&m1 m2 d 2. f ' The resultant formula has evolved to resemble Bayes' Theorem of conditional probability and is as follows: F t(i,j) P i. A j.

Transcription

1 GRAVITY MODEL DESCRIPTION This function accepts zonal trip end productions and attractions stratified by class of trip (purpose), geography, time of day, etc.), travel impedance factors, zone-to-zone travel indices, and K-factors (optional), and generates a zone-to-zone trip table file from the Gravity Model distribution formula. The function also checks the acceptability of computed attractions, and if necessary, adjusts the calculated attractions to each zone to equal the input attractions. The Gravity Model originally paralleled Newton's gravitational law, i.e., the assumption is that all trips starting from a given zone are attracted by various traffic generators in other zones and that this attraction is directly proportional to the relative attraction of the zone and inversely proportional to the separation between the zones in the gravity model. The measure of separation is generally accepted as the zone-to-zone travel time via the specified transportation network. However, because people as social beings do not order their lives according to exact physical laws, an adjustment is necessary to adjust the gravitational concept to fit the travel characteristics of the urban area being studied. The classical gravitational formula is: f ' &m1 m2 d 2 g where: f = force m1,m2 = mass of bodies d = distance separating 1 and 2 g = gravitational constant The classical gravitational formula is restructured for computer use as follows: o o o First, the separation is generalized to allow inclusion of any travel index. In TRANPLAN, time, distance, cost or a combination of them may be used. Most users select time as the indicator of separation. Second, the effect of separation for each minute time increment is represented by a table of "friction factors"; this replaces the squared quantity in the denominator. The travel separation function is then more easily represented. Friction factors may be input as explicit values by travel time, by purpose, or by a deterrence coefficient in the formulation F (t) = e -ut, where t is the travel time in minutes and u is the deterrence coefficient for a particular purpose. Third, a modification in the basic gravitational formulation is made to combine all these effects with the constant of proportionality. The resultant formula has evolved to resemble Bayes' Theorem of conditional probability and is as follows: T (i,j) ' P i A j F t(i,j) n j A x F t(i,x) x'1 K (i,j) K (i,x) where: T (i,j) = trips produced in zone I and attracted to zone j (analogous to gravitational force) MODELS 1-1

2 GRAVITY MODEL P i = trips produced in zone I (analogous to mass of body I) A j = trips attracted to zone j (analogous to mass of body j) t (i,j) = travel time in minutes between zone I and zone j (analogous to separation between bodies I and j) F t = empirically derived travel time factor that expresses the (i,j) average area-wide effect of spatial separation on trip interchange between zones that are t (i,j) apart K (i,j) = specific zone-to-zone adjustment factor to allow for the incorporation of the effect on travel patterns of defined social or economic linkages not otherwise accounted for in the gravity model formulation. Two methods of balancing attractions are available to the user: balancing on a district basis or on a zonal basis. If district equivalents are specified, the input attractions (AI) for each zone are read into the model, and are then aggregated on a district basis (AIG). After the basic trip distribution has been processed, the calculated trips are condensed on a district basis as attractions computed (AC). The model then examines the ratio of the computed attractions to input attractions, which theoretically should approach unity for each district. When computing new attractions, the following formula is used: New Attractions' AIG District AC District ( AI Zone Thus, when the user desires to balance attractions, the number of iterations and the convergence criteria are specified and the model iterates until either convergence or the number of iterations specified by the user is met. If no district equivalents are specified, attraction iterations are based on individual zonal level adjustments. Both methods of balancing are iterated until a convergence within user-specified limits is achieved or until the number of specified attraction iterations is reached. MODELS 1-2

