Improved Graphic Techniques in Signal Progression

47 mproved Graphic Techniqes in Signal Progression CRES E. W CE and KENNET G. COURGE BSTRCT The reslts of several research stdies into graphic representations of traffic signal system settings and traffic flow are presented. The research began with the fndamental time-space diagram, which is niversally nderstood by traffic engineers, and also with flow diagrams from the TRNSYT model. Three specific departres from these basic techniqes are presented, which inclde time-location diagrams, forward progression opportnities, and platoon progression diagrams. ll of these techniqes apply to linear arterial systems or sbsystems. nother graphic techniqe that applies to a network of coordinated signals is then discssed: signalized network animated graphics. nterpretation of signal timing-optimization strategies, namely maximal bandwidth optimization, is discssed sing the platoon progression diagram techniqe. This analysis demonstrates the pitfalls of the maximal bandwidth approach, ths demonstrating the power of the analysis techniqe. Traffic engineers have traditionally analyzed the qality of traffic flow in coordinated traffic signal systems by either direct field measrement or by the se of off-line analysis techniqes. Field stdies are typically the sperior approach to sch analysis; however, the alternatives that may be evalated by field stdies are limited to those that the traffic engineering agency can actally install in the system. The field stdy approach is not condcive to design becase of this limitation. Off-line comptational techniqes spport a wide range of designs and design strategies withot reqiring field implementation and evalation stdies. lthogh the assessment of traffic flow sing sch techniqes is limited by the assmptions and limitations of the selected techniqe, their se can nonetheless dramatically increase the prodctivity of the traffic engineering agency. Off-line techniqes generally consist of nmerical estimates of the pertinent measres of effectiveness (MOEs) and graphical representations. Nmerical estimates of MOEs are typically accomplished by deterministic, or analytical, techniqes; by simlation of traffic flow; or by a combination of these two. Sch techniqes vary considerably in their realism or accracy, depending on the theoretical basis of the estimates; bt, more significantly, they are simply nmbers (e.g., delay, nmber of stops, fel consmption, bandwidth) that do not offer any visal perception to the analyst as to the qality of. traffic flow. On the other hand, graphical techniqes do give a pictre of tohe perceived qality of traffic flow. lthogh it is tre that, ltimately, MOE estimates (or even field measres) are sed to qantify improvements, the graphic presentations can be of great assistance in assessing the qality of traffic flow as part of the design decision process. nmber of graphical representations of traffic signal timing and traffic flow that can be extremely sefl analysis and evalation tools for the practicing traffic engineer are presented here. First, the time-space diagram, which is niversally known and sed by traffic engineers, is presented, and later three specific departres that enhance the tility of this familiar graphical techniqe are discssed. second existing techniqe for illstrating simlated traffic flows is also reviewed. TME-SPCE DGRMS For coordinated systems, the classical graphic presentation of traffic signal timings is the timespace diagram (TSD) TSD, as shown in Figre 1, illstrates the relationship of a series of traffic signals in a coordinated system by showing the signal timing on the artery and the offset relationships. When the throgh bands are drawn, the slopes of the bands illstrate the desired speea (s) of the throgh bands. This is the inherent se of TSDs: to illstrate the perceived progression throgh a system of traffic signals. TSDs have been prodced manally for more than 50 years. Until recently, they were virtally the only method of optimizing progression on arterial rotes. Given the complexity of the task, it is logical that compterized techniqes wold replace the manal analysis. This has, in fact, happened gradally over the past 20 years. Compter models sch as PSSER 80 (1), MXBND (1_), TRNSYT-7F (_l), and SGOP (i) are among the more poplar models that prodce TSDs. The first two models have as their explicit objective fnction the maximization of throgh bandwidth. The TSD presents a gross oversimplification of the traffic flow process. ts primary disadvantage as an analysis tool is that no consideration is