Using Archived AVL-APC Data to Improve Transit Performance and Management (2006)

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54 Accuracy of automated passenger counts may be reduced by many types of errors, including counting error, location error, attribution error (i.e., attributing counts to the wrong trip), modeling error (e.g., assumptions about loops), and sampling error. It is also important to distinguish between the accuracy of raw counts and that of screened and corrected counts, and between the accuracy of directly measured items (ons and offs by stop) and aggregate measures such as load, passenger-miles, and trip-level boardings. Finally, for any type of error, it is important to distinguish between bias (systematic error) and random error. While random error, like sampling error, shrinks with increased sample size, correcting for bias is usually impractical; therefore, controlling bias becomes far more important than controlling random error. To a large extent, this chapter and the following one repeat material originally published in Furth et al. (7). 8.1 Raw Count Accuracy The accuracy of raw counts tends to be the focus of vendors and many buyers. Kimpel et al. recently studied Tri-Met counts and found statistically significant bias for one of the two bus types tested (bus type affects how sensors are mounted)—an average overcount of 4.24% for ons and 5.37% for offs (37). Overall, standard deviation of random count error was found to be rather large—about 0.5 passenger per stop for both ons and offs, for a coefficient of variation (cv) of 0.37. This value is surprisingly large; the researchers suspect newer systems are more precise. Kimpel et al. suggest applying correction factors to over- come biases. However, few agencies can afford the research needed to establish the level of systematic over- or undercount. They need counts whose biases are small enough to live with. Less onerous are bias corrections established by the APC ven- dor. One vendor includes in its processing software correction factors for counts of 1, 2, and 3+ passengers, yielding non- integer corrected counts. Test criteria for APC equipment often fail to distinguish between random and systematic error. For example, the crite- rion “the count should be correct at 97% of stops”does not con- sider whether there might be a tendency to over- or undercount. Another weakness of this criterion is that many stops may have zero ons and offs, which is rather easy to count correctly. To control bias, tests should require that the ratio of total counted ons to total “true” ons be close to 1. Using Tri-Met’s random stop-level error cv of 0.37, the hypothesis that the on counts have no systematic error can be accepted at the 95% confidence level if this ratio is in the range 1 ± 0.72 √n, where n equals the number of stops contributing to the test total. A less stringent test would allow a small degree of bias, for exam- ple, 2% (partly in recognition that the “true” count may itself contain errors); then the acceptance range becomes 1 ± (0.02 + 0.72 √n), which, with n equal to 5000, is the range 1 ± 0.03. One of STM’s tests is that, at the trip level, the average absolute deviation between automated and manual counts of boardings should be less than 5% of average trip boardings. Because it uses absolute deviations, this test masks systematic error. However, the strict criterion of 5% effectively forces both random and systematic error to be small. Acceptance tests should specify the screening criteria and the maximum percentage of trips (or blocks of trips) rejected, and then apply accuracy criteria to the remaining data. STM pro- vides a good example: it rejects trips with an imbalance of 5 or more passengers, requires that no more than 85% of trips be rejected, and applies accuracy criteria to the remaining trips. 8.1.1 Measuring Ground Truth One problem in testing APC accuracy is the difficulty of observing ground truth. Conventional manual counts can have greater counting error than a good APC. One vendor insists that clients use video cameras, at least one per door, in C H A P T E R 8 Passenger Count Processing and Accuracy

acceptance tests, as the vendor does in research and develop- ment. When the CTA tested its new APCs, it enhanced the reliability of its manual counts by using a three-person crew staffed by managers and data analysts who had a stake in the outcome and, therefore, reason to be meticulous in counting accurately. 8.1.2 Block-Level Screening Because APCs count both ons and offs, large errors (e.g., due to malfunctioning equipment) are easy to spot based on a large difference between total on and off counts over a bus’s daily duty (“block”). Screening criteria vary. Tri-Met rejects blocks whose on and off totals differ by more than 10%; King County Metro requires that a block’s total offs be no more than 7% below or 15% above the block’s on total. (The asym- metric criterion is a concession to recognized counting bias with its older APC system.) 8.1.3 Accuracy of Load and Passenger-Miles Measurements Because the accuracy of load and passenger-miles meas- urements depends not only on raw count accuracy, but also on the processing system’s ability to parse blocks into trips and deal with on-off imbalances, accuracy of load and related measures is a good system test and deserves to be examined in its own right. STM sets a good example, requiring that the average absolute error in departing load be less than 5%. Relative errors in load can be much greater than those of on and off counts. For example, Kimpel et al. found that, while sys- tematic error for Tri-Met’s on and off counts were below 2%, it was 6% for departing load (37). Because passenger-miles are a weighted accumulation of loads, one can expect its bias to be similar to that of load. One cause of load errors can be the balancing method used. Kimpel et al. determined load using their own trip-level balancing method, because the block-level balancing algo- rithm used by Tri-Met yielded loads with greater bias. Block- level balancing biases loads upward because upward errors are permitted to propagate through the day, while propaga- tion of downward errors is limited because of a restriction against negative departing loads. 