{"id":242,"date":"2017-03-29T15:05:35","date_gmt":"2017-03-29T15:05:35","guid":{"rendered":"http:\/\/ajhassoc.com\/?p=242"},"modified":"2017-05-17T01:36:33","modified_gmt":"2017-05-17T01:36:33","slug":"a-well-choreographed-od-table-dance-part-2-example","status":"publish","type":"post","link":"https:\/\/ajhassoc.com\/index.php\/2017\/03\/29\/a-well-choreographed-od-table-dance-part-2-example\/","title":{"rendered":"A Well Choreographed OD Table Dance, Part 2: Example"},"content":{"rendered":"
\n

This blog post provides a numerical example for the previous blog post.\u00a0 Recall that we are given a before OD table, a before travel time matrix and an after travel time matrix.\u00a0 We want to find the after OD table.<\/p>\n

A further goal of this problem is to avoid fancy software, so I have attempted to illustrate this technique solely in Excel.\u00a0 However, I later demonstrated the strength and weaknesses of the technique by comparing its results to travel demand forecasting software.\u00a0 I used the very familiar UTown test network in QRS II, starting with the outputted OD table and travel time matrix that comes from a \u201cbefore\u201d alternative of the model.\u00a0 The modification for the \u201cafter\u201d alternative was a 15% increment of free speeds on the UTown freeway.<\/p>\n

You have likely seen UTown in years past, but here is what it looks like in QRS II.<\/p>\n

\"\"<\/p>\n

There are 5 zones, and there are many congested links. Should you want to replicate the complete example and the comparison, you can do so easily with the free demo edition of QRS II, downloadable from ajhassoc.com<\/a>.\u00a0 The UTown network is included.\u00a0 Note:\u00a0 QRS II rounds travel times to the nearest whole minute for trip distribution calculations, so we will too in the spreadsheet.<\/p>\n

The Data<\/h3>\n

QRS II was used for creating the \u201ctrue\u201d before case and the after travel time matrix. \u00a0QRS II\u2019s default trip distribution step is a doubly-constrained gravity model.\u00a0 All parameters were QRS II defaults, except I substituted 0.07 for the HBW coefficient of the gravity model, as suggested in Part 1 of this blog.\u00a0 I also ran 30 iterations of MSA with feedback.\u00a0 The UTown network was originally set up for a PM peak hour (much preferred), but it was changed to a 24-hour time period for this example.\u00a0 UTown has three trip purposes \u2013 HBW, HBNW and NHB.\u00a0 The before OD table, rounded, is shown just below.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

45035<\/p>\n<\/td>\n

\n

4927<\/p>\n<\/td>\n

\n

9033<\/p>\n<\/td>\n

\n

16753<\/p>\n<\/td>\n

\n

8723<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

4929<\/p>\n<\/td>\n

\n

11101<\/p>\n<\/td>\n

\n

3110<\/p>\n<\/td>\n

\n

6489<\/p>\n<\/td>\n

\n

4441<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

9032<\/p>\n<\/td>\n

\n

3107<\/p>\n<\/td>\n

\n

28849<\/p>\n<\/td>\n

\n

20468<\/p>\n<\/td>\n

\n

5261<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

16649<\/p>\n<\/td>\n

\n

6449<\/p>\n<\/td>\n

\n

20344<\/p>\n<\/td>\n

\n

49062<\/p>\n<\/td>\n

\n

14750<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

8750<\/p>\n<\/td>\n

\n

4451<\/p>\n<\/td>\n

\n

5279<\/p>\n<\/td>\n

\n

14849<\/p>\n<\/td>\n

\n

21046<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Note that this table is almost symmetrical, as expected. All spreadsheet calculations were performed using unrounded trips so that I could get a clean evaluation of the technique.<\/p>\n

The rounded, before travel time matrix is shown next.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

23<\/p>\n<\/td>\n

\n

21<\/p>\n<\/td>\n

\n

30<\/p>\n<\/td>\n

\n

19<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

33<\/p>\n<\/td>\n

\n

17<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

20<\/p>\n<\/td>\n

\n

25<\/p>\n<\/td>\n

\n

5<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

27<\/p>\n<\/td>\n

\n

31<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

28<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

27<\/p>\n<\/td>\n

\n

36<\/p>\n<\/td>\n

\n

7<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0And finally, the after travel time matrix is shown, also rounded.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n

