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16 .1
Chapter 16
Network Assignment
In this chapter, the fourth, and last, com ponent of the crim e traveldem an d m od el w ill be described . Network assignment involves the assigning ofpred icted trips to particular routes. The p redicted trips are those that areeither pred icted from the trip distr ibution sta ge or from the m od e split stag e. In the form er case, all trips from each origin zone to each destination zone areassigned to a particular trave l rou te, usually on the assum ption that they alltrave l with the sam e m ode of travel (usu ally w alking, biking or driving). Inthe latter case, the predicted trips from each origin-destination zone pair byspecific trave l m od es are assign ed to a p articu lar rou te which is m od e specific. Thus, bus trips are assign ed to bus routes ; train trips are assigned to trainroutes; driving trips are assigned to a road ne twork; walking trips areassigned to a m ore limited road network; and biking trips are assigned to am ixture of roads and bike paths. In other words, the assignm ent of travelm odes is specific to a particu lar ne tw ork.
Once the trips are assigned to routes, several statistics can becalculated. First , the predicted path from an origin zone to a dest ination zonecan be displa yed. T his can very usefu l for p olice who cou ld in crease th eirpatrol on high crim e routes. Second, the entire trip load on road segm ents canbe calculated . Since m any crim e trip routes pass over the sam e netw orksegm ents (e.g., freewa ys, m ajor arterial roads), the total num ber of predictedtrips on a segm ent can be en um erated. The result is a m ap of the m ostheavily traversed segm ents in the network. Again, this can be very useful forpolice.
Thus, the network assignment completes the four stage modelingprocess of the crime travel dem and framew ork. To sum m arize, in the firststage - trip generation , sep arate m odels of th e num ber of crim es origin atingin each zone and the nu m ber o f crimes en ding in each zone are developed. Inthe second stage - trip distribution, the predicted num ber of crim esoriginating in each zon e are allocated to each destination zone; the result is aprediction of the num ber of trips that occur between each origin-destinationzone pair. In the third stage - mode split, each predicted origin-destinationtrip pair is separated (split) into distinct travel m odes (e.g., walking, biking,driving, bus, train) with the result being a m ode-specific origin-destinationzone pair. Finally, the fourth stage - network assignm ent, assigns these tripsto specific routes.
Theoretical Background
To un derstand the background, we need to look, first, at the nature ofnetw orks and second, at types of routing algorithm s.
16 .2
Networks
The m ost fundam en tal elem en t of assign m en t is, o f course, a netw ork. The netw ork can be a road netw ork , a bus netw ork (e.g., bus routes w ithstops ), a train ne tw ork (e.g ., train lines w ith station s), or even a b icyclenetwork (e .g ., a mixture of roads and bicycle paths). Other kinds of networkscan also be considered, for example telecom m unication lines or even traderoutes. W e w ill concentrate on urba n transportation n etworks, how ever.
Th e m athem atical properties of netw orks are know n as graph theory(Sedgewick, 2002). A network (or graph) is a set of nodes (or vertices) and aset of segm ents (or edges) that connect pairs of nodes. If there are V n odes(vertices), then there are V 2 pairs of nodes, including the distance from a nodeto itse lf. A grap h with V nod es has , at most, V(V-1)/2 segm en ts (edg es); ifm ultiple segm ents share nodes, then there w ill be even fewer.
Figure 16.1 illustrates a sim ple n etw ork . Travel occurs along thesegm en ts th rough the con necting n odes. A pa th is a sequ en ce of nodes inw hich each successive node is connected to its predecessor in the pa th. Thus,in the figure, there cannot be direct travel between node A and node C, butm ust go th rough an interm ediate node (e.g., through B or through a pathfrom D to E to C ).
Impedance of a Network
There are several properties of a network that are im portant for travelm odeling. First, the length of a segm ent is proportional to its im pedance (seechap ters 14 an d 15 ). The m ost simple kind of im pedance is distance in w hicheach unit length of the network corresponds to some unit o f distance in thereal w orld (e .g., on e inch = 1 m iles; one cen tim eter = 5 k ilom eters). T his isanalogous to the scale used in m apping systems. M ore complex types ofimped ance involve travel tim e, speed, or even generalized cost (a collection ofseveral cost elem en ts). Thus, to use th e exam ple in figure 16 .1, node A isconnected to nodes B and D . The path from A to B is 50 units long; sim ilarlengths are found for the other segm en ts in the exam ple . Th is couldrepresent distance (e.g., 50 m iles), travel tim e (e.g., 50 m inutes), orgeneralized cost (e.g., $50).1 To a graph, the units are irrelevant. As long asthe user is explicit about these an d consistent, path calculations w ill workproperly.
Bi-directional and Single Directional Networks
Bi-directional networks
Second , typical transportation netw orks are either bi-directional or singledirectional. In a b i-directional netw ork, trave l can occur in either direction. Again, using figure 16.1, if the netw ork is bi-directiona l, then travel can occu r
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from A to B or from B to A . A w ell know n exam ple of a bi-directiona l networkis the T IGE R system of the U .S. Cen sus B ureau (2004). Th is is arepresentation of all ma jor urban lines, including streets, railroad lines,census geography boundaries, jurisdictional boundaries, Congressionalboundaries, and other features . It is used to map out census areas for thepurpose of collecting the decennial Census. Virtually the entire Un ited Statesis now m app ed in the TIG ER system . Depend ing on how carefully eachjurisdiction updates the database for new roads and changes in existingroads, the TIGER system can be a very accurate spatial representation of thean u rban road system . It is a w idely available system and is often the firstnetwork that most police departments use when they create a crime m appingsystem. Figure 16.2 shows a TIGER network for Balt imore County and theCity of Baltim ore. There are 49,015 road segm ents in the TIG ER m ap show nin the figure.
Problems with the TIGER system for travel modeling
O n the other hand, for travel modeling, there are substantial problem sw ith bi-d irectional n etw orks and w ith TIG ER in p articu lar . TIG ER istypically less accurate with respect to rail lines and has virtually noinform ation about bus routes, wh ich are local in nature. Depending on h owdiligent the local governm ent is in upd ating the database, the representationm ay not be as accurate as possible (though, in general, it’s getting better overtim e).
A m ajor p roblem is that connectivity is often not tested. Since the aim ofthe TIGE R system is to represent a metropolitan area for the purpose ofcollecting the Cen sus, connectivity is not guaranteed since it’s irrelevant forthat pu rpose. It’s not clear that all roads are properly represen ted, a featurethat could substantially a lter a shortest path algorithm . For exam ple , infigure 16.1, if the segmen t from A to B w as not connected, then travel from Ato C w ould have to take a circuitous path from A to D to E to C. Having anaccurate and edited netw ork is critical for m odeling travel beha vior. W ith alarge number of segments in a TIGER system, it is often not c lear where in afile connectivity is not properly linked.
