - Phase II, and the remaining 4 were to be repaved in Phase III. Currently, transportation agencies would select any three of the ten streets in Phase I, then any three of the seven streets in Phase II. As will be seen in later sections, the congestion levels, travel times, and accident rates are dependent upon the order in which the streets are selected for rehabilitation. The computations conducted later in this paper show that the network wide costs of comfort and convenience can range from $9,000/hr to $12,000/hr, the total network travel time can range from 5,800 veh-hrs/hr to 6,000 veh-hrs/hr, and accident rates can vary from 1600 accidents/yr to 1800 accidents/yr. This paper has suggested a methodology which will always select streets that result in the minimum levels of congestion, travel delays, and accidents, on a town s network. Since the three attributes are measured in different units, they can not be added to compute a combined effect, using a simple mathematical formulation. However, if all of the three attributes can be translated into one common unit, they can be added together. A decision process, that uses Utility Theory, translates any subjective or numerical attribute into a zero to one number called utility, and has been used in this paper. The priority scheduling algorithm is illustrated in Figure GIS SOFTWARE: TRANSCAD TM APPLICATION 2.1 Geographic File and Network Data TransCAD TM, a GIS software for Transportation (GIS-T), was utilized in this research to import the town s street network and for analyzing traffic assignments on the entire network when a street is disabled. The Town of Amherst roadway system, located in western New York was used as an example. The town s geographic file and all network data were obtained from the Greater Buffalo Niagara Regional Transportation Council (GBNRTC). The example network, when applied in TransCAD TM, consisted of 155 links (streets), 109 nodes (intersections), 49 traffic analysis zones (TAZs), and 49 centroids. The geometric characteristic data for the network consisted of: (i) the roadway length, (ii) number of lanes, (iii) pavement width, (iv) median type, (v) pavement type, (vi) link speed limit, (vii) link capacity, (viii) link volumes, (ix) roadway classification, (x) location, (xi) route description, and (xii) connecting nodes. The attributes required to run the traffic assignment procedure with TransCAD TM are: (i) a representative origin-destination (O-D) matrix for the network, (ii) link free-flow times, and (iii) link capacities. TransCAD TM s O-D matrix estimation tool was utilized in order to develop a realistic network O-D matrix which was created from average daily traffic. 2.2 Street Links for Rehabilitation In order to develop a realistic model for optimizing the construction scheduling of roadway links, real data on the rehabilitation program of the Town of Amherst was acquired. 2

3 FIGURE 1. Priority Scheduling Process, Using GIS-T, and Multi-Attribute Utility Theory. The Amherst Town engineer provided information on their rehabilitation programs and the following assumptions were used in the model application: 1. Ten (10) street links are rehabilitated, every construction season. 2. Duration of construction season = 6 months. 3. Construction season is divided into 3 time segments of 2 months each 4. Three (3) or 4 links will be rehabilitated simultaneously in each time segment, and 3

4 5. Total lane closures on links will occur, i.e. the rehab links will be closed for traffic in both directions. From the 155 links of the Amherst street network, 10 links, having the lowest roadway score in conjunction with the highest traffic volume were selected for rehabilitation. These 10 links are displayed in Table 1. Link ID TABLE 1: Data of 10 Links Scheduled for Rehabilitation in Year 2002 A Node B Node Route Name Length (miles) No. of Lanes Speed Limit (mph) Road Score Peak Hour Vol. (vph) Link Capacity (vph) Kensington Ave , Hopkins Rd , Youngs Rd , N. French Rd , Sweet Home Rd , Audubon Pkwy , Hopkins Rd , Hopkins Rd , Hopkins Rd , N. Forest Rd , TOWN OF AMHERST REHABILITATION PROGRAM The demonstrated rehabilitation program was divided into three phases, as follows: PHASE I: A group of three links had to be selected for rehabilitation during Phase I. A set of 3 links out of 10, could be selected in 120 ways. All of the 120 combinations are listed in Table 2. Each of the 120 possible combinations will contain 3 unique links, which will be under construction simultaneously; therefore these 3 links were disabled during traffic assignment analysis. A network with all links enabled, which was termed as the base network, was also analyzed and used as a measure for comparison against the 120 different combinations. The most desirable combination was selected using a decision maker s preference. PHASE II: After Phase I is complete, the 7 remaining links were reconsidered during Phase II. Three (3) links could be selected out of 7 in 35 different combinations; the most desirable section was selected for rehabilitation during Phase II. PHASE III: Upon completion of Phase II, the remaining 4 links, which were not selected in Phases I or II, were scheduled for rehabilitation during Phase III. 4. IMPACTS OF URBAN STREET REHABILITATION The road closures during street rehabilitation have been found to cause the following adverse effects on urban travel (Sharma et. al. 1989, and Zhou et. al. 1997): (i) Traffic Congestion, (ii) Travel Delays, and (iii)increased Number of Accidents. These three factors will be called attributes in this paper. Prior research conducted on the three attributes, relevant to our project, is briefly described below: 4