8.2 Trip-Level Parsing Screening based on on-off balance protects on and off totals from substantial errors. However, because of a phe- nomenon called drift, substantial errors can still develop in calculated load (accumulated ons minus accumulated offs) and passenger-miles (a weighted sum of segment loads), even with small errors in raw counts. To illustrate, suppose each trip has 2 excess ons. After five trips, load on every segment will appear to be 10 passengers greater than it actually is. APC processing software controls drift by regularly resetting the system state (i.e., load on the bus) at points of known load. On most transit routes, these points are terminals or lay- over points at which, either by custom or operating rule, the through-passenger load is zero. Blocks are then parsed at known-load points into sections that may be called “sub- blocks,” which are usually single trips or round trips, with load at the start and end of each sub-block set to zero. Data structures and processing software need to account for some trip ends being points of zero load and others not; moreover, there may be points of known zero load that are not trip ends. 8.2.1 End-of-Line Identification and Activity Attribution The earlier review of automatic location measurement pointed out difficulties often encountered in correctly iden- tifying the end of the line. This problem is most severe in older APC systems that lack sign-in data and suffer from low schedule-matching rates. When the general location of a route endpoint can be cor- rectly matched, the end-of-line arrival and departure time issues that vex running time analysis are not a concern for pas- senger counts; rather, the main challenge is attributing ons and offs to the right trip. At a simple route terminal, the usual pro- cedure is to attribute alighting passengers to the arriving trip and boarding passengers to the departing trip. Sometimes, the boarding and alighting activity are sufficiently simultaneous that APCs make a single stop record, which processing soft- ware has to split. Sometimes many stop records will be gener- ated at the terminal (and at other stops as well) as the bus may go through several cycles of opening doors to let passengers board, then closing doors to preserve or keep out the heat. On-board APC analyzers vary in their ability to take external inputs (e.g., odometer pulses) and use them in determining when to close a stop event and start a new one. Off-line pro- cessing software has to have the flexibility to recognize and handle both single- and multiple-record cases. 8.2.2 Inherited and Bequeathed Passengers Operating practices for some routes allow passengers to remain on board at the end of one trip in order to ride on the next trip. One example is a route that ends with a loop; another example is a pair of interlined routes for which nom- inally transferring passengers actually remain on board. Data structures have to identify which route ends are not necessar- ily zero-load points and recognize passengers inherited from a previous trip. 55

To permit trip-level data analysis, the most direct way to deal with inherited passengers is for databases to include an extra stop record at the start and end of each trip indicating the number of passengers inherited from the previous trip and bequeathed (left on board) to the next trip. Manual ride check forms often start and end with a row for passengers left on board. An alternative arrangement, proposed by at least one ven- dor, makes no record of inherited passengers but assumes that any imbalance in ons and offs at the trip level can be explained as inherited or bequeathed passengers. If a trip has more offs than ons, the difference is treated as passen- gers inherited at the start of the trip; if more ons than offs, the difference is treated as bequeathed passengers at the end of the trip. However, this shortcut has several shortcomings. Imbalance can be due to counting errors as well as inherited passengers. In the face of counting errors, this approach will violate the law of conservation, because it does not guaran- tee that the number of passenger bequeathed by one trip equals the number inherited by the next. By forcing correc- tions to be positive (i.e., as opposed to correcting imbalance by reducing ons or offs), it biases upward the number of pas- sengers; and by concentrating the corrections at the route ends, it increases average passenger trip length. Together, these factors combine to bias passenger-miles upward. Also, this approach cannot resolve imbalances on routes with loops at both ends. 8.2.3 Routes Ending in Loops Many transit routes end in loops that lack a natural termi- nal point at which buses always empty out. Examples are radial routes with a loop at the suburban end for wider cov- erage and commuter routes with a collection/distribution loop through the downtown, such as NJ Transit routes into Philadelphia. There are three ways to deal with attributing passengers who board or alight on these loops; each approach has important implications for data structures. The Round-Trip Approach The simplest approach is