An other ma jor deficiency of the TIG ER system is the lack ofinform ation about trave l tim e or travel cost. Travel along a TIGER netw orkis defined by distance, wh ich does not change by tim e of day. It does not havecost inform ation either, wh ich m akes it less flexible for examining alternativeroutes as a function of additional cost factors (e.g., an ana lysis of travelthrough an area w ith h igh surve illance versus trav el through an area w ithlow security presen ce even if trave l through the firs t area is sh orter in t im ethan through the second area). The T IGE R system does have inform ationabout functional class of road (interstate, state highway, collector road) andit ’s possible to assign a priori speeds to the different segm ents based on theseclasses (e.g., 35 m iles per hour for Interstate highwa ys, 25 m iles per hour for
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principal arterial roads) . But, beca use the netw ork is bi-d irect ional, it ’simpossible to assign speeds for travel in opp osite directions; in reality, thereare usua lly differen ces in travel speeds in opposite d irections (e.g., travel intothe central business distr ict in the morning might be at 15 miles per hourw herea s travel in the op posite d irection m ight be at 35 m iles per h our).
Another m ajor problem with TIG ER and with a bi-directiona l networkin general is in the representation of one-w ay streets. The T IGE R systemdoes not provide this inform ation. Consequently, in using a TIGE R file formodeling travel, a shortest path could easily travel up a one-way street in thewrong direction. To make the system w ork properly, there needs to be anad ditional field in the datab ase that iden tifies a segm en t as one-w ay .
Single directional networks
A single directional (or uni-directional) network, on the other hand,allows travel in only one direction. This has the advan tage of keeping travelconsisten tly d efined . Tw o-w ay trave l is represen ted by tw o segm en ts, one ineach direction (e.g., one for travel from A to B an d one for tra vel from B to A ).O ne-w ay streets can be characterized by on ly one o f the paired directions. M ost transportation modeling networks are single directional since anaccurate representation of travel is critical. Travel t im es, speeds or costs canbe assigned to the different directions of travel between two nodes and can befurth er assign ed to different tim es of the d ay (e.g., 20 m iles per hour in them orning peak period, 15 m iles per hour in the afternoon peak period, 30 m ilesper hou r in the o ff-peak da ytim e period , an d 45 m iles per hou r at n igh ttim e).
An exam ple of a single directional network is that used for traveldem an d m od elin g by m ost M etropolitan Planning O rgan izations (M PO ). These are used to m odel travel over an entire metropolitan area (regionaltrave l) an d are generally up da ted regu larly; connectivity is continuou slytested an d errors a re few in n um ber. The travel m odeling n etw ork is usuallya ‘skeleton’ network, covering all the m ajor roads - freeways, principalarter ial roads , m inor arter ial roads , and som e collector road s. They usuallydo not include m uch inform ation about local or neighb orhood streets sincethese are not very relevant for regional travel mod eling. Figure 16.3 show s am odeling netw ork used by the Baltim ore M etropolitan C ouncil for their traveldem and m odel. There are only 11,045 road segm ents in the file, less than onefourth the size of the corresp ond ing TIGER netw ork. Considering that eachsegment in a single direction, effectively only about 5,000-6,000 actual roadsare bein g rep resented in the file .
M ost im portantly, modeling networks usually include informationabout travel t im e or travel speed (which can be converted to travel t im e bydiv idin g d istance by speed) and are usually broken dow n into d ifferen t tim eperiods. Thus, it becomes possible to analyze travel at different times of theday to account for the major congestion effects that occur at the peak travel
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periods, particularly the afternoon peak. Som e m odeling networks alsoinclude information on travel costs, which include parking, toll roads, andother costs that im pact a trip. As m entioned in chapter 11, any analystwishing to develop a crim e travel demand m odel should contact the localM PO about obtaining a copy of the m odeling network used.
H int: A single directional netw ork can also be treated as bi-directional. In th is case , all the trips on that roadw ay will gen era lly be assign ed toonly on e of the paired segm ents (for a two-way pa ir). For the networkload output, particularly, this can be useful for showing the totalnum ber of trip s on a road segm en t, indep en den t of direction. O therw ise, if defined as a single directional netw ork, the loads in ea chdirection w ill be displayed separately.
Problems with modeling networks
M odeling networks also have their problems. The biggest one is thatthey do no t include all road s, but on ly th e m ore im portant regional ones. Th iscan lead to unrealistic paths bein g m od eled at a n eighborhood level (e .g.,entering or leaving a neighborhood from a centroid, rather than from a realstreet; tak ing c ircu itou s routes to travel a short distance in spa ce when , infact, there are connecting local roa ds that actually ex ist but aren ’t included inthe file). H ow ever, neighb orhood roads can usua lly be added to the netw ork toprovid e m ore detail at the neighborhood level and to correct m od elin g errors. I t’s a tedious process , but a police department could slowly update such asystem over tim e and imp rove its accuracy. Care m ust be taken in doing this,however, to ensure that connectivity is correctly portrayed.
Another problem , wh ich m ay or m ay not be critical, is that th erepresentation of roads in a m odeling network is spatially sim plif ied. Roadsegm ents are stra ight lines, rather tha n h aving curvature. In th e TIGERsystem , the basic record of a segm ent is a straight line connecting two n odes,bu t also includes up to 10 in term ediate ‘shap e gram m ar ’ nodes that de finecurvature (integrated with spatially m ore accurate inform ation from the U .S.G eolog ical Survey ). Thus , a m odeling netw ork looks a little ‘unreal’ at aneighborhood level since there are nothing but straight lines. But, asm entioned above, additional segm ents can be added to the file to improvelocal connectivity as well as fam iliarity.
Transportation Networks
The third property of a network for travel m odeling is the type ofnetw ork. Road n etw orks w ere m en tion ed above. B ut there are also tran sitnetworks (e .g ., bus routes, train routes) and even bicycle networks (e .g ., bikepaths).
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If a trip distribution m atrix of tr ips from origin s to destin ations isan alyzed by trave l m od e, th en it is critical to hav e a m od e-specific n etw ork. Using TIGER or a sim ple modeling network will im ply that all trips occur bythe existing road system . For transit trips (bus and rail) particularly, butalso for bik ing trips and possibly walking trips, featu res th at are sp ecific tothe travel m ode must be included. Bus routes will use the existing roadsystem , bu t they don’t use all roads, typica lly on ly the m ajor arteria l road s. Train systems rarely use the existing road system, but usually have dedicatedtracks. There are exceptions. Some l ight rail system s do run on arterialroads. Other rail system s will run on an arterial road, but with a gradeseparation. Depending on how the MP O conceptualizes this, there may besepara te lines for the ra il or not.