5 TABLE 2: All Possible s of the 10 Streets in Groups of 3 Phase I Number Street Numbers in the Number Street Numbers in the Number Street Numbers in the Cost of Comfort and Convenience The traffic congestion gives rise to driver s frustration and stress, over time. This factor has been measured in terms of the Cost of Comfort and Convenience (CCC). Sharma and Lingras (Sharma et. al. 1989) performed research on the cost of driving comfort and convenience for two lane highways. The formula developed to compute the cost of comfort and convenience is shown in Equation 1 below: 5

6 where: v CCC = A c CCC = cost of comfort and convenience (cents/veh-mile) v/c = volume to capacity ratio A, B = model parameters B (1) By summing the values of CCC on each of the individual links in a combination, a total value of CCC can be computed for each combination and will become a variable in the multi-attribute utility model. All values for the CCC for the 120 possible combinations are shown in Figure 2. Figure 2 illustrates that if none of the links are closed/disabled, the total network cost of comfort and convenience (CCC) will be $9,460/hr. However, if combination 80 (Links , from Table 3) is selected for rehabilitation in Phase I, the CCC will be $11,150/hr, and if combination 120 (Links , from Table 2) is selected, the CCC will be $9,580/hr. FIGURE 2. Costs of Comfort & Convenience (CCC) for the 120 s. 4.2 Vehicle Travel Time Vehicle travel time on a roadway network is dependent on roadway characteristics such as link capacity, free flow travel time, link volumes, speed limits, and geometric roadway characteristics. The TransCAD TM SUE traffic assignment model provides output reports on the total vehicle travel time for each combination of disabled links network. The range of values for total network vehicle travel times from the TransCAD TM SUE traffic assignment model are shown in Figure 3. 6

7 FIGURE 3. Vehicle Travel Times (VTT) for the 120 s. 4.3 Accident Rate Model A study conducted by Zhou et. al. (Zhou et. al. 1997), analyzed the relationships between hourly accident rates and hourly traffic volume/capacity ratios on a six-lane urban freeway (I-94) in Michigan. The calculation of the hourly accident rate was performed by Equation 2 as below. where: 2 ( v ) ( v ) AR = c c 2 R = 0.57 AR = accident rate per hundred million vehicle miles v/c = volume to capacity ratio (2) Each network link in each of the combinations will have an associated accident rate (AR) that depicts the accident rate per year. The values for the AR for each of the 120 combinations are displayed in Figure MULTI-ATTRIBUTE UTILITY FUNCTION (MAUF) The Amherst Town Engineer, a person who could represent the best interests of the residents of Amherst, NY was selected as the sole decision maker. The decision maker was interviewed, and his certainty-equivalents for the three attributes were assessed. The attributes contain terminal values representing either the worst situation or the best situation. The decision maker was presented with a standard lottery in which he was given a 50/50 gamble where he has a chance of receiving either the least desirable situation or the most desirable situation, not both, or a guaranteed alternative (called certainty equivalent) in order to avoid the gamble. The decision maker then decides on a certain value of a particular attribute between terminal values which makes him/her indifferent to the gamble. 7

