Project Description
Table1: Summary of Population & Originating Typical Weekday TripsCounty / Population / Census Blocks / Originating Trips / Pixels w/Originations / Average Length of Originating Trips
name / # / # / # / # / miles
… / integer / integer / integer / integer / Single decimal
… / integer / integer / integer / integer / Single decimal
Somerset / 323,444 / 3,836 / 1,268,224 / 1,049 / 15.4
… / integer / integer / integer / integer / Single decimal
State Total / integer / integer / integer / integer / Single decimal
External Zones
NYC / NA / NA / integer / integer / Single decimal
PHL / NA / NA / integer / integer / Single decimal
… / NA / NA / integer / integer / Single decimal
Rockland / NA / NA / integer / integer / Single decimal
External Total / NA / NA / integer / integer / Single decimal
Total (State +Externals) / NA / NA / integer / integer / Single decimal
County Analyses
Somerset County
Somerset County is located in central New Jersey. It is a mid-sized New Jersey county that has 21 municipalities and area of 304.86 square miles with a population of 323,444. Its largest city is Franklin Township. It enjoys a balance between urban/suburban neighborhoods and rural countrysides. One of the oldest counties in America, Somerset County is also the ninth-wealthiest county in the US by per capita income and the wealthiest county in New Jersey in that regard.
Source:
Somerset County Government Website:
http://www.co.somerset.nj.us/
Wikipedia:
http://en.wikipedia.org/wiki/Somerset_County,_New_Jersey
Figure1: Map of Somerset County
(Source: “Somerset County, New Jersey”, Wikipedia)
Figure 2: County View on Google Earth
Somerset County Summary DataItem / value
Area (sq miles) / 304
# of pixels generating at least one O_Trip / 1,049
Area of pixels / 262
% “Open Space” / 13.4%
# of pixels generating 95% of O_Trips / 566
# of pixels generating 50% of O_Trips / 95
# of Intra-pixelTrips / 8,431
# ofO_ WalkTrips / 64,326
#All_O_Trips / 1,268,224
Average All_O_TripLength*(miles) / 14.6
# O_aTaxiTrips / 1,195,467
Average O_aTaxiTripLength (miles) / 15.4
Median O_aTaxiTripLength (miles) / 6.8
95% O_aTaxiTripLength (miles) / 17.8
*All TripLengths are ManhattanDistances between pixel centroids
Intra-pixel Trips
[2D plot of # of intra-pixels trips vs. rank of pixels]
[CDF (0,1) of normalized intra-pixel trips vs. pixels]
[3D volume plot of intra-pixel trips – only top 50 volumes]
[Google Earth 3D skyscrapers of pixels]
Analysis on the Top Intra-pixels with the Most Trips
If we zoom into the top intra-pixels in Google Earth, we will find that most of those pixels are either residential areas, town centers, or shopping centers. The #1 intra-pixel corresponds to the large shopping area on the northeast corner of the county, which will be further discussed in the top aTaxi stands section. The #2,#4,#5 intra-pixels are all residential districts, one of which also has an elementary school (Mt. Prospect Elementary school) nearby, while #3 intra-pixel is right in the center of Bound Brook borough. It is not surprising that most of the shortest distance trips (those that are within a pixel) occur in places with the most concentrated populations. Regarding the residential areas, there are usually a number of restaurants, stores, or recreational facilities in those pixels, so it seems that people are walking to get food, shop everyday stuff, or do sports.
Pixel Coordinates:
Y_aTaxi / X_aTaxi / Latitude / Longitude365 / 172 / 40.64109986 / -74.42067085
347 / 146 / 40.51085384 / -74.65940665
354 / 159 / 40.56150507 / -74.54003875
335 / 157 / 40.42402315 / -74.55840304
367 / 149 / 40.65557164 / -74.63186021
[Google Earth image of the #2 intra-pixel]
O_Walk Trips
[2D plot of # of intra-pixels trips vs. rank of pixels]
[CDF (0,1) of normalized intra-pixel trips vs. pixels]
[3D volume plot of intra-pixel trips – only top 50 volumes]
[Google Earth 3D skyscrapers of pixels]
Analysis on the Top Walk Pixels with the Most Trips
Similar to intra-pixel trips, walk trips are the ones that are relatively short in distance where people are most likely to use their feet instead of cars or other transit modes to get to their destinations. The #1 pixel again corresponds to the large shopping area on the northeast corner of the county. The #2 pixel is the same residential area of the #4 pixel of the intra-pixel trips. The #3 to #5 are adjacent pixels and represent the center of Franklin Township, the largest city in Somerset County. Apparently, most walk trips happen in the center of a city or residential areas.