given to the actal traffic demand. s a reslt, time-space or so-called maximal bandwidth-based designs may reslt in apparently satisfactory green bands, bt in reality traffic wo1jld only be progressed into the rear of standing qees. The seflness of TSDs is also practically limited to linear arterials. Several attempts have been made to develop three-dimensional TSDs, bt this practice is extremely laborios. Frthermore, threedimensional TSDs are difficlt to interpret. Ths the seflness, and particlarly the flexibility, of standard TSDs for networks is limited. TSDs may also be extremely lengthy for long arterials. TRFFC FOW PTTERNS The concept of sing traffic flow distribtions to simlate traffic flow was introdced by Robertson <2>, who described traffic flow as falling into two basic patterns, or profiles (simplified here): 1. The arrival pattern, which is the periodic flow rate of traffic arriving at a reference point on a street, which is sally the stop line; and 2. The departre pattern, which is the periodic rate of flow departing the stop line, sbject to the signal display facing the traffic. [f a qee exists at the start of effective green (i.e., green start pls lost time), it departs at the maximm

48 Transportation Research Record 957 _J l FGURE Typical TSD. 3 TME N C.YCES rate, or satllration flow and arrivals contine to add to the bdt..: k of the qee. Once the qee has dissipated, departres eqal arrivals and are not delayed.] These patterns are illstrated in Figre 2. This concept has been implemented in the Traffic Network Stdy Tool (TRNSYT) model (_~), which has K 40 1 11X FOW 3400 YE/ FT. OEX 0.64 s 0 000 0 00000 0000000 0000 0000000 00000000000000000 000000000000000000 SSssSS 00000000000000000000 5~5555 QOOOOOQOJOOOJ00'30000!ll!! oooooaoooooooooooooon n oooocooooooooonoooooon n SSSSSS OOOOOOOOOOOOOOOOOOOOO oooooooooooooooooooo oooooooooooooooooooooo SSS SSS 0000000000000000000000 ll l 11000005 0000000000000000000000 ll Key: S - Dep;irtr'= of the qee. - rrivals that qee. 0 - rrivals and departres on green. K ld1 MX FOW 34 0 D YE PT. OEX 0.75 ss ss 0 ss 00 ss 000 ss 0000 ss 00000 sss 00000 sss ooooco sss 0000000 SSSS5SSSS 00000000 SSSSSSSSS 00000000 S55SSSSSS 00000000 SSSSSSSSS 0000000000 SSSSSSSSS 0000000000 SSSSSSSSS 0000000000 tl S SSSSSSS55000000C0000 SSSSS SSS 5500000000000 s ssooooooooooooo l SS SS SS SSSOOOOOOOOOOOOO ss s s scoooooooooooo1 1 l 1 ;ooooooooooooo r 1111111111 n sssooooooooooooo 11 11 r 111 ssoooooooocooooo 111111 n! n l l ll oooosss SOOUOOOOOOOOOOOl ll ll ll n FGURE 2 Typical flow pattern diagrnm. frther evol.yed to ve:rs1onc TRNSYT-=7F (3), which is sed in the United States, and 'l'rnsyt-i (6), which is available from the Transport and Road- Research aboratory. The flow profile represents a snapshot of traffic flow on a single approach, or link, for one signal cycle; ths it represents the average traffic behavior that might exist over a longer period of, for example, 1 hr. This is the distinct advantage of this form of graphic display, becase the simlated traffic flows, arrivals, and departres are actally shown. When TR/NS YT is optimized to mi11imize stops and delay (or excess fel consmption), it is sally trying to position the green interval on every link to clear the qees before the arrival of the moving platoons, provided the proper stop penalty is sed. The same prpose is served by the qee clearance options in the PSSER 80 and MXBND models, bt in TRNSYT the adjstment is made explicitly. Of the available graphic techniqes, these profiles best visalize the qality of tri'lffk f Wo For example, Figre 2 shows two links, where (a) the traffic platoon arrives after the qee has dissipated, and (b) the platoon arrives jst at the departre of the qelle. n both cases there is minimal delay to the primary platoons, bt if this offset relationship was plotted on a TSD, the band wold appear to be too fast. The disadvantages of this techniqe are as follows. 1. Some traffic engineers find the profiles difficlt to interpret becase the vertical scale is a flow rate. (The horizontal scale is time in steps of the cycle.) 2. The profiles are at the stop line at each link: ths the system interrelationships are d iff i clllt to visalize, althogh they can be aligned to show traffic progression down (sothbond) one siae of the compter otpt and p (northbond) the other side. 3. Similarly, the not readily apparent, will typically reslt signal timing parameters are and optimization by TRNSYT in offsets that appear to be too early becase of the qee clearancp.~ nn~pn pr~viosly. Engineers accstomed to TSDs do not visal-.