3 GRAVITY MODEL OVERVIEW OF FUNCTION CONTROLS Function controls are coded free-format. The first character of each record (except those beginning with $) may be in any column. $GRAVITY MODEL $FILES INPUT FILE = GMSKIM, USER ID = $fname$ INPUT FILE = GRVDATA, USER ID = $fname$ OUTPUT FILE = GMVOL, USER ID = $fname$ OUTPUT FILE = GMTVOL, USER ID = $fname$ $HEADERS (up to three header records) $OPTIONS CONTROL ON ATTRACTIONS F FACTOR INTERPOLATION GRVDATA MERGED PURPOSE FILE MINIMUM TRIP ENDS PRINT ACCESSIBILITY INDICES PRINT ALL ITERATIONS PRINT ATTRACTIONS PRINT TRIP ENDS PRINT TRIP LENGTH STATISTICS SUPPRESS DATA TOTAL PURPOSE FILE $PARAMETERS ATTRACTION CLOSURE = prct DETERRENCE COEFFICIENTS = (p1,cf1) (p2,cf2)... IMPEDANCE = list ITERATIONS ON ATTRACTIONS = num KFACTOR DISTRICTS = kdis MAXIMUM PURPOSE = mp MAXIMUM TIME = mt NUMBER OF DISTRICTS = nd SELECTED PURPOSE = list SELECTED TRIP END ZONES = list SKIM FACTOR = flist $DATA Production/Attraction Data Friction Factor Data District Equivalence Data K-Factor District Equivalence Data K-Factor Data $END TP FUNCTION MODELS 1-3

4 GRAVITY MODEL DETAILED DESCRIPTION OF FUNCTION CONTROLS File Identifiers These define the input and output files for this function; only the first is required. INPUT FILE = GMSKIM INPUT FILE = GRVDATA OUTPUT FILE = GMVOL OUTPUT FILE = GMTVOL A selected summation file containing the interzonal skim impedances which determine the friction factor selection. (Required) A data file containing all the data transactions for the function execution. This file is optional; if not present, all data are assumed to be present in the $DATA section of the control file. This file specification will be ignored if GRVDATA is not specified in the $OPTIONS section. (Optional) A trip table file containing zone-to-zone distributed trips for up to 15 purposes. This file specification will be ignored if MERGED PURPOSE FILE is not specified in the $OPTIONS section. (Optional) A single purpose trip table file containing zone-to-zone distributed trips which are the totals of all selected purposes. This file specification will be ignored if TOTAL PURPOSE FILE is not specified in the $OPTIONS section. (Optional) Headers Up to three header identifications may be specified. These are written onto any specified output files and printed at the top of each report page. If $HEADERS is not specified, the headers from the file GMSKIM are used instead. MODELS 1-4

5 GRAVITY MODEL Option Specifications The following option(s) may be specified. CONTROL ON ATTRACTIONS F FACTOR INTERPOLATION GRVDATA MERGED PURPOSE FILE MINIMUM TRIP ENDS Specifies that the gravity model will be "attraction conserving" rather than the default "production conserving", i.e., the trip table matrix column totals will govern. Specifies that F-Factor application will be based upon interpolation between the minute values of time. The default application is to utilize the nearest minute. Specifies that all data transactions are on file GRVDATA which, in this case, must be identified as an input file. If the option is not specified, all data transactions must be on standard input following the $DATA record. Specifies that all selected purposes (trip tables) generated by this function are to be output on file GMVOL which, in this case, must be identified as an output file. If this option is not chosen, no multi-purpose file is generated. Specifies that all zones which have neither origins (productions) nor destinations (attractions) will not be included in the trip end summary report. The default condition reports all zones. PRINT ACCESSIBILITY INDICES Specifies that a report of zonal accessibility indices computed during the last iteration, by purpose, is to be included in the message/report file. These represent the denominator of the gravity model formula. This option may generate much printed output and should be used only when detailed information concerning the action of the model is desired. PRINT ALL ITERATIONS PRINT ATTRACTIONS Specifies that the attraction reports, the trip length statistics, and the accessibility indices, as selected, are reported for EACH iteration. This option may generate much printed output and should be used only when detailed information concerning the action of the model is desired. Specifies that a report of input and computed zonal attractions, and the ratios between these, is to be included in the message/report file (last iteration only). Any ratios which are out of the specified closure range after the maximum number of iterations are marked by asterisks. (NOTE: If attraction balancing is at the district level, the district attraction report is always printed after each iteration). PRINT TRIP ENDS Specifies that a report of the trip end summary of all output purposes plus the total purpose, is to be included in the message/report file. The format of this report is the same as that of the REPORT MATRIX function. PRINT TRIP LENGTH STATISTICS Specifies that a report of trip length frequency distributions, graphs, and trip length summaries, for each purpose, is to be included in the message/report file (last iteration only). SUPPRESS DATA TOTAL PURPOSE FILE Specifies that input data specifications will not be echoed to the message/report file. Specifies that the selected purposes generated by this function are to be added and output as a one-purpose trip table on file GMTVOL which, in this case, must be identified as an output file. If this option is not chosen, no total purpose file is generated. MODELS 1-5