treating the round trip as a single trip. However, the way an agency defines its trips is part of a business model that carries into its scheduling database, with which the APC database must be consistent. Therefore, this solution is only available to the extent that the schedule data- base is constructed in terms of round trips. The Terminal-Stop Approach A second way—perhaps the most common—to deal with a loop is to designate a terminal stop somewhere in the loop; there may be a short layover scheduled there. Through load at this point is treated as passengers inherited by the trip leaving the loop. The Overlapping Loop Model for Short Loops A third approach, used by NJ Transit on its Philadelphia routes (38), is to model a bus in a loop as serving two trips at once, attributing alightings to the trip entering the loop and boardings to the trip exiting the loop. Figure 19 illustrates the overlapping loop model. With this model, boardings and alightings occurring within a loop are attributed to the trip that “naturally” serves those passengers; there are no explicit inherited passengers, avoiding messy apparent transfers. This model is also well suited to making balancing corrections. The overlapping loop model relies on two assumptions about passenger travel: • General Loop Assumption: No passenger rides around the entire loop. • Short Loop Assumption: No passenger’s trip lies entirely within the loop. Discretion is needed in defining the boundary between the entering and exiting trip for boardings. For NJ Transit routes into Philadelphia, boardings on the exiting trip clearly begin at the first Philadelphia stop. However, on some routes with loops, the exiting trip’s boardings may begin at the last trunk stop (Stop A in Figure 19) if travel time around the loop is smaller than the service headway, in which case passengers waiting at A' have nothing to lose by boarding at A and circling the loop. With the overlapping route model, a short loop effectively serves as a fixed-load point for parsing, screening, and on-off balancing. For the entering trip, load is fixed at zero when it has finished serving the loop; for the exiting trip, load is fixed at zero as it begins serving the loop. An example of fixing and balancing load on a loop with four stops (A through D) is shown in Table 9. In Table 9(a), there is an imbalance of 2 excess offs; however, after the data is split into entering and exiting trips, one can see that the entering trip actually has 4 excess offs and the exiting trip 2 excess ons. Corrections are made in Table 9(b) to the entering and exiting trip separately, following the balancing procedure described later in Section 8.3. Applying the overlapping route model requires data struc- tures that recognize loop start and end points and the rela- tionship between the trips entering and exiting the loop. The model can be used only as part of processing the raw counts; corrected counts are returned to a database without overlap- ping routes. If the model is used in such a manner, a stop in the loop is designated as the terminal where stop records are inserted that give the number of bequeathed and inherited passengers. It is easy to show that 56

where EarlyOns equal ons in the loop before the terminal, and LateOffs equal offs in the loop after the terminal. As shown in Table 9(c), inherited passengers = (5+5) + 9 = 19. It is also possible to have an overlapping route data struc- ture in the final database of corrected counts. Such a data structure would allow analyses that treat the entire loop as part of both the trip entering and the trip exiting the loop, with passenger movements on the loop appropriately attributed. That data structure requires methods to prop- erly deal with overlapped sections. For example, the actual vehicle load within the loop is equal to the sum of load on the entering trip and load on the exiting trip. As another example, care must be taken not to double count operat- ing statistics on the loop such as vehicle-miles or schedule deviations. 8.2.4 Routes Without a Fixed-Load Point or Short Loop The few routes that do not have a zero-load point or short loop at either end pose a challenge for preventing drift. Exam- ples are downtown circulators and routes with long loops at Inherited Passengers EarlyOns LateOffs= + ( )2 both ends. Simply letting ons and offs accumulate all day long, and taking the difference as load, invites drift errors if ons are overcounted early in the day, even after total ons and offs over the day have been balanced. The only solution that has been suggested involves opera- tor intervention: having the operator count and enter, via the control head, the load at a certain point in each cycle, prefer- ably a point where the load is normally low. While requiring operator input violates the traditional design philosophy of APCs, it may be the only way of ensuring reliable load data on routes without zero-load points. Buyers in this situation can request that a new APC system support an operator-initiated “observed load event,” including an automatic prompt at the designated location. 8.2.5 Accounting for Operator Movements Most operator off/on movements occur at layover points when the bus is empty. Absent counting errors, an operator who gets off and back on an empty bus at a layover point can be detected because such movements cause an apparent through load (arriving load minus offs) of −1, or a still more negative number if the operator gets off and on several times, for example, to adjust a mirror. 57 A' A B a. Attributing Boardings Trip Entering Loop Trip Leaving Loop A' A B b. Attributing Alightings Trip Entering Trip Leaving Figure 19. Overlapping loop model.