Wallace and Corage 49 ize the progression becase the apparerit i;peed too fast. With regard to the last point, it appears that the concept of throgh bands representing progress ion is misleading, and a better interpretation of satisfactory progression is the ninterrpted propagation of platoons. This is discssed in more detail later. NNOVTVE TECNQUES n recent years several new concepts of traffic progression and the graphical representation thereof have emerged, particlarly for coordinated systems. These are described in the following sbsections. Time-ocation Diagrams s mentioned earlier, TSDs can be lengthy for long arterials, This not only wastes paper, bt also cases problems with report reprodction. More significantly, TSDs generally do not fit on video monitors, and the increasing se of compterized tools wold render this a disadvantage. The progression speed (i.e., the slope of the bands) is sally given and is therefore of l~ss concern than the bandwidth, which is the MOE. TSO can be easily modified by correcting the plotted offset to accont for travel time, sch that the is slope of the band becomes zero at the desired speed. The plot can then be rotated from link to link so that a horizontal line (assming the vertical axis is time and distance is on the horizontal) wold represent the desired speed, or zero slope. The distance between intersections is no longer meaningfl, so the diagram can be collapsed. Ths the vertical axis remains time, bt only the relative order of intersections is important on the horizontal scale. When this is done for both directions of travel, two so-called time-location diagrams (TDs) can be plotted next to one another. The TD techniqe was first reported by Wallace and Corage (7), and an example is shown in Figre 3, which was installed in a modified version of TRNSYT-6C (8). This TD represents a design based on PSSER T' s bandwidth optimization. More significantly, the TD concept has been incorporated into the arterial analysis package (P) (_~) microcompter rotine SPN (10). By sing either keyboard entry on an PPE compter or transfer of special otpts of the P from the mainframe compter to the PPE, a TD can be plotted directly on the monitor, as shown in Figre 4. By observing the TD and recalling that zero slope represents the desired speeds, progression in the classical sense is visalized as a horizontal tnnel of green throgh all the intersections for both directions. This diagram can be maniplated to change offsets to improve progression if desired. The TD is a simpler tool to se than the TSO becase it is compact and the qality of progression FDRwND "" DPP0~1Ul1111 ~OT CC9'0ll ON C.U.[S\'11\ &.. 11111. et DSNT.l68 CYCE 'Jti ~lt.:.,.5 t.0 Tr ' J ", : : J..., : : t... T 10,. ~ ll 11 '" d 20 11 " 23 2 2~ 21 20 2' lo ll l~ lj l> J J1 311 Jl 40 4 ~ 0.. '...,0 ~ "'1 ~ h '~ ~, t~ ' 2 ~ 6 1 -.--,--.--.~,~-~,-,------------ o!..'------.. t t r--1 : t :. : ' f.. 1 1--- Throgh Bands NTEtrilSCCTON h\mdettt <--- FT-DOUND l 4 6 1.-.--....-1--~, --- -----------, 1--~ ~-- t+...n-_ t t :. -:--1.. 1 r---- i : : '1 l r--5t i : ill..--~ : : : : t t t ' J t. t 1 : t : ~ J : Dashed reas: The additional foli'/ard link opportnities otside the throgh bands. FGURE 3 Printed TD.

50 Transportation Research Record 957 is mch more apparent visally. t is particlarly sefl for visalizing progression throghot a portion of the system and for identifying critical signal locations. Forward Progression Opportnities The concept of the TD was extended by the athors to improve on the basic concept of traffic signal design based on time-space relationships, partic- larly in compterized optimization models. Maximal bandwidth models sch as PSSER 80 and MXBND are only concerned with throgh bands. Some intersections are noncritical, and their reslting offsets will not he ;:::dgnpn with ~~~, sp~cific cbjective in mind. Frthermore, there are often progression opportnities that do not exist over the entire length of an artery bt do exist in short sections where progression cold be beneficial. The concept of forward progression opportnities (PROS) was developed to overcome this deficiency (2,_!!l. forward progression opportnity is simply the opportnity presented to the motorist arriving cl11ring var oi; time& in the oyolc to travel forward on one link of an arterial system withot being stopped by a signal at either end of the link. PROS can ths be qantified by examinin9 the progression opportnitico pericdicolly tl gh t;. tin~ cycle and snning them. Signal timing optimization can likewise be based on maximizing PROS. The difference between a maximal bandwi dth design a nd "' PROS desig!! on the same facility (optimizing offsets only) clearly illstrates the advantage of the PROS approach, as seen in Figre 5 (i.e., compare the dashed areas representing PROS with the similar areas in Figre 3) The PROS concept has been implemented in TRNSYT-6C and has been proposed as an enhancement t o TRNSYT- 7F and the P. Platoon Progression Diagram FGURE 4 Compter plot of TD. n the earlier section on existing graphics tech- '"" ow,c NK OPP0~1UhlfleS P01 (0hDl1 Ot\ Gl~(SVE J.. J6 0$T.S268 NT!SClJON UM8Ett....... &C<k1 - l!dund - > 2 l ~ '? -.-.--,-1--1--r::i--.----- i < 6 ' : r--, 9 : i : 1: 1 l r--, : l ; ;_ l' : lft 19 ~~ 11 n n at : d 29 lo? l> l) l ll )ft n ~ 0 ~....,., ~.. 1! t! J!< t; [ 51,. ~,, : i :. t..c~c"n: h GJ!t T tt POS 10 F JGUKJ<; 5 TU from a l'ku:::i optimization. Throgh Bands C'f'C fld Si'~ t.0 <-- trt-oouo 3 5 6 ------...---!!'1-.-.-.---------------., t t t t t.,.............,..., t ' :. : '.... J :.... Dashed reas: The ilili11dl frwdrd link opportnities otside the throgh bands...