Thus, it’s very im portant to check an d ed it all netw orks th at are u sed. For transit networks, in particular, the lines needs to be connected andthoroughly tested. Figure 16.4 repeats the B altimore bus netw ork m ap fromchapter 15 (figure 15 .12). Each of the lines on the m ap represen t bus routes;there can be (and usu ally a re) m ore than on e bus rou te at an y one lin e. Typically, these are draw n as separa te line ob jects and are overlaid on eachother . This particu lar netw ork does not hav e in form ation ab ou t bus stops. Con sequently, a shortest path algorithm will choose the end nodes ofsegments to allow a trip to “enter” or “leave”. Thus, it is possible that a bustrip w ould start at a location w here there is not a bus stop. How ever, giventhat buses in B altimore and elsewh ere stop very frequently (every two orthree b locks on average), the am ou nt of error introdu ced is qu ite sm all.
W ith trains, however, it is absolutely critical that station locations beused to define the rail lines; people cannot enter or leave a train betw eenstations. Figure 16.5 shows each of the four intra-urban rail lines with thestation location s. Later in this ch apter, there w ill be a d iscussion of a u tilityfor creating rail lines from station locations. But a critical point is that eachof the end points of the rail segm ents be associated rail stations. In the figure,each of th e four ra il lines is show n in separate color. For m odeling inCrimeStat, how ever, the ind ividual lines need to be m erged in to a single file inorder for the shortest p ath routine to be able to m ove betw een rail lines (i.e.,if there are separate line objects for each line, the routine w ill not know howto m ove from one line to an oth er). Figure 16 .6 show s the fu ll rail linenetwork.
Shortest Path Algorithms
O nce a network h as been created, edited and thorough ly tested foraccurate connectivity, it can be used for a shortest path analysis. In a shortestpath for a sin gle trip (from an origin zon e to a destination zone), the routewith the lowest overall im pedance is selected. As m entioned, im pedance canbe defined in term s of dista nce, travel tim e, speed , or gen era lized cost.
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There are a num ber of shortest path algorithm s that have beendeve loped (Sedgew ick, 2002). They differ in term s of wh ether they arebreadth-first (i.e., search all possibilities) or depth -first (i.e., go stra ight to thetarget) algorith m s and whether they exam ine a on e-to-m an y rela tionsh ip (i.e.,from a s ingle origin node to m an y n odes) or a m an y-to-m an y relation sh ip (A llpa irs; from each node to ev ery other n ode).
The algorithm that is m ost com m only used for shortest path analysis ofm oderate-sized data sets (up to a million cases) is called A*, which ispronounced “A-star” (Nilsson, 1980; Stout, 2000; Rabin 2000a, 2000b;Sedgew ick, 2002). It is a one-to-man y algorithm but is an improvem ent overanother comm only-used algorithm called Dijkstra (Dijkstra, 1959). Therefore,I ’ll start first by describing the Dijkstra algorithm before explaining the A*algorithm.
Dijkstra Algorithm
The Dijkstra algorithm is a one-to-many search strategy in which ashortest path from a s ingle node to a ll other nodes is calculated . Th e rou tineis a breadth-first algorithm in that it searches all possible paths, but it buildsthe path one segm en t at a tim e. Starting from an origin loca tion (node), itiden tifies the n ode that is nearest to it and wh ich has not already beenidentified on the shortest path. After each node has been identified to be onthe shortest pa th, it is rem oved from the search possibilities. Th e algorithmproceed s until the shortest path to all nodes has b een d eterm ined. In term sof a matrix of origin nodes (on the vert ical) and dest ination nodes (on thehorizon tal - see figu re 14.1 in cha pter 14 ), the search a lgorithm estim ates theshortest path for an y one row (i.e., from a particu lar origin to a lldestinations ).
The algorithm can also be structured to find the shortest path betw eena particu lar origin node an d a particular destin ation node . In this case, it willqu it once the destination nod e h as been iden tified on the shortest p ath. Thealgorithm can also be stru ctu red to find the shortest path from each originnode to each destination node. It does this one path at a tim e (e.g., it findsthe shortest path from node A to all other nodes; then it finds the shortestpa th from node B to a ll other n odes; and so forth ).
Let ’s use the n etw ork in figu re 16 .1 as an exam ple. F igu re 16 .7presents the network in terms of a particular origin node (A = Start) and aparticular destination n ode (G = F inish ). In the first step (not show n), thealgorithm finds the node that is closest to A that has not already been put onthe shortest path. In this case, it is to itself ( i.e ., A to A is the shortest path atthis point). It thus removes A from the list o f possible nodes and puts it in ashortest path node list. Next, the routine finds the node that is closest to Athat has not already been put on the shortest path list. This will be node B ,w hich is 50 units distance from A (figure 16.8). Thu s, the shortest path now
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goes from A to B . Su bsequen tly, node B is rem oved from the list of possib lenew nodes an d is put on th e shortest pa th list.
In step 2, the routine finds the node that is closest to one of the existingnodes on the shortest path list but which has not already been put on thatlist. Th is w ill be node D , which is 70 un its from A (figure 16.9). That is, if Aand B have already been put on the shortest path list, then only tw o nodesare connected to these - C and D . The distance from A to C is 120 (50 + 70)w hile the d istan ce from A to D is 70. T hus, th e rou tine selects nod e D next. Subsequen tly, node D is rem oved from the list of possib le new nodes and ispu t on the shortest pa th list.
In step 3 (figure 16.10), the routine determ ines the node that is closestto A and w hich has not yet been put on the shortest pa th. There are tw opossib ilities - C an d F ; both are 120 u nits distan ce from A. In the case o f atie , the rou tine ‘flips a coin ’ and chooses one, in this case n od e F . Subsequen tly, node F is rem oved from the list of possib le new nodes and ispu t on the shortest pa th list.
In step 4 (f igu re 16 .11 ), the rou tine adds nod e C to the shortest p ath. N ote that had the ‘coin flip ’ in step 3 chosen node C instead of F, in this stagenode F would have been selected; thus, the routine produces the samesolution, just in a d ifferent order. Both nodes C and F are 120 un its distancefrom node A. Node C is now removed the list o f possible new nodes and is puton the shortest pa th list.
In step 5 (figure 16.12), the routine adds node E to the shortest path listbecause the distance to E through B is shorter than any other route that hasnot yet been determ ined (130 un its from A). N otice that the path to Ethrough C or D would have been longer than through B (180 and 140 un itsrespectively ).