The researchers are not aware of efforts in APC data pro- cessing to identify and exclude operator movements; clearly, there is a need for such algorithms, especially those that work well in the presence of possible counting error. 8.3 Trip-Level Balancing Methods Comparing on and off totals gives APCs a built-in error check. Large errors can simply be screened out; that is part of the advantage of the large sample size that comes with auto- mated data collection. Counts with smaller imbalances will be accepted, leaving the question of how counts should be cor- rected in order to balance ons and offs. Besides achieving on-off balance, corrections aim to pre- vent negative loads. The algorithms the researchers have seen consider only departing load. A more stringent feasibility test looks also at through load. For example, suppose a bus arrives at a stop with a load of 2 passengers; on-off counts then indi- cate that 6 passengers got off and 5 got on. The departing load is calculated to be 1, a positive number that raises no alarm. However, something about these figures is not right; how could 6 passengers get off when only 2 were on the bus? This discrepancy is clear when one calculates that through load based on these figures is −4. Negative through loads can occur if passengers (or the bus operator) get on and off at the same stops (e.g., passenger steps on the bus, finds out it is the wrong 58 Combined Entering Trip Exiting Trip Stop Off On Load Off On Load Off On Load Inherited 0 0 0 Before loop 6 42 36 6 42 36 A 10 5 31 10 26 5 5 B 10 5 26 10 16 5 10 C 10 5 21 10 6 5 15 D 10 5 16 10 -4 5 20 After loop 18 0 -2 18 0 2 Total 64 62 46 42 18 20 Entering Trip Exiting Trip Stop Off On Load Off On Load Inherited 0 0 Before loop 6 44 38 0 A 10 28 5 5 B 9 19 5 10 C 10 9 4 14 D 9 0 5 19 After loop 19 0 0 Total 44 44 19 19 Entering Trip Exiting Trip Stop Off On Load Off On Load Inherited 0 Before loop 6 44 38 A 10 5 33 B 9 5 29 C (off only) 10 19 Bequeathed / inherited 19 19 C (on only) 4 23 D 9 5 19 After loop 19 0 0 Total 35 54 28 9 (a) Splitting Data into Entering and Exiting Trips (b) Correcting Entering and Exiting Trips (c) Splitting Trips at Terminal (Stop) C Table 9. Balancing load on a loop.

bus, and steps off); but that is a rather rare occurrence, except perhaps at terminals. To account for an occasional balker or an operator getting off and back on, correction algorithms can set −1 as the lower limit on through load, something illus- trated in the following example. Offs occurring at terminals well after the bus has arrived and discharged its load are likely to be balkers, and processing algorithms may explicitly seek to identify and deal with them. 8.3.1 Selecting Target On/Off Total In a sub-block, boundary conditions require that the differ- ence between total ons and offs equal the difference between bequeathed and inherited passengers. If the totals do not bal- ance, should total ons be adjusted to match total offs, or vice versa, or should the correction be shared between the two? If the counting system has known error patterns, they can be taken into account in selecting the target. Let Ton , Toff = target (corrected) sub-block ons and offs total Ton, Toff = block level raw totals for ons and offs M = bequeathed–inherited passengers for the sub- block (given) kon, koff = external adjustment factors for ons and offs s2on, s 2 off = variance of sub-block errors for on and off totals con = 1/s 2 on, coff = 1/s 2 off The external adjustment factors are correction factors an agency might have that account for known systematic bias; for example, kon = 1.03 implies that ons have a systematic undercount of 3%. From information theory, the best (least variance) esti- mates are given by When M = 0, this expression is a weighted average of adjusted on and off totals, using relative certainty as weights. For example, if con/coff = 3 and a sub-block had 4 excess ons, the correction would be to reduce ons by 1 and increase offs by 3. Even if on counts are known to be more accurate than off counts, or vice versa, the target is more