Pixel Coordinates:
Y_aTaxi / X_aTaxi / Latitude / Longitude365 / 172 / 40.64109986 / -74.42067085
335 / 157 / 40.42402315 / -74.55840304
343 / 165 / 40.48191027 / -74.48494587
344 / 166 / 40.48914616 / -74.47576373
345 / 166 / 40.49638205 / -74.47576373
[Google Earth image of the #4 walk pixel]
All Trips
[stacked plot of intra-pixel, O_Walk, and all other O_Trips vs. rank of pixels]
As the summary table indicates, more than 94% of the trips belong to aTaxi Trips. Walk trips contribute to about 5% of the total, while intra-pixel trips are only 1% of the total trips originated in Somerset County.
O_Trips (trips without intra-pixel and walk)
[2D plot of # O_Trips vs rank of aTaxiStand]
[Cumulative Distribution (0,1) of normalized # O_Trips vs rank of aTaxiStand, the biggest first]
[Cumulative distribution of all aTaxi trips vs. distance (in pixels)]
[Cumulative distribution of all aTaxi trips vs. time of day]
[Google Earth 3D skyscrapers of pixels]
Analysis of Selected aTaxi Stands
#1 aTaxi Stand
[Google Earth Pixel Grid Image]
[Cumulative distribution of #1 aTaxi trips vs. distance]
[Cumulative distribution of #1 aTaxi trips vs. time of day]
The #1 pixel of aTaxi trips represent the large shopping area in Plainfield mentioned earlier as the #1 pixel for both intra-pixel trips and walk trips. There are 31,964 trips originated from this pixel during the day. This shopping area (the diagonal stripe in the above image) consists of major shopping attractions such as Walmart, Modell’s Sporting Goods, Bed Bath and Beyond, Home Depot, Petco, etc. As indicated by the cdf distance graph above, most of those trips are less than 5 miles in distance, therefore it seems that most of the shoppers are local residents. It is right to the west of the border between Somerset County and Union county so residents from both counties are visiting this area.
The cdf time of day graph has no morning peak, which is consistent with the fact that there is no morning home-work or home-school trips generated in the shopping area. There is a slight jump right after noon, possibly indicating some shoppers are leaving the area and heading for lunch. The afternoon trip numbers increase smoothly, indicating the fact that the departure times when people leave from shopping to (possibly) home are uniformly distributed through out the afternoon and into late evening from 3 pm to 10 pm. For shoppers, obviously, there is no “rush hour” effect since most people leave whenever they want to.
#5 aTaxi Stand
[Google Earth Pixel Grid]
[Cumulative distribution of #5 aTaxi trips vs. distance]
[Cumulative distribution of #5 aTaxi trips vs. time of day]
The #5 aTaxi pixel has 12,937 originated during the day. It is an area with concentrated professional offices in Franklin Township. There are companies, such as MetLife, Blenheim Capital Management, Aon Consulting, Maitra Associates, Tuner Construction Co., Sun Microsystems, Phillips Lighting Co., Applied Info Partners, as well as many hotels in this area. Most trips have longer distances than the ones in the #1 aTaxi pixel discussed above, possibly due to the fact that people need to drive longer distance to go home at the end of day. While shoppers are quite unlikely to go very far for a Walmart, employees are much more likely to drive a relative long distance to go to work. There is no morning peak since it is not a residential area. One interesting observation is that the number of originated trips jumped up dramatically after 7:30 pm. It could either be employee going home after work or visitors going back to their hotels after meetings, etc. While the usual after-work peak hours are 4pm to 7pm, in this case, it is more like 7:30 pm to 9 pm. Interestingly, most of the companies in this area are consulting or financial services firms. It seems that employees in the financial and consulting industries do work very hard and usually do not get out of their offices until after 7:30 pm.