F inally, in step 6 (f igu re 16 .13 ), the rou tine goes to the fin ish , nod e G . The path through B and E is shorter than by any other path to G (180 totalun its). Thus, the D ijkstra algorithm has searched every nod e in the networkan d de term ined a shortest p ath from nod e A to each of them (figure 16 .14 ). Even though we are only interested in the path from A to G, the algorithmsolves all shortest paths from A to all nodes.
A* Algorithm
The biggest problem with the Dijkstra algorithm is that it searches thepath to every single node. If the purpose w ere to find the shortest path froma s ingle nod e to a ll other nod es , then this w ou ld prod uce the best so lution. H ow ever, with an origin-destination m atrix , we rea lly wan t to kn ow thedistan ce betw een a p air of nod es (on e orig in an d on e destination ). Consequently , the D ikjstra algorithm is very , very slow com pared to w ha t we
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need. It would be a lot quicker if we could find the distance from each origin-destination pair one at a tim e, but qu it the a lgorithm as soon as that d istancehas been determined.
This is w here the A * algorithm com es in . A* was d eve loped w ithin theartif icial intelligence research area as a means for developing a heuristic ru lefor solv ing a prob lem (Nilsson , 1980). In th is case , the heuristic rule is theremaining distance from a solved node to the final destination. That is , atevery step in the D ijkstra routine, an estim ate is m ad e of the rem ain ingdistance from each possible choice to the final destination . Th e node th at ischosen for the shortest path is that which ha s the least total combined distancefrom the previously determ ined node to th e final goa l. Th us, for an y step , ifD i1 is the distance to a node, i, which has n ot already been pu t on the shortestpath and D i2 is an estim ate of the distance from that node to the finaldestination, the estim ated total distance for that node is:
D i = D i1 + D i2 (16.1)
O f all the n odes that could be chosen , the node, i, w hich has theshortest tota l distan ce is se lected next for th e shortest pa th. There are tw ocaveats to this statem ent. First, the node, i, cannot have already beenselected for the shortest pa th; this is just re-stating the rules by w hich w esearch for nod es which hav e n ot yet been pu t on the shortest p ath list. Second, the estim ate of the rem aining distance to the final destination m ustbe less than or equal to the actual distance to the final destination. In otherw ords, th e estim ated dista nce, D i2, can not be an overestim ate (N ilsson , 1980 ).H ow ever, the closer the estim ated d istance is to the real distance, the m oreefficient w ill be the search.
H ow then do w e determ ine a reasonable estimate for D i2? The answ er isa straight line from the possible node to the final dest ination since thesh ortest d istan ce betw een tw o poin ts is a stra igh t line (or, on a sphere, aGreat Circle distance since the shortest distance between two points is anarc). If we sim ply calculate the straight-line from the node tha t we areexploring to the final node, then the heuristic will work.
Let’s look at the exam ple aga in. Figure 16 .15 displays the netw orkagain. Like the Dijkstra algorithm , the routine first finds a node closest to A,w hich is itself. Next, it finds a node that has the least total distance from Ato the final destination, G (figure 16.16). There are two possibilities, gothrough B or go through D. The distance from A to B is 50 and the remainingdistan ce from B to G is 130 . Thus, th e total dista nce through B wou ld be 18 0. O n the other hand, the distance from A to D is 70 and the rem aining d istancefrom D to G is 120. Thu s, the total distance through D would be 190 . Since180 is smaller than 190, we choose node B .
Start Finish30
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Figure 16.16:
16.26
In step 2 (figure 16.17), three possibilities are explored for reaching Gfrom A - through B and E; through B and C; and through D. The totaldistance through B and E is 180 (50 + 80 + 50) w hile the total distancethrough B and C is 200 (50 + 70 + 80) and throu gh D is 190 (70 + 120). Thus,the routine chooses through B and E.
In step 3 (f igure 16.18), it is but a short path from E to the finaldestination G. The total distance through B and E to G is 180 while the totaldistance through B and C is 200 and through D is 190. Thus, the A *algorithm ha s determ ined a shortest path in three step s, rather than the 6 ittook th e D ijkstra a lgorithm (figure 16.19).
In gen eral, if V is the nu m ber of nod es in the network, the D ijkstraalgorithm requires V 2 searches whereas the A* algorithm requires only Vsearches (Sedgewick, 2002). As can be seen, this is much m ore eff icient thanhaving to search every single possible node, wh ich is wh at Dijkstra requires.
Applying A* to multiple origins
As w ith the D ijkstra algorithm , A* can be applied to m ultiple origins. Itdoes it one origin-destination combination at a tim e. If an origin-destinationm atrix is represented by the origins as rows and the destinations as colum ns,then the A* algorithm takes each origin-destination com bination and findsthe shortest path. Sin ce it does no t search all possib le nodes (on ly th ose inw hich the to tal distance to th e destination is sh ortest), it cannot determ ine inon e step the d istance from an origin to a ll possible destin ations. H ow ever, itis so quick as an algorithm that it can be applied to each cell o f the or igin-destination m atrix and still come out m uch faster than a D ijkstra search.
Weighting of Segments
As m entioned above, the units of the network can be any type ofimp edan ce - distance, travel tim e, or cost. These can be thou ght of as weightsapplied to a segment. The A* algorithm does not really care what are theunits of the segm en ts a s long as th ey are con sistent and prop ortional to cost. The algorithm w ill determine the path with the shortest total cost (or totalw eight).
Thus, th is algorithm can be applied to a trip distribution or m ode splitm atrix of origin-destination pairs. It will determine the shortest path fromeach origin zone to each dest ination zone and can do this in the measurementunits that are selected for weighting.
The advantages for travel demand m odeling are enorm ous. It m eansthat if the w eigh ting variable is travel tim e, then th e algorithm will find theshortest time path through the n etw ork for each origin-destination pair. Ifthe weigh ting variable is gen era lized cost, then the algorithm will find the
Step 2
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A* solved in 3 steps
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A* AlgorithmFigure 16.19:
16.30
sh or test cost pa th th rough t he network. F ina lly, if the weight ing var iable is speed , th enth is must be convert ed int o an impeda nce weight by dividing the dist ance of the segmentby t he speed to yield t r avel t im e. In shor t , t he A* algor it hm is an amazing on e and a llowsthe bu ildin g of a r out ing algor ithm.2
R ou t in g Alg o ri th m s
In applyin g a shor test pa th ana lysis to a network assignment , severa l a ssumpt ion sha ve to be ma de. As ment ioned earlier, network assignm ent involves assigning trips topa r t icula r rout es . Given a net work of segmen ts (e.g., r oad segmen ts, t r a in segmen ts), aroutin g algorithm a lloca tes t he pr edicted n umber of t r ips t o one or more rou tes. In otherwords , the net work ass ignmen t is done t h rough a rout ing algor ithm. What makes th iscomplex is th at th ere ar e a nu mber of different rout ing algorith ms, of which a short estpa th is on ly one. Most of them are bas ed on the assu mpt ion of t r avel cost relat ive tonetwork capacit y (Or tuza r and Willumsen , 2001).