6 GRAVITY MODEL MODELS 1-6

7 GRAVITY MODEL Parameter Specifications The following parameter(s) may be specified. ATTRACTION CLOSURE = prct Specifies the attraction closure percentage (floating point) for the program. When all computed attractions by zone (or, if districts are specified, by district) are within +/- prct of given attractions, then the program considers the iterations complete regardless of the specified number of iterations on attractions. The default value is 10.0 percent. DETERRENCE COEFFICIENTS = (p1,cf1) (p2,cf2)... Each pair of numbers specifies the deterrence function coefficient, cf (real number), that is applied to trip purpose p (integer). If this parameter is specified for a given trip purpose, any friction factor data provided for that trip purpose will be ignored. (Note: The negative sign for the deterrence function is not input.) IMPEDANCE = list Specifies the impedances to be used from the file GMSKIM. The list contains an impedance for each purpose. Allowable values in the list are as follows: COST DISTANCE TIME 1 TIME 2 USER TABLE 1... TABLE 15 The default value for each purpose is TIME 1 (TABLE 3). ITERATIONS ON ATTRACTIONS = num Specifies the number of attraction iterations. A value of zero produces one distribution with no balancing on attractions. The default value is two (three distributions--two after attraction adjustments). KFACTOR DISTRICTS = kdis MAXIMUM PURPOSE = mp MAXIMUM TIME = mt NUMBER OF DISTRICTS = nd SELECTED PURPOSES = list Specifies the number of districts for applying K-factors. This assumes that all K-factor data records are at district levels to be expanded to zonal levels by the program. Specifies the maximum purpose of the input data transactions. The default value is one. Specifies the maximum time, in integer minutes, for which friction factors are present. If this parameter is not specified, a value of 200 minutes is assumed. All times (impedances) greater than the maximum will be truncated to the maximum and will reference the F-factor for the maximum. Specifies the number of districts expected in the list of district equivalents. This parameter and the district equivalents should only be specified if attraction balancing is to be on a district and not zonal level. Specifies the list of trip purposes to be distributed by the model. The values specified must be less than or equal to the maximum input purpose. If this parameter is not specified, all trip purposes are distributed. SELECTED TRIP END ZONES = list Specifies zones to be included in the trip end summary report. All zones are included in the default condition. MODELS 1-7

8 GRAVITY MODEL SKIM FACTOR = flist Specifies a weighting factor (real number) for each impedance listed in the IMPEDANCE parameter, in the specified order, to convert the input skim table impedances to units which match the F-Factor specifications. Skim factors of 0.01 are assumed unless specified otherwise. If the skim table has been built in units other than hundredths of units, a skim factor should be specified. For example, to use a skim table built in tenths of minutes, a skim factor of 0.01 should be specified. As an example of multiple impedances, if the following parameters were input: IMPEDANCE = TIME 1, DISTANCE, TIME 1 SKIM FACTOR = 1.0, 0.01 The "1.0" would be applied to DISTANCE and the "0.01" would be applied to both the TIME 1 impedances. MODELS 1-8

9 GRAVITY MODEL Data Specifications The following data are input either on standard system input or on file GRVDATA. The order of the production, attraction, and F-factor records is immaterial because each record is uniquely identified. However, all of these records must occur before any district equivalent or K-factor records. Most users would probably maintain the order presented below. 1. Production/Attraction Data Record Field Columns Name Description 1-2 Record Identifier These columns must have "GP" to indicate a Identifier production record, or "GA" to indicate an attraction record. 4-7 Zone Zone number (right-justified) 9 Record Number Indicates whether this is the first or second production/attraction record for the zone. Allowable values are: 1 = purposes start at 1 2 = purposes start at Purpose 1/11 Production/Attraction trip ends, right-justified Purpose 2/12 Production/Attraction trip ends, right-justified Purpose 3/13 Production/Attraction trip ends, right-justified Purpose 4/14 Production/Attraction trip ends, right-justified Purpose 5/15 Production/Attraction trip ends, right-justified Purpose 6 Production/Attraction trip ends, right-justified Purpose 7 Production/Attraction trip ends, right-justified Purpose 8 Production/Attraction trip ends, right-justified Purpose 9 Production/Attraction trip ends, right-justified Purpose 10 Production/Attraction trip ends, right-justified. 2. Friction Factor Data Record Field Columns Name Description 1-2 Record Identifier These columns must have "GF" to identify the record as a friction factor record. 4-7 Impedance Time, in units (e.g., minutes), right-justified, decimal point is optional. 9 Record Number Indicates whether this is the first or second record for the specified impedance. Allowable values are: 1 = purposes start at 1 2 = purposes start at 11 MODELS 1-9