Pixel Coordinates:
Y_aTaxi / X_aTaxi / Latitude / Longitude365 / 172 / 40.64109986 / -74.42067085
347 / 164 / 40.51085384 / -74.49412802
349 / 161 / 40.52532562 / -74.52167446
343 / 165 / 40.48191027 / -74.48494587
350 / 161 / 40.53256151 / -74.52167446
RideSharePotential (RSP)
For any aTaxiStand (pixel) during any Time-of-Day (ToD) the RideSharePotential (RSP (ToD, Occ, CD, DD) ) is described by the distribution of the number of normalized aTaxis dispatched during the appropriate ToD, (RSP (ToD)) versus the occupancy of the dispatched vehicles (Occ), where Occ is the number of customers that arrive at an aTaxiStand destined to Common ride-sharing Destinations (CD) within a fixed DispatchDelay (DD) time interval. These customers are served by a common aTaxi. The more CDs the greater the RideSharePotential but the worse the quality service. Also, the longer the DD, the greater the RideSharePotential but the worse the quality of service. Initially CD is taken as 1(destination aTaxiStand must match identically) and values of DD are be taken as integer minutes from 1 through 5. By taking all of the O_Trips(i,j) arriving at aTaxiStand (i,j) and during the specified ToD, sort O_Trips(i,j) in ascending arrival time. Ride sharing is simulated by taking the time of the next arriving passenger, dispatching all waiting aTaxis that have exceeded their DD, recording their occupancy at time of dispatch, scanning the yet-to-be-dispatched aTaxis for a CD match, if found: direct this arriving passenger to the CD matched aTaxi, thus increasing its occupancy by one and delaying this passenger’s departure time to the departure time of this aTaxi (which was set to be DD minutes after the first occupant’s original departure time); else: direct the passenger to occupy a new waiting aTaxi, set its destination to that of this first passenger and delay this passenger’s and this aTaxi’s departure time by DD . Sequencing through the set of O_Trips will yield the RSP (ToD, Occ, CD,DD) for that set of O_Trips.
CD=1 (one common destination)
#1 aTaxi Stand
#2 aTaxi Stand
#3 aTaxi Stand
#4 aTaxi Stand
#5 aTaxi Stand
All Stands
As indicated by the graphs above, even for the #1 aTaxi pixel and departure delay of a value of 5 minutes, with only one common destination, we do not see many ride share opportunities.
Additional analysis on the most important aTaxi Stand: #1 aTaxi Stand (OY=365, OX=172)
[Top 100 trips in the day from #1 aTaxi Stand]
[Top 50 trips in the peak hour from #1 aTaxi Stand]
This is the shopping area we mentioned above. Most of the departure trips are heading to nearby neighborhoods, confirming my analysis earlier that most of trips are generated by shoppers and most shopper are local residents either from Somerset County or Union County. The destinations seem to be dispersed quite evenly except that there are a few longer distance trips heading down to the south parts of New Jersey such as Middlesex county. From the second graph, it seems that most of those long distance trips are generated during the peak hours, possibly explained by the fact that employees working in the shopping area are travelling relatively long distance to go to work, and most of them are from areas south of the shopping center.
Again, the above two graphs are very helpful for us to understand where the destinations of the trips from the top trip-generating pixel are distributed. For shoppers, they are heading to all the nearby surrounding areas; while for employees, they are mostly travelling relatively far to the southeast areas, which are very likely to be where they actually live.
Appendix A
Relevant Code
SOM_Volume.nb
(https://www.dropbox.com/home/ATaxi%20Project%20Code/Final%20Mathematica%20Documents/Current)
SOM_RideShare.nb
(https://www.dropbox.com/home/ATaxi%20Project%20Code/Ride%20Share%20Code/Final%20Mathematica%20Documents)
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