The simplest type of rout ing algorith m is an All or None assignment . F or eachorigin -dest ina t ion pa ir (eith er for a ll t r ips or t r ips by specific t r avel mode), th e a lgor ithmcalculat es the shortest pa th th rough th e network an d assigns all t r ips to th a t pa th . Thisis the most ra t iona l model in tha t the cost of t r avel (whether measu red by dist ance, tr aveltime, or some cost m easur e) is minimized.
A second r out ing algorith m is a stochastic path in which each rou te has a cer ta inpr obability of being selected. Mu lt iple pa ths can be selected, bu t wit h a pr obabilityin versely propor t ion a l t o their cost . The shor test pa th will be selected most often ; thesecond short es t pa th next most oft en ; th e t h ird short es t pa th th ird m ost oft en ; an d so fort h . This type of a lgor it hm a t t empts to capture the va r ia bilit y in t r avel behavior tha t can comefrom t raveler ’s per cept ions or in complete in format ion a bout the choice of pa th .
A th ird rou t ing a lgor ithm is a congested assign m ent in which there is feedback fromthe capa city of the network t o the choice of rou te. In t he classic case, as t r avel volum esincrea se on network segmen ts, the capa city of the segment to absorb t r a ffic is appr oached.The h igher the ra t io of t he volume-to-capacit y (V/C), t he slower t r a ffic becomes on thesegment . In oth er words, t he cost of t r avel increa ses. Event ua lly, if the volum e keepsin creasin g, the speed slows so much as to eventua lly r educe the amount of t r a ffic t ha t canenter the segm ent (ITE, 2000). In theory, if t here is so much t ra ffic volu me rela t ive to thecapa city, tr a ffic comes t o a complete ha lt (gr idlock). However, in pract ice th is doesn’thappen as dr ivers t ake oth er rou tes. Consequ ent ly, with h igh V/C ra t ios, other rou tesbecome more desir able and some t ra ffic spills over on to those segm ents. This type ofmodel is frequent ly used in met ropolit an t r avel demand models for t r anspor ta t ion sin cecongestion is a ma jor factor in m ost u rban ar eas.
16.31
There are ad va ntages and disadva ntages to each of these approaches . The “All or none” ass ignm ent is the c losest to a ra tiona l choice m odel; theroute w ith the low est tota l cost is chosen. O n th e oth er han d, this a lgorithmw ill continue to assign trips to a route even if the road segmen t becomesextrem ely congested, w hich is not realistic. A stoch astic m odel has theadvantage of accounting for variability. I f individual-level data could beobta ined that m easu red individual choices a nd perceptions o f routes, then it’spossib le that a rea listic proportional sp lit am on g rou tes cou ld be de tected. M ore often, however, such information is lacking and a variation on the modesplit mod el is used to proportion the trips am ong the different possible routes(see Ortuzar an d W illum sen , 2001 , cha pter 10 for m ore inform ation).
The “C on gested assign m en t” algorithm can be seen as a m ore rea listicvariation on the “A ll or non e” in that the costs of travel chan ge as the netw orkcapacity is reached. M ost transportation m odels use that type of m odelbecause it is a more realistic representation.
Lack of information about crime trips
The problem with crim e tr ips , how ever, is that the num ber of trips isliable to represent only a very small proportion of the total tr ips on anysegment of a network. Thus, there is not liable to be any feedback from thecapacity limits of segm ents to crim e trips per se. An y feedback is liable toap ply to a ll trips, of w hich the crim e tr ips are a sub-set. It m igh t be possibleto link a cr ime trip route choice algorithm to a general congested assignmentin order to approxim ate this situation, but the amount of information thatwould be necessary to be obtained and the complexity of the modelingalgorithm would probably not produce m uch tang ible bene fits beyond w ha t asimp le mod el predicts.
Further, there could be feedback from surveillance and other polic ingpractices that might increase the cost to an offender of traveling along aparticular route. H owever, without any detailed inform ation about perceivedcosts of particular routes, it is difficult to postulate any type of m odel forchoosing a lternatives. This w ou ld be a very va luab le area o f research inundersta nding the trave l behav ior of o ffenders.
But, short of th at inform ation , an “A ll or n on e” assign m en t routine isprobably th e easiest to im plem ent for alloca ting the predicted cr im e trips toroutes.
The CrimeStat Network Assignment Routine
The CrimeStat network assignm ent routine imp lements an “All or none”ass ignm ent based on the A* shortest pa th a lgorithm . Figu re 16.20 show s thesetup page for netw ork assignm ent. On the page, there is a netw ork
Figure 16.20:
Network Assignment Module
16.33
ass ignm ent routine and there are som e netw ork utilities. Let’s start w ith thenetwork assignm ent routine.
Network Used
The first in put that needs to be m ad e is which netw ork is to be used. The choices are the network specified on the Measurem ent parameters page(the defa ult) or an alternative netw ork.
Network on measurement parameters page
Check the ‘Network on M easurement parameters page’ box to use thatnetwork. All the param eters will have been defined for that setup (seeM easu rem en t param eters pag e).
Alternative network
If an altern ative netw ork is to be used , it m ust be d efined. Check th e‘Alternative network’ box and click on the ‘Parameters’ button. Figure 16.21shows the dialogue box for the alternative network.
N ote: if a network is also used on the M easurem ent Param eters page,then it m ust b e defin ed there as w ell. CrimeStat will check whether thatfile exists; if it does not, th e rou tine w ill stop and an error m essage willbe issu ed . Th erefore, if an alternative ne tw ork is used, th e user sh ou ldprobably change the distance measurement on the MeasurementParam eters page to direct or indirect distance.
Type of network
N etwork files can be bi-directional (e.g., a TIGER file) or single directional(e.g ., a tra nsportation m odeling file ). In a bi-d irectional file , trave l can be ineither direction. In a s ingle directional file, trave l is only in on e d irection. Specify the type of network to be used.