10 GRAVITY MODEL Purpose 1/11 Friction factor, right-justified, decimal point optional Purpose 2/12 Friction factor, right-justified, decimal point optional Purpose 3/13 Friction factor, right-justified, decimal point optional Purpose 4/14 Friction factor, right-justified, decimal point optional Purpose 5/15 Friction factor, right-justified, decimal point optional Purpose 6 Friction factor, right-justified, decimal point optional Purpose 7 Friction factor, right-justified, decimal point optional Purpose 8 Friction factor, right-justified, decimal point optional Purpose 9 Friction factor, right-justified, decimal point optional Purpose 10 Friction factor, right-justified, decimal point optional. 3. District Equivalence Data Zone/district equivalence records define the range(s) of zones comprising each district for balancing of attractions. These records are optional, if any are present, the NUMBER OF DISTRICTS parameter must be specified. One equivalence record is required for each district; these may be in any order as long as each district is specified. Each district is defined by the following free-format statement(s): DISTRICT = d, ZONES = list ID = user identification This record specifies the list of zones comprising the current district number, d. One such record is required for each district and these may be followed by ID records if desired. Any number of zones may be specified as long as they are not specified for other districts. This record is useful in describing the current district. All characters on the record to the right of ID are skipped during execution of this function, but the record is printed within the list of function controls given as standard output. The record is optional; however, if it is used, nothing other than the user identification may be punched to the right of ID on the same record. 4. K-Factor District Equivalence Data Zone/district equivalence records define the range(s) of zones comprising each district for the application of K-factors. These records are optional, if any are present, the KFACTOR DISTRICTS parameter must be specified. Each district is defined by the following free-format statement(s): KDISTRICT = d, ZONES = list or KDIST = d, ZONES= list This record specifies the list of zones comprising the current K-factor district number, d. Any number of zones may be specified as long as they are not specified for other districts. 5. K-Factor Data GK, purp, o1-o2, d1-d2, fac Specifies K-factor adjustments to be performed by the program. The format is free-field where: purp = purpose number MODELS 1-10

11 GRAVITY MODEL o1-o2 = d1-d2 = origin zone (or district, if K-factor districts specified) range, if the range contains only one zone/district, the zone/district number may replace the range specifications. destination zone/district range if, the range contains only one zone/district, the zone/district number may replace the range specifications. fac = positive floating point factor Any zones/districts for which no K-factors are specified are given factors of 1.0; i.e., no adjustments are performed. MODELS 1-11

12 GRAVITY MODEL EXAMPLES Example 1 This example illustrates the use of the GRAVITY MODEL function to distribute trips for seven purposes, for FTOWN. Skims are based on TIME 1. A maximum of ten iterations are to be performed, with an allowable closing error of ten percent on the attractions. Attraction balancing is to be on a zonal level. A maximum time of 50 minutes is input on the friction factor records. All reports (for the last iteration only) and a seven purpose trip table file are to be produced. Control records for this function and portions of the output message/report file are shown below. $GRAVITY MODEL $FILES INPUT FILE = GMSKIM, USER ID = $total.skm$ OUTPUT FILE = GMVOL, USER ID = $person.trp$ $HEADERS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) $OPTIONS MERGED PURPOSE FILE PRINT ATTRACTIONS PRINT TRIP ENDS PRINT TRIP LENGTH STATISTICS $PARAMETERS ATTRACTION CLOSURE = 10.0 ITERATIONS ON ATTRACTIONS = 10 MAXIMUM PURPOSE = 7 MAXIMUM TIME = 50 SELECTED PURPOSES = 1-7 $DATA GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GP GA GA GA GA GA GA GA GA GA GA GA GA MODELS 1-12

13 GRAVITY MODEL GA GA GA GA GA GA GA GA GA GA GA GA GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF GF $END TP FUNCTION MODELS 1-13