Wallace and Corage 51 n iqes, TSDs and platoon profiles were introdced, and the relative advantages and disadvantages of each were given. review of these techniqes sggests that the disadvantages of one approach were advantages of the other to some extent. The logical qestion is, Why not combine the two? Considering that both reqire two dimensions (i.e., time verss distance and flow rate verss time), a total of three dimensions are needed; therefore, a method is reqired to represent the third dimension in a two-dimensional graphic to display on a monitor or to print. The approach taken by the athors was to plot a standard TSO in two dimensions and express the platoon profiles as a density fnction. platoon profile can be sliced into several relative levels of flow rate as shown in Figre 6, where the higher the flow rate, the denser the area to be plotted. microcompter program was developed to accept varios otpt data readily available in the TRNSYT model (which incldes timings, satration flows, platoon dispersion factors, and the departre patterns on each link), and to se these data to prodce a platoon progression diagram (PPD) display. The program applies TRNSYT's platoon-dispersion model every 50 ft along the artery and converts the propagated profile to a density fnction, normalized to the maximm flow rate, which is then plotted. simplified PPD is shown in Figre 7. The dark areas departing from pstream intersections represent flow 100 0 00 0 0000 000 0 ;::- 80 00 z: 0000000000000000 000 UJ 0000000000000000 000 00000000000000000 000 UJ "' ~ 60 :J: 0 _,... ~,.. ~ 0 _,.... 40 20 c 0000000000 :::! 0 UJ "' 0.. TME N CYCE FGURE 6 Flow profile illstrating density fnction. 00000 00000 00000 000000 0 bo SECOND CYCE b( STEPS PER CYCE RUN TTE1 ---------- TEST DT FOR PPG - 4 NODES POT TTEt E) ----------- PERFECT PROGRESSON 0The cycle length and step size are TRNSYT inpts. E) The titles are also entered into TRNSYT. E) SGN STTUS - (red or green) is shown jst like a time-space d1agram. () The platoon is satrated as it leaves the intersection. 0 The platoon spreads ot as it progresses down the street. 0 small qee bilds p here becase a few vehicles have been stopped on the red. @This platoon reslts from trning traffic entering the link on the cross street green: 0 This large qee bilds p becase the 1 ink volmes are near capacity. FGURE 7 Typical PPD.