accurately estimated using information from both sets of counts, rather than ignoring the weaker set. 8.3.2 Distributing Corrections One simple way to distribute corrections that has already been mentioned is to put them at the end (or start) of the sub- block. The method used in TriTAPT is to make the correc- T T Moff on = − ( )4 T c k T c k T Mc c c on on on on off off off off on off  = + + + (3) tions to the largest counts, the assumption being that count- ing errors are more likely to have occurred there. Another systematic method uses proportional corrections. One simply multiplies all the ons in a sub-block by the cor- rection factor f = Ton /Ton, and all offs by the correction factor f = Toff /Toff. This method has two desirable properties: first, it leaves the alighting and boarding centroids unchanged, leav- ing average passenger trip length unaffected; second, it calls for greater corrections where counts were greater, which is consistent with the notion that the bigger the count, the more likely an error. A rounding procedure is illustrated in the example that fol- lows. To round ons, first generate the profile of cumulative adjusted ons; round the cumulative profile; and then gener- ate rounded ons by stop as the difference between successive cumulative ons. As mentioned earlier, this rounding proce- dure can be applied to force counts in the database to be inte- gers, or it can be applied when generating reports. 8.3.3 Correcting Negative Loads After a sub-block is balanced, calculated loads may be neg- ative at one or more points along a route. Most commonly checked is departing load; however, a stronger test is for through load (departing load minus ons). There should be thresholds for negative departing load and negative through load beyond which a trip should be rejected. Trips not rejected should be adjusted to eliminate negative loads. One option, illustrated in this section, is to allow through loads of −1 to account for an operator exiting and re- entering an otherwise empty bus, or a passenger boarding and then alighting an empty bus (e.g., upon discovering it was the wrong bus). If there are multiple points with negative load, the point of greatest violation should be corrected first, because its cor- rection is likely to cure negative loads elsewhere. The point of correction becomes a new sub-block boundary, dividing the sub-block into two new sub-blocks which are then balanced, making the procedure recursive. A balancing example is given in Table 10. Original counts [Table 10(a) and (b)] have 36 ons and 34 offs. First, target on and off totals are calculated to be 35, then ons and offs are adjusted and rounded. A check for negative loads in Table 10(c) finds the greatest violation at Stop 5. Through load there is −4, but because through loads of −1 are allowed, the violation is −3. The trip is split at Stop 5 into two new sub-blocks, which are balanced in Table 10(d) through (k). Stop 5’s offs belong to the early sub-block (the one ending at Stop 5), and its ons to the late sub-block. The early sub-block [Table 10(d) and (e)] begins with an imbalance of −3 (25 ons, 29 offs, and a target difference of −1). 59

60 Stop Input Ons Cumulative Ons Scaled Cumulative Rounded Cumulative Balanced Ons 1 12 12 11.67 12 12 2 8 20 19.44 19 7 3 6 26 25.28 25 6 4 0 26 25.28 25 0 5 2 28 27.22 27 2 6 5 33 32.08 32 5 7 2 35 34.03 34 2 8 0 35 34.03 34 0 9 1 36 35.00 35 1 10 36 35.00 35 0 Total 36 35 Target 35 f = 0.972 Stop Input Offs Cumulative Offs Scaled Cumulative Rounded Cumulative Balanced Offs 1 0 0.00 0 0 2 2 2 2.06 2 2 3 4 6 6.18 6 4 4 10 16 16.47 16 10 5 12 28 28.82 29 13 6 0 28 28.82 29 0 7 1 29 29.85 30 1 8 0 29 29.85 30 0 9 3 32 32.94 33 3 10 2 34 35.00 35 2 Total 34 35 Target 35 f = 1.029 Stop Off On Thru Load Dep Load Violation Comment 1 0 12 0 12 2 2 7 10 17 3 4 6 13 19 4 10 0 9 9 5 13 2 -4 -2 -3 split here 6 0 5 -2 3 -1 7 1 2 2 4 8 0 0 4 4 9 3 1 1 2 10 2 0 0 0 (a) Balance Ons (b) Balance Offs (c) Check for negative load (continued on next page) Table 10. Balancing initial load and correcting negative load.