Input file
The n etwork file can either be a shape file (line, polyline, or polylineZfile) or another file, either dBase IV ‘dbf’, M icrosoft Access ‘m db’, Ascii ‘dat’, oran O D BC -com pliant file. The default is a shape file. If the file is a shape file,the routine w ill know the locations of the nodes. For a dB ase IV or other file,the X and Y coordinate variables of the end nodes m ust be defined. These arecalled the “F rom ” node and the “E nd” node . An option al w eight va riable isallow ed for both a shape or d bf file. The rou tine identifies nod es and segm entsand finds the shortest path. I f there are one-way streets in a bi-directionalfile, the flag fields for the “From” and “To” nodes should be defined.
Figure 16.21:
Alternative Network Dialogue
16.35
Weight field
By d efault, each segm ent in the network is not weighted. In this case,the routine calculates the shortest distance between two points using thedistance of each segment. How ever, each segm ent can be weighted by traveltim e, speed or travel costs. If trave l time is used for w eigh ting the segm ent,the routine calculates the sh ortest tim e for an y rou te betw een two po ints. Ifspeed is used for weighting the segm ent, the routine converts this into traveltim e by dividing the distance by the speed. Finally, if travel cost is used forw eighting the segm ent, the routine calculates the route w ith the sm allesttotal trave l cost. Specify the w eigh ting field to be used and be sure to indicatethe m easurem ent un its (distan ce, speed , trave l time, or travel cost) at thebottom of th e page. If th ere is n o w eighting fie ld assign ed , then the rou tinew ill calculate using distance.
From one-way flag and To one-way flag
On e-way segm ents can be identified in a bi-directional fi le by a ‘f lag’field (it is not necessary in a single d irectional file). Th e ‘flag’ is a field for theend nodes of the segmen t with values of ‘0 ’ and ‘1’. A ‘0’ indicates that travelcan pass through that node in either direction whereas a ‘1 ’ indicates thattravel can only pass from the other node of the same segm ent (i.e. , travelcannot occur from another segment that is connected to the node). Thede fau lt assum ption is for trave l to be a llow ed through each node (i.e., there isa ‘0’ assum ed for each node). T here is a ‘From one-w ay flag’ fie ld and a ‘Toone-way flag’ field. For each one-way street, specify the flags for each endnode. A ‘0’ allow s travel from an y con necting segm en ts w hereas a ‘1’ on lyallows travel from the other n ode of the sam e segm ent. Flag fields that areblank are assumed to allow travel to pass in e ither direction.
FromNode ID, ToNode ID
If the network is single directional, there are individual segm ents foreach direction. Typically, two-wa y streets hav e two segm ents, one for eachdirection. On the other han d, one-w ay streets h av e only one segm en t. TheFromN ode ID and the ToNode ID identify from w hich end of the segmenttravel should occur . If no From N ode ID and T oN ode ID is defined , theroutine w ill chose th e firs t segm en t of a pa ir that it find s, w heth er trave l is inthe right or w rong d irection . To identify correctly travel d irection , define theFrom N ode an d ToN ode ID fields.
Type of coordinate system
The type of coordinate system for the network file is the same as for theprimary file.
16.36
Measurement unit
By defau lt, the shortest path is in term s of distance. How ever, eachsegm en t can be weighted by trave l tim e, trav el speed, or trave l cost.
1. For travel tim e, the un its are m inutes, hours, or unspecified costunits. For speed, the units are miles per hour and kilometers perhou r. In the case of speed as a weighting var iab le, it isautom atically conv erted into travel time by d ividing the distanceof the segm ent by the speed , keeping units constant.
2. For travel cost, the units are undefined and the routine identifies
routes by those w ith the sm allest tota l cost.
Network Utilities
There are tw o n etw ork utilities th at can be used.
Check for one-way streets
First, there is a routine that w ill identify one-way streets if the ne tworkis single directional. In a single directional file, one-way streets do not have areciprocal pa ir (i.e., a segm en t trave ling in the opp osite d irection). Th is isindicated by a reciproca l pair of ID ’s for the “From ” and “To” nodes . Ifchecked, the routine identif ies those segments that do not have reciprocalnode ID’s. The network is saved with a new field called “Oneway”. One-waysegm ents are assigned a value of ‘1 ’ value and two-way segm ents are assigneda value of ‘0 ’. The output is saved as an ArcView '.shp', MapInfo '.mif ' orAtlas*GIS '.bna' file.
Create a transit network from primary file
Second, there is a routine that wi ll create a transit network from theprimary file. This is useful for creating a transit network from a collection ofbu s stops (bus netw ork) or rail station s (ra il netw ork). If checked , the routinew ill read the primary file and w ill draw lines from one point to another in theorder in w hich the points appear in the prim ary file. N ote, it is essentia l toorder the points in the sam e order in which the network should be drawn(oth erw ise, an illogical ne tw ork will be obtained ). It is ea sy to do th is in aspreadsheet program.
Transit Line ID
The routine can hand le multiple lines, for exam ple different rail lines orbu s rou tes (e.g., Line A , Line B , Route 1, Route 2). In the prim ary file, thepo ints m ust be grouped by lines , how ever, and m ust be classified by a TransitLine ID field. W ithin each group, the points mu st be arranged in order of
16.37
occurrence; the routine will draw lines from one point to another in thatorder. In th e Tran sit Line ID field, indica te w hich variable is theclassif ication variable. The output is saved as an ArcView '.shp', MapInfo '.m if'or Atlas*GIS '.bna' file.
Figure 16.5 above shows the effect of creating four separate rail linesfrom the station locations while figure 16.6 shows the m erged four linesim plem en ted with the G roup ID .
Network Output
There are three typ es of output for th e n etw ork assignm en t routine. First, the m ost frequent inter-zonal (i .e., trips between different zones) routescan be output as polylines. Second, the m ost frequent intra-zonal (i.e ., tripsw ithin the sam e zone ) routines can be output as p oints. Third, the entirenetw ork can be output in term s of the total num ber of trips that occur on eachsegm ent (network load).
Save routes
The shortest routes can be saved as separate polyline objects for use in aG IS. Specify the outpu t file form at (ArcView '.shp', MapInfo '.mif' or Atlas*GIS'.bna') and the file nam e.
Save top routes
Becau se the output file is very large (num ber of origin zones x num berof destination zones), the user can select a zone-to-zone route with the m ostpredicted trip s. The defa ult is the top 10 0 orig in-destination com bination s. Each outpu t object is a line from the origin zon e to the destination zon e w itha R ou te prefix . The prefix is p laced be fore the output file nam e. T hegraph ical output includes:
1. An ID number from 1 to K, where K is the number of links output(ID)
2. The feature prefix (ROU TE)3. Th e origin zone (ORIGIN )4. The destination zone (DEST)5. Th e X coord inate for th e origin zone (ORIGIN X)6. Th e Y coord inate for th e origin zone (ORIGIN Y)7. The X coordinate for the destination zone (DESTX )8. The Y coordinate for the destination zone (DESTY )9. The nu m ber of trips on tha t particu lar route (F REQ )10. The distance between the or igin zone and the destination zone
(DIST).