52 Transportation Research Record 957 at or near the maximm, whereas the lighter areas are flows of lesser magnitde, perhaps ndelayed arrivals. s the platoon travels downstream it disperses, so that the length of time to which the highest flow rate applies will decrease: ths the dark areas become narrower and eventally disappear. The lighter areas appear to diverge, again representing the physical lengthening of the platoon in time as it disperses. The PPD therefore graphically shows the platoon behavior over the entire block or link length. Cross-street traffic is shown as platoons departing pstream in the red of the arterial. s the traffic approaches the downstream intersection and if it arrives on red, it bilds a qee as shown in Figre 7. The qeing model is based on inpt-otpt calclations and assmed vehicle lengths. Platoons that are not ~elayed pass throgh on green. This graphic has the following advantages: l. The best featres of TSDs and platoon profiles are combined: 2. Traffic progression (as opposed to green time alone) is clearly represented: 3. The effect of qeing is clearly shown: 4. The point made earlier (i.e., the desirability of clearing the qee before the arrival of the platoon) is made obvios: and 5. The graphic is easier to interpret than flow pr:c.files, particlarly in C.~r.1118 of system performance, and it shows the pitfalls of a straight bandwidth approach. The otpts to this program are directly available from Release 3 of TRNSYT-7F. The PPD shown in Figre 7 was prodced by the BTE (11) program. Signalized Network nimated Graphics t was also noted earlier that TSDs for networks are extremely difficlt to constrct and perhaps even more difficlt to interpret. The problem again is the need for three dimensions where only two are available on a monitor or on a printed page. One approach to solving this dilemma is to actally se three dimensions, where time is the third dimension. magine a TSD on a linear rote with the throgh band drawn. f a slice or cross section of the band is dawn on the distance axis every short increment of time, the physical location of the green band can be located on the rote as a fnction of time. f the green band was sperimposed over the street it =~lf, D.iid sbscqci"it f1.aff1ii:s r ~t..:li d ~ic..:tre were viewed in sync, the band wold appear to move along the rote. The same representation can also be shown on a network of streets, and the bands wold then be moving along all streets in the appropriate directions. This concept was first implemented by Corage (12) by sing a compter otpt microfilmer, an expensive machine that has now become obsolete. The concept remaine qite compelling, and wil11 the power of microcompters and compter graphics, the athors have crrently developed a microcompter-based model called signalized network animated graphics (SNG), which will be economically viable for widespread se. This model ses an BM Personal Compter with medim-resoltion color graphics. Samthe cycle are presented in Figre 8. nother extremely important advantage of the SNG animated network is its pblic appeal. The concept is intitively simple to nderstand and can be sed as a pblic relations tool to demonstrate to the general pblic and administrative officials how eftective a completed or proposed traffic signal system improvement project has been or will be. Con~id~ring the earlier co!!'.ments abot the nc!aflness, or rather limitations, of TSDs per se, a frther extension of the SNG concept will be to animate the movement of traffic platoons rather than green bands. This development shold prove far more sefl to the traffic engineer. USNG GRPCS TO NTERPRET DESGN EFFECTVENESS. Progression Band Positions t the Beginning of Cycle s p " [ E ' / - p " E \ / - The foregoing discssions have briefly described several commonly sed and several innovative graphic tools for analyzing signal timing and traffic flow. t is noteworthy to repeat that traffic signal system timings have traditionally been based on timespace relationships by sing manal methods or compter models like PSSER! 80 and MXBND. Recently, however, an increasing nmber of practitioners are shifting to strategies that optimize system efficiency, sing models sch as TRNSYT-7F and S GOP. This shift in strategies holds merit, and an exs ' B. Proqression Band Positions a Few Seconds fter the Beginning of Cycle iii ;,; C. Fll NPtwnrk Plnt FGURE 8 Sample frames of three points in cycle from the SNG program. s p " E t [ F -..