\n

21<\/p>\n<\/td>\n

\n

30<\/p>\n<\/td>\n

\n

18<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

34<\/p>\n<\/td>\n

\n

17<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

20<\/p>\n<\/td>\n

\n

25<\/p>\n<\/td>\n

\n

5<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

21<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

27<\/p>\n<\/td>\n

\n

32<\/p>\n<\/td>\n

\n

22<\/p>\n<\/td>\n

\n

6<\/p>\n<\/td>\n

\n

28<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

23<\/p>\n<\/td>\n

\n

24<\/p>\n<\/td>\n

\n

26<\/p>\n<\/td>\n

\n

36<\/p>\n<\/td>\n

\n

7<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0Only a few cells are affected by the speed change, given the rounding.<\/p>\n

The Model<\/h3>\n

I factored the before OD table into 4 component tables: HBW, P-A; HBW, A-P; HBNW+NHB, P-A; and HBNW+NHB, A-P.\u00a0 Simple constant factors of 0.1, 0.1, 0.4, and 0.4, respectively, were used.\u00a0 Singly-constrained gravity models (exponential form) were fitted to each table, conventionally.\u00a0 The process for the A-P tables were almost exactly the transpose of the P-A tables.\u00a0 That is, for the P-A tables row totals were held constant and for the A-P tables column totals were held constant. For example, the computed HBW, P-A table is shown below.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4491<\/p>\n<\/td>\n

\n

486<\/p>\n<\/td>\n

\n

1241<\/p>\n<\/td>\n

\n

1067<\/p>\n<\/td>\n

\n

1161<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

703<\/p>\n<\/td>\n

\n

767<\/p>\n<\/td>\n

\n

482<\/p>\n<\/td>\n

\n

415<\/p>\n<\/td>\n

\n

641<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1327<\/p>\n<\/td>\n

\n

333<\/p>\n<\/td>\n

\n

2993<\/p>\n<\/td>\n

\n

1279<\/p>\n<\/td>\n

\n

741<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

1257<\/p>\n<\/td>\n

\n

338<\/p>\n<\/td>\n

\n

1408<\/p>\n<\/td>\n

\n

6970<\/p>\n<\/td>\n

\n

753<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

1167<\/p>\n<\/td>\n

\n

415<\/p>\n<\/td>\n

\n

747<\/p>\n<\/td>\n

\n

643<\/p>\n<\/td>\n

\n

2465<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Observe that symmetry was no longer preserved, but symmetry is never expected in a P to A table or an A to P table, anyway.<\/p>\n

The after case was calculated by changing the travel time matrix.\u00a0 The total before and total after OD matrices were then found by summing across purposes and by summing across P-A and A-P.<\/p>\n

The Adjustments<\/h3>\n

Below is the total calculated before OD table.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

53049<\/p>\n<\/td>\n

\n

5237<\/p>\n<\/td>\n

\n

10427<\/p>\n<\/td>\n

\n

7219<\/p>\n<\/td>\n

\n

10910<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

5343<\/p>\n<\/td>\n

\n

10828<\/p>\n<\/td>\n

\n

3513<\/p>\n<\/td>\n

\n

2434<\/p>\n<\/td>\n

\n

5739<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

11237<\/p>\n<\/td>\n

\n

3402<\/p>\n<\/td>\n

\n

37247<\/p>\n<\/td>\n

\n

9816<\/p>\n<\/td>\n

\n

6558<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

9211<\/p>\n<\/td>\n

\n

3036<\/p>\n<\/td>\n

\n

11838<\/p>\n<\/td>\n

\n

82654<\/p>\n<\/td>\n

\n

5796<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

8066<\/p>\n<\/td>\n

\n

3628<\/p>\n<\/td>\n

\n

4873<\/p>\n<\/td>\n

\n

3401<\/p>\n<\/td>\n

\n

27426<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Comparing the calculated and \u201ctrue\u201d before OD matrices revealed some large errors, particularly for the Eastern Zone, but the calculations seemed good enough to give reasonable sensitivities, so I continued.<\/p>\n

Next I found the ratio of the calculated after table to the calculated before table. Numbers greater than 1 represent forecasted increases.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

0.987109<\/p>\n<\/td>\n

\n

1.037067<\/p>\n<\/td>\n

\n

0.988521<\/p>\n<\/td>\n

\n

1.000678<\/p>\n<\/td>\n

\n

1.057502<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

1.037<\/p>\n<\/td>\n

\n

1.006882<\/p>\n<\/td>\n

\n

1.000194<\/p>\n<\/td>\n

\n

0.976218<\/p>\n<\/td>\n

\n

0.977942<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

0.988516<\/p>\n<\/td>\n

\n

1.000166<\/p>\n<\/td>\n

\n

0.991816<\/p>\n<\/td>\n

\n

1.002809<\/p>\n<\/td>\n

\n

1.055211<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

1.000671<\/p>\n<\/td>\n

\n

0.97618<\/p>\n<\/td>\n

\n

1.002801<\/p>\n<\/td>\n

\n

1.001599<\/p>\n<\/td>\n

\n

0.999468<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

1.057384<\/p>\n<\/td>\n

\n

0.97781<\/p>\n<\/td>\n

\n

1.055104<\/p>\n<\/td>\n

\n

0.999466<\/p>\n<\/td>\n

\n

0.966808<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Notice that the largest fractional increases corresponded to those cells that experienced significant travel time decreases.\u00a0 The remaining cells changed seemingly at random, but nothing is truly random in this problem.<\/p>\n