16.38
Figure 16.22 shows the top 300 routes calculated with the modelingnetwork. The assignment was weighted by travel time and the thickness andcolor of the lin e is prop ortional to the n um ber of predicted trip s.
To see how this differs from the trip distribution matrix, figure 16.23zoom s into a high vo lum e rou te in eastern Baltim ore C ou nty. Th e m odelingstreets are displayed as are the predicted links from the trip distribution forthat area. As seen, the trip distribution sim ply produces straight-line linksbetw een origins an d destination s. In th is case , the cr im e trips com e into tothe centroid of the Traffic An alysis Zone (TAZ ) in the m iddle of this hot spotof crim es (TAZ 610). The actua l routes, on the other han d, follow the streets(in this case , the m odeling netw ork ) and are m ore circuitous . Severa l of thestreets a re used m uch m ore h eavily than others, according to the assign m en t.
An addit ional poin t shou ld be noted, how ever. Sin ce the m odelingnetwork w as used rather than the T IGE R n etwork, the trips into and fromthe centroid of the TA Z do not follow any particu lar road ; the a lgorithmsim ply d raw s a straigh t line from the cen tro id to the n earest road segm en t. In sub sequent m odeling , it m ight be w orthw hile to d igitize ad ditional streetsin this neighborhood since there are m an y crim es be ing a ttracted to it. Acrim e m apping analyst can easily add the additional features to im provereso lution . The m odel w ould have to re -run , how ever, to get a m ore accu ratedisplay.
Save points
Intra-zonal trips (trips in which the origin and destination are the samezone) can be output as separate point objects as an ArcView '.shp', MapInfo '.m if'or Atlas*GIS '.bna' file. Ag ain, the top K points are ou tput (defau lt=100). Ea chou tput obje ct is a p oin t representing an intra -zonal trip w ith a R ou tePoin ts. The prefix is p laced be fore the output file nam e.
Th e graph ical output for each includes:
1. An ID number from 1 to K, where K is the number of links output(ID)
2. Th e feature prefix (RO U TE Points)3. Th e origin zone (ORIGIN )4. The destination zone (DEST)5. Th e X coord inate for th e origin zone (ORIGIN X)6. Th e Y coord inate for th e origin zone (ORIGIN Y)7. The X coordinate for the destination zone (DESTX )8. The Y coordinate for the destination zone (DESTY )9. The nu m ber of trips on tha t particu lar route (F REQ )
These are not illustrated in th is cha pter becau se they a re identica l tothe intra-zon al ou tpu t of the trip distribu tion m odule (see chapter 1 4).
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Assigned trips by travel time25 or less26 - 4950 - 7475 - 99100 or more
0 10 20 Miles
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Predicted Baltimore County Crime Trips: 1993-1997Routes and Links for Zone-to-Zone Trips: All Crimes
Weighted by Travel Time
Figure 16.22:
City of BaltimoreBaltimore County
Predicted top inter-zonal trips25 or less26 - 4950 - 7475 - 99100 or more
Assigned trips by travel time25 or less26 - 4950 - 7475 - 99100 or more
0 1 2 Miles
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Predicted Baltimore County Crime Trips: 1993-1997Routes and Links for Zone-to-Zone Trips: All Crimes
Weighted by Travel Time
Figure 16.23:
16.41
Save network load
It is also possible to save the total network load as an ArcView '.shp',MapInfo '.mif' or Atlas*GIS '.bna' file. Th is is the total num ber of trips on eachsegm ent of the network. The routine takes every origin zone to destinationzone com bination and su m s the num ber of trips that occur on each segm ent ofthe network. Click on the “Save output network” box and specify a file namefor the ou tpu t.
Figure 16.24 sh ow s the entire crim e trip volum e on the netw ork(network load). The assignm ent was w eighted by travel time. Notice howthere are m an y trips on the circular B altim ore Beltw ay (I-695 ). Becau se theroad is a freew ay , trave l is gen erally m uch faster th an on m ost arteria l road s. Con sequently, there are m any crime trips being assigned to the freeway eventhou gh it is longer th an m an y d irect lin ks.
To see how this d iffers from a shortest distance assignm en t, the rou tinewas re-run using only distance as the weighting variable. Figure 16.25displays the results. As seen, the rou tine does n ot use the Be ltway verym uch, but instead uses the arterial roads more, particularly the diagonalarterial roads coming out of the City of Baltim ore. Since the routine wasdeterm ining th e shortest path on the bas is of d istance on ly, it w ill inevita blyfind the m ost direct routes in terms of distance. In term s of travel tim e,how ever, many of those routes w ill be much slow er because of traffic lights,cross-traffic, drivers pulling in and ou t of parking spa ces, and so forth. Thu s,the freeway is alm ost always quicker for travel than an arterial road exceptat peak rush hour conditions. This points out the im portance of using traveltime and , better yet, travel cost as an im pedance variable. Distance is muchtoo sim ple an indicator of it.
The n etwork load routine can even be used for specific travel modes(and usually is for transportation travel dem and m odeling). Figure 16.26, forexam ple, show s the network volum es (load) of bus crim e trips, again weightedby travel tim e. According to th e m odel, man y of these trips originate in theCity of Baltim ore. But at the high crim e locations, multiple bus routes tendto converge producing a high bu s tr ip vo lum e on the adjacen t streets. Because of the very small num ber of bus crim e trips predicted by the modesp lit m od el, th e volu m es are n ot high , even for the h igh est volu m e lin ks. A lso, notice how the Beltw ay is not used very m uch for bus trips , com pared tothe total network load in f igure 16.24. The reason is that most bus routes donot use the freeway but stay on arterial roads (express buses would be anexcep tion , but those tend to be used prim arily for com m uting ).