14 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 3 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 F-FACTOR REPORT TIME PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE PURPOSE MODELS 1-14

15 GRAVITY MODEL UAG - URBAN/SYS BUILD INTRAZONAL IMPEDANCES -- FTOWN PAGE NO. 1 TRANPLAN SYSTEM FREE-FLOW SKIMS -- DISTANCE (2) AND TIME (3) -- WITH INTRAZONALS DATE 21AUG96 VERSION 9.0 TIME 12:54:13 INPUT FILE NAME GMSKIM FILE CHARACTERISTICS USER FILE IDENTIFICATION - total.skm FILE HEADER BUILD INTRAZONAL IMPEDANCES -- FTOWN FREE-FLOW SKIMS -- DISTANCE (2) AND TIME (3) -- WITH INTRAZONALS GENERATING FUNCTION BUILD INTRAZONAL IMPEDANCES TYPE OF FILE HWYSKIM GENERATION FILE NAME IZOUT GENERATION DATE AUG96 CURRENT DATE AUG96 GENERATION TIME :54:09 CURRENT TIME :54:13 FILE SIZE MAXIMUM ZONE = 24 MAXIMUM TABLE NO. = 4 UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 2 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 PURPOSE 1 INPUT ATTRACTIONS ( 30614) ADJUSTED TO INPUT PRODUCTIONS ( 40974) PURPOSE 2 INPUT ATTRACTIONS ( 50084) ADJUSTED TO INPUT PRODUCTIONS ( 43957) PURPOSE 3 INPUT ATTRACTIONS ( 37189) ADJUSTED TO INPUT PRODUCTIONS ( 44720) PURPOSE 4 INPUT ATTRACTIONS ( 28624) ADJUSTED TO INPUT PRODUCTIONS ( 54586) PURPOSE 5 INPUT PRODUCTIONS = ATTRACTIONS = PURPOSE 6 INPUT PRODUCTIONS = ATTRACTIONS = PURPOSE 7 INPUT PRODUCTIONS = ATTRACTIONS = MODELS 1-15

16 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 3 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 MODEL/INPUT TRIP ATTRACTIONS REPORT -- ITERATION 5 ON ATTRACTIONS PURPOSE PURPOSE PURPOSE PURPOSE AT AT AT AT ZONE MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODELS 1-16

17 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 4 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 MODEL/INPUT TRIP ATTRACTIONS REPORT -- ITERATION 5 ON ATTRACTIONS PURPOSE PURPOSE PURPOSE PURPOSE AT AT AT AT ZONE MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODEL INPUT RATIO CL MODELS 1-17

18 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 5 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP LENGTH FREQUENCY DISTRIBUTION GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS PURPOSE NO. 1 PURPOSE NO. 2 PURPOSE NO. 3 PURPOSE NO. 4 ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE MINUTES TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT MODELS 1-18

19 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 6 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP LENGTH FREQUENCY DISTRIBUTION GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS PURPOSE NO. 1 PURPOSE NO. 2 PURPOSE NO. 3 PURPOSE NO. 4 ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE MINUTES TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT MODELS 1-19

20 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 7 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP LENGTH FREQUENCY DISTRIBUTION GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS PURPOSE NO. 5 PURPOSE NO. 6 PURPOSE NO. 7 PURPOSE NO. 8 ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE MINUTES TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT MODELS 1-20

21 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 8 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP LENGTH FREQUENCY DISTRIBUTION GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS PURPOSE NO. 5 PURPOSE NO. 6 PURPOSE NO. 7 PURPOSE NO. 8 ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE ACCUMULATIVE MINUTES TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT TRIPS PERCENT UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 9 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP LENGTH FREQUENCY DISTRIBUTION GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS SUMMARY TOTAL TRIPS TRIP-HOURS AVE. TRIP LENGTH (MIN) VARIANCE (MIN) STANDARD DEVIATION (MIN) PURPOSE NO PURPOSE NO PURPOSE NO PURPOSE NO PURPOSE NO PURPOSE NO PURPOSE NO MODELS 1-21