The Forecast<\/h3>\n

The ratios were then applied to the original \u201ctrue\u201d OD table, recalling that the only relevant output of this exercise was the set of cell adjustment factors. Here, finally, is the computed after OD table.<\/p>\n\n\n\n\n\n\n\n\n
<\/td>\n\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n<\/tr>\n

\n

3\u00a0\u00a0\u00a0 Northern<\/p>\n<\/td>\n

\n

44455<\/p>\n<\/td>\n

\n

5110<\/p>\n<\/td>\n

\n

8929<\/p>\n<\/td>\n

\n

16764<\/p>\n<\/td>\n

\n

9225<\/p>\n<\/td>\n<\/tr>\n

\n

4\u00a0\u00a0\u00a0 Northwestern<\/p>\n<\/td>\n

\n

5112<\/p>\n<\/td>\n

\n

11177<\/p>\n<\/td>\n

\n

3111<\/p>\n<\/td>\n

\n

6335<\/p>\n<\/td>\n

\n

4343<\/p>\n<\/td>\n<\/tr>\n

\n

2\u00a0\u00a0\u00a0 Central<\/p>\n<\/td>\n

\n

8928<\/p>\n<\/td>\n

\n

3108<\/p>\n<\/td>\n

\n

28613<\/p>\n<\/td>\n

\n

20525<\/p>\n<\/td>\n

\n

5551<\/p>\n<\/td>\n<\/tr>\n

\n

1\u00a0\u00a0\u00a0 Eastern<\/p>\n<\/td>\n

\n

16660<\/p>\n<\/td>\n

\n

6295<\/p>\n<\/td>\n

\n

20401<\/p>\n<\/td>\n

\n

49141<\/p>\n<\/td>\n

\n

14742<\/p>\n<\/td>\n<\/tr>\n

\n

5\u00a0\u00a0\u00a0 Southwestern<\/p>\n<\/td>\n

\n

9253<\/p>\n<\/td>\n

\n

4352<\/p>\n<\/td>\n

\n

5570<\/p>\n<\/td>\n

\n

14841<\/p>\n<\/td>\n

\n

20347<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0Since, the total of all trips closely matches the “true” OD table, further scaling was not needed.<\/p>\n

The Evaluation<\/h3>\n

When the QRS II after OD table (being the “true” result) was compared with the spreadsheet calculated OD table, the largest deviation in any cell value was less the 0.5 trip (a negligible amount).\u00a0 Thus, one could reasonably conclude that this techniques is a decent substitute for a full travel demand forecasting model run, with some provisos.\u00a0 Particularly important is the need for a good set of friction factors.\u00a0 In this experiment the good quality of the friction factors was assured, so it is likely that truly borrowed friction factors will not perform quite as well.<\/p>\n

Perhaps this technique should be added to a revised NCHRP Report 765 or the Hawaii Guidelines.<\/p>\n

Alan Horowitz, Whitefish Bay, March 29, 2017<\/em><\/p>\n

 <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

This blog post provides a numerical example for the previous blog post.\u00a0 Recall that we are given a before OD table, a before travel time matrix and an after travel time matrix.\u00a0 We want to find the after OD table. A further goal of this problem is to avoid fancy software, so I have attempted …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"enabled":false},"version":2}},"categories":[6],"tags":[],"class_list":["post-242","post","type-post","status-publish","format-standard","category-project-level-forecasting","anons"],"yoast_head":"\nA Well Choreographed OD Table Dance, Part 2: Example - QRS II Page<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ajhassoc.com\/index.php\/2017\/03\/29\/a-well-choreographed-od-table-dance-part-2-example\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Well Choreographed OD Table Dance, Part 2: Example - QRS II Page\" \/>\n<meta property=\"og:description\" content=\"This blog post provides a numerical example for the previous blog post.\u00a0 Recall that we are given a before OD table, a before travel time matrix and an after travel time matrix.\u00a0 We want to find the after OD table. 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