Stop (d) Balance Ons, Early Subblock (g) Balance Ons, Late Subblock (j) Balance Counts (k) Differences (Balanced - Original) (h) Balance Offs, Late Subblock (i) Check for Neg Load, Late Subblock (e) Balance Offs, Early Subblock (f) Check for Neg Load, Early Subblock Input Ons Cum Ons Scaled Cum Round'd Cum Bal'c'd Ons 1 12 12 12.96 13 13 2 7 19 20.52 21 8 3 6 25 27.00 27 6 4 0 25 27.00 27 0 5 25 27.00 27 0 Total 25 f = 27 Target 27 1.080 Stop Input Ons Cum Ons Scaled Cum Round'd Cum Bal'c'd Ons 5 2 2 1.60 2 2 6 5 7 5.60 6 4 7 2 9 7.20 7 1 8 0 9 7.20 7 0 9 1 10 8.00 8 1 10 10 8.00 8 0 Total 10 f = 8 Target 8 0.800 Stop Offs Ons Thru Load Dep Load 1 13 0 13 2 2 8 11 19 3 4 6 15 21 4 9 0 12 12 5 13 2 -1 1 6 0 4 1 5 7 1 1 4 5 8 0 0 5 5 9 4 1 1 2 10 2 0 Total 35 35 Stop Input Offs Cum Offs Scaled Cum Round'd Cum Bal'c'd Offs 1 0 0.00 0 0 2 2 2 1.93 2 2 3 4 6 5.79 6 4 4 10 16 15.45 15 9 5 13 29 28.00 28 13 Total 29 f = 28 Target 28 0.966 Stop Input Offs Cum Offs Scaled Cum Round'd Cum Bal'c'd Offs 5 0 0.00 0 0 6 0 0 0.00 0 0 7 1 1 1.17 1 1 8 0 1 1.17 1 0 9 3 4 4.67 5 4 10 2 6 7.00 7 2 Total 6 f = 7 Target 7 1.167 Stop Offs Ons Thru Load Dep Load Violation 1 0 13 0 13 2 2 8 11 19 3 4 6 15 21 4 9 0 12 12 5 13 -1 Stop Offs Ons Thru Load Dep Load 1 0 1 0 1 2 0 0 1 1 3 0 0 1 1 4 -1 0 2 2 5 1 0 1 1 6 0 -1 1 0 7 0 -1 0 -1 8 0 0 -1 -1 9 1 0 -2 -2 10 0 -2 -2 Total 1 -1 Stop Offs Ons Thru Load Dep Load Violation 5 0 2 -1 1 6 0 4 1 5 7 1 1 4 5 8 0 0 5 5 9 4 1 1 2 10 2 0 0 0 Table 10. (Continued).

Target ons is calculated to be 27, target offs to 28. Corrections are distributed proportionally and rounded as before. Note that in balancing the late sub-block in Table 10(i), through load at Stop 5 is initialized to −1, the correction target. Both segments, after balancing, have no negative load vio- lations, so the correction procedure ends. 8.3.4 Other Count Correction Issues Independent of the balancing procedure, several questions related to databases and corrected counts arise: • Should the database store corrected counts, or should corrections be made on the fly? In the APC analysis sys- tems studied, corrections are made on the fly. However, those systems used simple algorithms, not accounting for inherited passengers or loops. With more complex cor- rection algorithms, it seems preferable to make correc- tions during entry processing, storing the corrected counts in the database. • Should raw counts be stored as well as corrected counts? If corrected counts are stored, agencies and vendors both still want raw counts retained as well. Storing raw counts helps preserve the integrity of the data, is useful for investi- gations, and can be used for testing new balancing methods. • Can records with invalid counts be retained? There are likely to be many trips for which count data is judged invalid, but for which time and location data, useful for analyzing operations measures such as schedule adherence, is not. The reverse can also be. This concern is met by including flags in the database for “counts invalid” and “times invalid.” • Should corrected counts be forced to be integers? Most users prefer that corrected counts be integers. The appear- ance of fractional counts in a database tends to raise ques- tions and emphasizes that the raw counts were deemed incorrect. On the other hand, it is quite possible to store fractional counts and simply round analysis results. • Should the database store load, or should it be derived from counts? Passenger load can be derived on the fly from counts starting at the beginning of a trip, provided there are records for inherited passengers. However, storing cor- rected load can be a way of compensating for not storing corrected on/off counts or inherited passengers, as is the practice at Tri-Met. Tri-Met uses uncorrected counts in analyses of boardings, while for analyses involving load it uses balanced load estimates. 62