Figure 16.27 shows the network volum es of train trips. Since there wasno data on travel tim es along each train segm ent, the volum es are weightedon ly by d istance. Th e num ber of trips, of cou rse , are very few , as was no ted inchapter 15. Also, notice how most of the cr ime trips taken by train occur on
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Road volumes by travel time01 - 99100 - 199200 - 299300 - 399400 - 499500 - 599600 - 699700 - 799800 - 899900 or more
0 10 20 Miles
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Crime Volume by Road SegmentWeighted by Travel Time
Figure 16.24:
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Road volumes by distance01 - 99100 - 199200 - 299300 - 399400 - 499500 - 599600 - 699700 - 799800 - 899900 or more
0 10 20 Miles
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Crime Volume by Road SegmentWeighted by Distance
Figure 16.25:
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Bus volumesLess than 0.50.5 - 0.91 - 1.41.5 - 1.92 or more
0 10 20 Miles
N
EW
S
Crime Volume by Bus Route SegmentWeighted by Travel Time
Figure 16.26:
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Train volumesLess than 0.250.25 - 0.490.5 - 0.740.75 - 0.991.0 or more
0 10 20 Miles
N
EW
S
Crime Volume by Rail SegmentWeighted by Distance
Figure 16.27:
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tw o lines , the M etro line to th e w est and the M arcP line to th e east. In bothcases, the train trips start in the City of Baltimore and travel to Ba ltim oreCou nty. Th ese, of cou rse , are pred ictions of crim e travel volum es on the railnetw ork, not empirical verifications.
Crime Types
The n etw ork assignm en t routine can be ap plied to specific crim e typ es . In general, it is a good idea to calibrate a general assignm ent for all crim esbe fore analyzing specific crim es. Th e reason is that there are vo lum edimen sions that assign m ost crim e trips to the sam e segm ents. Still, som edifferences can be observed . Figure 16 .28 show s the likely routes for vehiclethefts (in blu e) and com pares it to the lik ely routes for a ll crim es (in red). There are similarities and differences. There is overlap in the predictedroutes in the southeast and southwest edges of the C ounty w ith the City ofBaltim ore, and there is som e overlap at the northwest border with the City ofBaltim ore. At the sam e tim e, though, some differences are visible,particu larly at the w estern border w ith the C ity of B altim ore.
In other words, the network assignm ent m odel shows different routesfor vehicle thefts than for crim es in general. This difference, of course,represents differen ces in the trip d istribution m atrix of the veh icle theftscom pared to all crimes.3
Uses of Network Assignment
A n etwork assignm ent routine is the culmination of the crim e traveldem and m odeling process. Essentially, it assigns predicted trips (whether forentire origin-destination trip pairs or for mode-specif ic trip pairs) to an actualnetw ork and usually on the basis of least cost. The algorithm used in theCrimeStat netw ork assignm ent routine calculated the sh ortest path (in term sof d istance, trave l tim e, or cost) and assign ed all th e tr ips for each origin -dest ination pair to this route . The representation is more complex than asimple tr ip link (which is a straight line) s ince it uses information on theactu al netw ork used . The result is a p red iction o f routes that are taken tocom m it crim es and a prediction of the total crim e trip volum e on ea chnetw ork segm en t. This is clearly an advance on the geograp hicprofiling/journey-to-crim e approach, which has simply analyzed traveldistance as an explanatory variable.
N etw ork assignm en t also has m an y u ses for police . First, it ca n po intout where police need to focus their deploym ent. In this sense, theprogression of the four modeling stages represents adding information to theknow ledge of the crime events. Simp ly mapping the crim e events tells apo lice d epartm en t w here th e crim es are occu rrin g. A nalyzing th e tr ipdistribution tells the department from wh ere the crim es might be originating.
Baltimore County
City of Baltimore
City of BaltimoreBaltimore County
Most common routes25 or less26 - 4950 - 7475 - 99100 or more
Auto theft routesLess than 22-3.94-5.96-7.98 or more
0 7 14 Miles
N
EW
S
Predicted Routes by Crime Type: 1993-1997All Crimes and Vehicle Thefts
Weighted by Travel Time
Figure 16.28:
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Split t ing the dist r ibu t ion by t ravel model pr ovides in format ion about the likelyt ravel m ode used. F in a lly, assign in g t he predict ed t r ips to actua l r outes gives in format ionabout how offenders may h ave t raveled to the cr im e loca t ion . The model provides a lotmore informat ion than a simple descript ion of a h igh cr ime a rea .
Second, kn owing the likely rout es of offender s can a llow for increa sed surveillance’and t a rget h arden ing. Not on ly can police pa t rol th e likely rout es in a more focusedmanner , but other su rveillance tools can be used, too. For exam ple, sur veillance camerasth at monitor t ra ffic can be used for a var iety of pur poses. In th e U.S., th ey ha ve tended tobe u sed for monit orin g t ra ffic sign a ls for red-light running (IIHS, 2004). However , inEurope t hey ar e widely used for a var iety of t r a ffic monitoring pur poses - speeden forcemen t , bus la ne en forcemen t , en ter ing the London congest ion zone, a s well a smonit orin g t ra ffic sign a ls. In London, for example, the en t ire m onit orin g pr ocess isau tomated. For a veh icle ma king a violat ion , the camera takes a picture an d a softwarepacka ge identifies th e license plat e. The license num ber is then ma tched against ada taba se of veh icles and a t r a ffic cita t ion is sen t to th e owner . Ther e is n o rea son wh y th istype of t echnology could not be st ructured t o a lso look for st olen vehicles or vehiclesbelon ging t o in dividua ls for which out standin g cit a t ion s have been issued. In shor t ,knowin g on which roads h igh cr im e t r ips volumes are likely to occur can help police focus arange of surveilla nce tools on those loca t ion s.
Co n clu s io n s
In shor t , n etwork assignment is a logica l s t ep in the modeling of cr im e t r ips and onetha t br ings t he t r ips down to actua l rout es tha t a re u sed. It is a more r ea list icrepr esen ta t ion of t r avel beha vior and one tha t can a llow focused deploymen t by police.
In the next cha pt er , two case st udies a re exa mined. Dick Block and Dan Helm sapp ly the cr ime t ravel dem and t heory to Chicago and Las Vega s r espectively.
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1. Speed could be used, but it is inversely pr oport iona l to impeda nce (i.e., the h igherthe speed, the les s t he im peda nce). Most sh ort es t pa th a lgorit hms t rea t the weightas p ropor t iona l. However , speed can be conver ted in to tr avel t ime by dividin gdis tance by speed. To use the exa mple, if the len gth is 1 m ile long and t he speed is50 miles per hour , t hen the t r avel t im e is 1/50 hours (or 1.2 min utes).
2. For la rger da taba ses gr ea ter than , sa y, 1 million r ecords , however , A* is too slow. An a lgor ithm tha t is appropr ia te for very la rge da tabases can be found in Shekharand Ch awla (2003).
3. The differ en ces could be du e t o th e m ode sp lit rout ine a s well a s t he t r ipdis t r ibu t ion mat r ix. H owever , in the case of veh icle theft s, t he t r avel m ode is notvery relevant since the return t r ip is alwa ys by vehicle - the st olen vehicle.
En dn ot e s fo r Ch ap te r 16