22 GRAVITY MODEL TRIP LENGTH FREQUENCY DISTRIBUTION -- GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS -- PURPOSE NO. 1 PERCENT OF TRIPS 10.0 * * 9.8 * * 9.6 * * 9.4 * * 9.2 * * 9.0 * * 8.8 * * 8.6 * * 8.4 * * 8.2 * * 8.0 * * 7.8 * * 7.6 * * 7.4 * * 7.2 * * 7.0 * * 6.8 * * 6.6 * * 6.4 * * 6.2 * * 6.0 * * 5.8 * * 5.6 * * 5.4 * * 5.2 * * 5.0 * * 4.8 * * 4.6 * * * 4.4 * * * * 4.2 * * * * 4.0 * * * * * 3.8 * * * * * * * 3.6 * * * * * * * 3.4 * * * * * * * 3.2 * * * * * * * * * * 3.0 * * * * * * * * * * * * * * * 2.8 * * * * * * * * * * * * * * * * * 2.6 * * * * * * * * * * * * * * * * * 2.4 * * * * * * * * * * * * * * * * * 2.2 * * * * * * * * * * * * * * * * * 2.0 * * * * * * * * * * * * * * * * * 1.8 * * * * * * * * * * * * * * * * * * * * 1.6 * * * * * * * * * * * * * * * * * * * * * * 1.4 * * * * * * * * * * * * * * * * * * * * * * * MODELS 1-22

23 GRAVITY MODEL TRIP LENGTH FREQUENCY DISTRIBUTION -- GRAVITY MODEL -- ITERATION 5 ON ATTRACTIONS -- CUMULATIVE DISTRIBUTION -- PURPOSE NO. 1 PERCENT OF TRIPS * * * * * * 96.0 * * * * * * * * 94.0 * * * * * * * * * 92.0 * * * * * * * * * * * 90.0 * * * * * * * * * * * * * 88.0 * * * * * * * * * * * * * 86.0 * * * * * * * * * * * * * * 84.0 * * * * * * * * * * * * * * * 82.0 * * * * * * * * * * * * * * * 80.0 * * * * * * * * * * * * * * * 78.0 * * * * * * * * * * * * * * * * * * 76.0 * * * * * * * * * * * * * * * * * * 74.0 * * * * * * * * * * * * * * * * * * * * 72.0 * * * * * * * * * * * * * * * * * * * * * 70.0 * * * * * * * * * * * * * * * * * * * * * * 68.0 * * * * * * * * * * * * * * * * * * * * * * * * 66.0 * * * * * * * * * * * * * * * * * * * * * * * * 64.0 * * * * * * * * * * * * * * * * * * * * * * * * * * 62.0 * * * * * * * * * * * * * * * * * * * * * * * * * * 60.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * 58.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * 56.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * 54.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 52.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 50.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 48.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 46.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 44.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 42.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 40.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 38.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 36.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 34.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 32.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 30.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 28.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 26.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 24.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 22.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 20.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 18.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 16.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 14.0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * MODELS 1-23

24 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 24 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP END SUMMARY --- PURPOSE 1 ZONE/DIST ORIG/PROD DEST/ATTR TOTAL INTRATRIPS ZONE/DIST ORIG/PROD DEST/ATTR TOTAL INTRATRIPS TOTALS MODELS 1-24

25 GRAVITY MODEL UAG - URBAN/SYS GRAVITY MODEL -- FTOWN (HIGHWAY IMPEDANCES WITH TOLLS) PAGE NO. 31 TRANPLAN SYSTEM PURP1 = HB-WORK PURP2 = HB-SHOP PURP3 = HB-SOC/REC PURP4 = HB-OTHER DATE 21AUG96 VERSION 9.0 PURP5 = NON-HB PURP6 = TRUCK-TAXI PURP7 = INT/EXT (zones 16-24) TIME 12:54:13 TRIP END SUMMARY --- PURPOSE 1 TOTAL ALL PURPOSES ZONE/DIST ORIG/PROD DEST/ATTR TOTAL INTRATRIPS ZONE/DIST ORIG/PROD DEST/ATTR TOTAL INTRATRIPS TOTALS MODELS 1-25