8 FIGURE 4. Accident Rates (AR) for the 120 s. The second step of the interview process was to determine scaling factors, or weights of each of the three attributes. For this, the decision maker was presented with standard lottery scenarios between the three attributes now lumped into bundles. Two standard bundles, best and worst scenarios, were presented and assigned index values to the decision maker as follows: Best Bundle: All the attributes (total travel time, accident rate, and cost of comfort and convenience) are at the most desirable levels. The index value assigned to this bundle is equal to one. Worst Bundle: All attributes are at the least desirable levels, and the index assigned to this bundle is equal to zero. Then three other bundles were presented separately to the decision maker, in each bundle, one attribute is placed at its most desirable level and the remaining two attributes at their least. The decision maker places an index value between 0 and 1, on these bundles in which he/she was indifferent to the standard lottery. The index value was the scaling factor for the attribute. 5.1 Decision Maker s Utility Plots Subsequent to the interview process mentioned earlier, the utility curves of the decision maker were plotted for each of the three attributes. The decision maker s utility curves and scaling factors are presented in Figure 5. In this case, since the decision maker s scaling factors equated to one, the MAUF model was additive, and is shown in Equation 3, below (Keeny, 1972): u( x) = k U ( x ) + k U ( x ) + k U ( x ) (3) TT TT AR AR CCC CCC 8

9 FIGURE 5. Utility Curves of the Decision Maker. After calculating the MAUF for each of the 120 combinations, the combination yielding the highest MAUF was ranked number one (1). Figure 6 displays the MAUF s of the decision maker for all of the 120 combinations. From Figure 6, it can be seen that section 120 (links 125, 126, & 138) yields the highest MAUF (0.67) of the decision maker, therefore this section is selected for rehabilitation in Phase I. After the Phase I combination, we have to select 3 out of the remaining 7 streets for Phase II, which can be done in 7 C 3 = 35 ways. Figure 7 illustrates all the MAUF s for the 35 combinations. From Figure 7, combination 15, having a MAUF of 0.54 comprising of streets: 17, 82, and 118, was selected for rehabilitation in Phase II. Phase III begins immediately after the completion of Phase II and contains the remaining four links which are links 62, 67, 76, and 81. Once the three phases were complete, a prioritized schedule of the rehabilitation projects was developed using SureTrak TM scheduling software, as in Figure 8. 9

10 FIGURE 6. Multi-Attribute Utility of the 120 Rehabilitation s. FIGURE 7. Multi-Attribute Utility of the 35 Rehabilitation s. 6. CONCLUSIONS A priority scheduling system which minimizes the (i) cost of comfort and convenience, (ii) total network travel time, and (iii) accident rate during road closures has been formulated and demonstrated in an example. In the example application, the combination of the 3 streets selected by the suggested method saved 13 veh-hrs/hr in network wide travel time, $127/hr on the cost of comfort and convenience, and 11 accidents/yr in the accident rates compared to the average of 10 random selections. The proposed algorithm can be coded into an expert system which practitioners can easily learn to use and draw priority schedules for their road rehabilitation programs. 10

11 Phase II Phase I Phase III FIGURE 8. Priority Schedule of the 10 Streets, for Rehabilitation. 7. PARTICIPATING AGENCIES All of the data obtained in this research for the demonstration application was obtained from the Town of Amherst Highway Department and the Greater Buffalo Niagara Regional Transportation Council (GBNRTC), located in Western N.Y. 8. REFERENCES Sharma, S. and Lingras, P. J. (May 1989). Cost of Driving Comfort and Convenience for Two-Lane Highways. J. of Transp. Engrg., ASCE, 115(3), Zhou, M. and Sisiopiku, V. P. (1997). Relationship Between Volume-to-Capacity Ratios and Accident Rates. Transp. Research Record 1581, TRB, National Research Council, Washington, D.C., Mohan, S. and Bushnak, A. (July 1985). Multi-Attribute Utility in Pavement Rehabilitation Decisions. J. of Transp. Engrg., ASCE, 111(4), Fishburn, P. (Jan. 1968). Utility Theory. Management Science, 14(5), Keeny, R. (Jan. 1972). Utility Functions for Multiattributed Consequences. Management Science, 18(5),