Innovations in Travel Demand Modeling, Volume 2: Papers (2008)

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sequently, it was necessary to identify data points when the counted volume did not equal the demand and drop these points from the data set. CANDIDATE SPEED–FLOW EQUATIONS Several candidate speed–flow equations might be fitted to the observed data. Table 2 describes several candi- dates. The first five candidates—linear, logarithmic, exponential, power, and polynomial—are standard mathematical functions commonly used in data analysis. The last two equation forms—Bureau of Public Roads (BPR) and Akcelik—are unique to travel time and delay analysis. The BPR equation has been the traditional method for predicting vehicle speed as a function of vol- ume–capacity (v/c) ratio in travel demand models. where S  average link speed (mph or km/h), S0  free-flow link speed (mph or km/h), X  v/c ratio, a  0.15, and b  4. The BPR equation was originally fitted to 1965 Highway Capacity Manual freeway speed–flow data (1). Since then additional research has indicated a less significant effect of v/c ratio on mean speeds until capacity is reached (see Exhibit 13-4 of the 2000 Highway Capacity Manual). The Akcelik equation was derived by Akcelik from the steady state delay equation for a single-channel queuing system. He derived the following time-dependent form: (1) 110 INNOVATIONS IN TRAVEL DEMAND MODELING, VOLUME 2 TABLE 1 Speed Survey Site Characteristics Lanes Speed Length Facility Area (both Signals Limit ADT Street From To (miles) Type Type dir.) (#) (mph) (2-way) 1st St. Ford Blvd. Gage Ave. 0.90 3 4 4 4 35 19,300 Aviation Blvd. W 120th St. W 135th St. 0.99 2 4 4 4 40 33,800 Beverly Blvd. Robertson Blvd. La Cienega Blvd. 0.44 2 2 4 4 40 34,700 Lincoln Blvd. Fiji Way Venice Blvd. 1.43 2 3 6 7 35–40 54,600 San Vicente Blvd. Curson Ave. Hauser Blvd. 0.64 2 2 6 4 35–40 39,900 Sunset Blvd. N La Brea Ave. N Cherokee Ave. 0.51 2 3 6 4 40 33,200 Verdugo Rd. Colorado Blvd. N Shasta Circle 0.83 3 5 4 4 35–40 16,000 Western Ave. W 111th St. W 120th St. 0.68 2 4 4–6 4 35 21,300 Note: Facility type: 2, principal arterial; 3, minor arterial. Area type: 2, central business district; 3, urban business district; 4, urban; 5, suburban. M ea n Sp ee d (m ph ) SCAG Arterial Speed Study 60 50 40 30 20 10 0 One-Hour Volume/Capacity Ratio 0 0.2 0.4 0.6 0.8 1.0 1.2 y = 43.663e –1.5385x R2 = 0.3047 FIGURE 1 Hourly speed–flow observations. S S a X b = + ( )⎡⎣⎢ ⎤⎦⎥ 0 1 S L L S T x x Jx cT = + −( ) + −( ) +⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥ / .0 2 0 25 1 1 8