26 CALIBRATE GRAVITY MODEL DESCRIPTION This function generates gravity model distribution rates ("F-Factors") from origin-destination survey data. F-Factors are used as input in distributing future trips in subsequent runs of the GRAVITY MODEL function. In essence, the model is calibrated by an interactive process during one computer run, thereby eliminating the need for multiple runs and laborious hand calculations between runs. A trip length frequency distribution of the survey data, associated productions and attractions, and F-Factors (initially set to 100) are input on a Gravity Model History File. Alternatively, the trip length frequency may be input in the DATA section of the input controls. An impedance (skim or selected summation) file is read and the gravity model distribution formula is applied, the attractions balanced, and the synthesized trips grouped according to trip length (e.g., travel time). This produces a synthesized trip length frequency table for each trip purpose. If, for each trip purpose, the average trip length derived from the gravity model distributions is within a specified percent of the average trip length of the O-D trips, the model is considered balanced. If the model is not balanced, and the user-specified maximum number of iterations has not been reached, the F-Factors are adjusted for each purpose and another iteration is performed. In adjusting F-Factors, the number of trips for each trip length increment is divided by the total number of trips to yield the percent of trips in each time increment. This is done for O-D trips and for synthesized (gravity model) trips. The ratio is O-D percent over Gravity Model percent is calculated for each trip length increment and, in turn, multiplied by the "old" F-Factor to compute a "new" F-Factor: F&Factor(new) ' O&D % gravity % ( F&Factor(old) The natural logarithms of the new F-Factors are used in fitting a straight line by the method of least squares. This straight line determines the general trend of F-Factors. F-Factors are not considered to be reliable at relatively large values of time; therefore, theoretical values of F-Factors computed from the straight line equation just developed are used to replace F-Factors for trip lengths greater than a user-specified value. The new F-Factors, including the revised factors for large trip length values, are used to develop a best fit curve of a third degree equation by the method of least squares. Adjusted F-Factors for each time increment are then computed from the exponential curve equation. The program recalculates interzonal trips using the adjusted F-Factors, balances attractions as specified, tests the average trip length for each purpose, and then repeats the F-Factor adjustment process until the model is calibrated to the user's specifications or until the number of iterations specified by the user is reached. Whether or not the model has converged before the maximum number of iterations is reached, the F-Factor calibration run is finalized and all reports are produced for the final iteration, including F-Factor listings, convergence summaries and trip length frequencies. MODELS 2-1

27 CALIBRATE GRAVITY MODEL OVER VIEW OF FUNCTION CONTROLS Function controls are coded free-format. The first character of each record (except those beginning with $) may be in any column. $CALIBRATE GRAVITY MODEL $FILES INPUT FILE = GMSKIM, USER ID = $fname$ INPUT FILE = GMHIST, USER ID = $fname$ INPUT FILE = GRVDATA, USER ID = $fname$ OUTPUT FILE = GMVOL, USER ID = $fname$ OUTPUT FILE = GMTVOL, USER ID = $fname$ OUTPUT FILE = NEWHIST, USER ID = $fname$ OUTPUT FILE = NEWDATA, USER ID = $fname$ $HEADERS (Up to three header records) $OPTIONS CONTROL ON ATTRACTIONS F FACTOR INTERPOLATION GRAVITY MODEL HISTORY FILE GRVDATA MERGED PURPOSE FILE MINIMUM TRIP ENDS NEW HISTORY FILE OUTPUT DATA FILE PRINT ACCESSIBILITY INDICES PRINT ALL ITERATIONS PRINT ATTRACTIONS PRINT TRIP ENDS PRINT TRIP LENGTH STATISTICS SUPPRESS DATA TOTAL PURPOSE FILE ZERO INTRAZONALS $PARAMETERS ATTRACTION CLOSURE = prct F FACTOR CLOSURE = fc F FACTOR ITERATIONS = numf IMPEDANCE = list ITERATIONS ON ATTRACTIONS = num KFACTOR DISTRICTS = kdis MAXIMUM PURPOSE = mp MAXIMUM TIME = mt NUMBER OF DISTRICTS = nd SELECTED PURPOSE = list SELECTED TRIP END ZONES = list SKIM FACTOR = flist SMOOTH PERCENTAGE = sprct $DATA Production/Attraction Data Friction Factor Data Trip Length Frequency Data District Equivalence Data K-Factor District Equivalence Data K-Factor Data $END TP FUNCTION MODELS 2-2

28 CALIBRATE GRAVITY MODEL DETAILED DESCRIPTION OF FUNCTION CONTROLS File Identifiers These define the input and output files for this function; only the first two files are required. INPUT FILE = GMSKIM INPUT FILE = GMHIST INPUT FILE = GRVDATA OUTPUT FILE = GMVOL OUTPUT FILE = GMTVOL OUTPUT FILE = NEWHIST OUTPUT FILE = NEWDATA A selected summation file containing the interzonal skim impedances which determine the friction factor selection. (Required) A data file containing origin/destination data (in production/attraction format), initial F-Factors (100 for all impedances) or F-Factors from a previous calibration run, and the origin-destination survey trip length frequency distribution. This file is generated by the GMHFIL program, described in the Miscellaneous Utilities section of the URBAN/SYS User Manual, and is optional. If not present, all production/attraction data, friction factor data and trip length frequency data are assumed to be input in the $DATA section or in the GRVDATA file. This file specification will be ignored if GRAVITY MODEL HISTORY FILE is not specified in the $OPTIONS section. (Optional) A data file containing all the data transactions for the function execution. This file is optional; if not present, all data are assumed to be present in the $DATA section of the control file. This file specification will be ignored if GRVDATA is not specified in the $OPTIONS section. (Optional) A trip table file containing zone-to-zone distributed trips for up to 15 purposes. This file specification will be ignored if MERGED PURPOSE FILE is not specified in the $OPTIONS section. (Optional) A single purpose trip table file containing zone-to-zone distributed trips which are the totals of all selected purposes. This file specification will be ignored if TOTAL PURPOSE FILE is not specified in the $OPTIONS section. (Optional) A gravity model history file similar to the GMHIST file except that F-Factors are those generated in the current calibration run. This file may be used to restart the calibration for additional convergence, if necessary. This file specification will be ignored if NEW HISTORY FILE is not specified in the $OPTIONS section. (Optional) An ASCII file containing the production, attraction and F-factor records in Gravity Model/Spatial Allocation Model format. This file specification will be ignored if OUTPUT DATA FILE is not specified in the $OPTIONS section. (Optional) Headers Up to three header identifications may be specified. These are written onto any specified output files and printed at the top of each report page. If $HEADERS is not specified, the headers from the file GMSKIM are used instead. MODELS 2-3

29 CALIBRATE GRAVITY MODEL Option Specifications The following option(s) may be specified. CONTROL ON ATTRACTIONS F FACTOR INTERPOLATION Specifies that the gravity model will be "attraction conserving" rather than the default "production conserving", i.e., the trip table matrix column totals will govern. Specifies that F-Factor application will be based upon interpolation between the minute values of time. The default application is to utilize the nearest minute. GRAVITY MODEL HISTORY FILE Specifies that the Gravity Model history is on file GMHIST which, in this case, must be identified as an input file. GRVDATA MERGED PURPOSE FILE MINIMUM TRIP ENDS NEW HISTORY FILE OUTPUT DATA FILE Specifies that all data transactions are on file GRVDATA which, in this case, must be identified as an input file. If the option is not specified, all data transactions must be on standard input following the $DATA record. Specifies that all selected purposes (trip tables) generated by this function are to be output on file GMVOL which, in this case, must be identified as an output file. If this option is not chosen, no multi-purpose file is generated. Specifies that all zones which have neither origins (productions) nor destinations (attractions) will not be included in the trip end summary report. The default condition reports all zones. Specifies that a new Gravity Model history is to be output on file NEWHIST which, in this case, must be identified as an output file. It will be identical to file GMHIST except that F-Factors determined in the calibration run will be written on the file in place of those input. Use of this option requires that the GRAVITY MODEL HISTORY FILE option also be specified. Specifies that the production, attraction and F-factor records are to be output (in Gravity Model/Spatial Allocation Model format) on file NEWDATA which, in this case, must be identified as an output file. PRINT ACCESSIBILITY INDICES Specifies that a report of zonal accessibility indices computed during the last iteration, by purpose, is to be included in the message/report file. These represent the denominator of the gravity model formula. This option may generate much printed output and should be used only when detailed information concerning the action of the model is desired. PRINT ALL ITERATIONS PRINT ATTRACTIONS Specifies that the attraction reports, the trip length statistics, and the accessibility indices, as selected, are reported for EACH iteration. This option may generate much printed output and should be used only when detailed information concerning the action of the model is desired. Specifies that a report of input and computed zonal attractions, and the ratios between these, is to be included in the message/report file (last iteration only). Any ratios which are out of the specified closure range after the maximum number of iterations are marked by asterisks. (NOTE: If attraction balancing is at the district level, the district attraction report is always printed after each iteration). MODELS 2-4