Wallace and Corage 53 PO~TE: BEEC-D V TME SPCE DGRM ::01"11'1ENT: PSSER 'Z: CFFSETS CYCE El'lGT:-t 8l SECOMOS: SCPE! NC == 1(i; : :J~ CYCE: J J:!E= :. 1 l ~ T, :.. /x:,.:xx.i:xxx..o: '1 { l(/'.{ i X'>'.XX':O'\\ l.: /; xxx :co: ' : '. t'l f XXXXXXUXXX \ \ \ FGURE 9 SPN TSD of Beech-Daly system. ample is given in this section by sing the PPO concept to graphically illstrate the advantages of the system efficiency strategy. The following example compares the TSO with the PPD and the TD for a section of Beech-Daly Road in Detroit. The same design (PSSER optimization) is depicted in each case. constant speed of 45 mph is assmed throghot this section, which contains seven traffic signals. The TSO is shown in Figre 9. This is a standard printed otpt from the SPN program, ato-scaled to fit conveniently on one page. The progression bands have been added to this figre for emphasis. The corresponding TO is shown in Figre 101 this also is an otpt of the SPN program. gain the leading and trailing edges of the progression bands have been added. Note that in this case the bands do not have the characteristic slope of the TSO becase of the correction for travel time. This permits the entire rote to be compressed into a mch smaller space. The advantages of the compression are as follows. 1. Compatibility with the shape of the videoscreen on a microcompter: The SPN program displays the TD on the screen and allows maniplation of offsets from the keyboard. This is a powerfl editing featre for the design of simple arterial systems. 2. ssessment of the qality of progression: Progression throghot a portion of the system is easier to visalize on the TD becase all of the signals are immediately adjacent to each other. Critical signals that interrpt progression are also more apparent. Note, for example, how intersection 3 stands ot as the critical signal for rightbond progression in Figre 10. Some sefl MOEs n addition to the width, efficiency, vales are provided. are also inclded in Figre 10. commonly sed measres of bandand attainability, three other 1. System offset: This is not really an MOE bt simply an indication of the amont by which all offsets were shifted to center the progression bands on the page for easier interpretation. 2. Performance index: This measre indicates the total PROS, as defined earlier in this paper. t is expressed as a proportion of the cycle length. ts vale is sally greater than the progression efficiency becase of progression opportnities that occr throghot a portion of the system (e.g., between intersections 2 and 4, rightbond). 3. nterference: This measre indicates the proportion of time in which a vehicle released from one signal will be stopped at the next signal. t has at least an intitive connection with safety and driver comfort. nterference is mch more apparent on the TD becase of the adjsted alignment of the red intervals. The TO and TSO only show time relationships among the signals. s sch, they are not concerned with the actal movement of traffic. s noted earlier, this is their main shortcoming. They reflect

54 Transportation Research Record 957 TRNSPORTTON RESERC CENTER RTER PROGRESSON DESGN PSSER 2 OFFSETS NTERSECTONS 7 CY CE ENGT 8~ SYSTEM OFFSET: 5) BNDWDT EFT :5 RGT 21 F ERFORMl'CE i JDE,; : 3'3 EFFCENCY: ~7 '4TT1~ NBT Y : 8 1 MTEFFERENCE: 15 ~~~~~--~~---~~~~~----- --- - - --~-~--~ ~---- NO.... TME-OCTON DGRM...... DST NCE SFEED RGTBOUND RED DOWN EFT ~igt F FT RGT 2 4 5 6 7 xxxx. ;;:~xx>:x;;xxx x x ~ x x 11-c xxxxxxx... x:x~: =-~~: t17~, ~xx ~~YX~xx~~,y 1~=s ~5 1 XXXXXXYX ( t t~-,! ~= 5 :>x.xx :o.xx xx>::<x xx.x ~c":> XX XX XX XX XX X :XX XX>'. X): XX.X Y, X \ 1 -, _1! 75: -~; -, ; -.c-:xxx:xx:o~xx>:xxxxx ),... X. x..:..: 1 17t), JO:,: 13 15 1 5..:jr: 4 ~ 1'.:: ::..+5! ';; 15,]~.;.5 - l ~ NO. OFFSET if'ercentj 95 88 9 1), 2 7 5 s:: 6 98 7 45....... TME-OCTON D GRM... EFTBOUND... RED UP "i">::.o : xxx xx xx:.1.,. )' >' xx ~x,;x>:x '5 FGURE 10 SPN TD of Beech-Daly system. what the motor i st can expect to enconter only nder extremely light traffic conditions. s traffic volmes increase, the actal conditions will depart sbstantially from the ideal pictre presented by the TSO and the TD. The PPD provides the soltion to this problem. The PPD for the Beech-Daly system is shown in Figre 11. Two points are apparent: 1. Considerable movement of traffic occrs otside of the progression bands (note that the bands are added to the drawing for prposes of comparison), and 2. Qees bild p within the bands at several intersections; in other words, the progression bands travel smoothly throgh the system, bt most of the vehicles mst stop. The PPD clearly shows how the traffic is affected by the signals. t also provides some insight into the rationale behind the signal timing design prodced by the TRNSYT model. The TRNSYT view of the system operation is exactly what i s s hown on the PPD. CONCUSONS iii The recent massive increase in the se of microcompters has provided the traffic engine e r with greatly enhanced graphics capabilities. n excellent example is fond in signal progression design. The time-space diagram, which has been sed niversally for the past 50 years, is primitive and inadeqate for many prposes. The graphics techniqes presented in this paper extend the concept of the time-space diagram. The techniqes may be implemented easily and are powerfl tools i n t he design and analysis of traffic control systems. :;;;.. ' REFERENCES 1. PSSER 80 User's Manal. Texas State Depart-.,.,.,:. - -.:... _,.:- "'" -- -- -.-.&... -.! -- lllcll l... UJ. fl.&.':fllwq}'i::> CUU r..'-".j..j..qllotjl..q\...j.ullr stin, Dec. 1982. FGURE 11 PPD of Reech-Daly ~y!ll:em.... -~-: ' _.. '

55 2. J.C.D. ittle and M.D. Kelson. Optimal Signal Timing for rterial Signal Systems. Operations Research Center, Massachsetts nstitte of Technology, Cambridge, Dec. 1979. 3. C.E. Wallace et al. TRNSYT-7F ser's Manal. Transportation Research Center, University of Florida, Gainesville, Feb. 1983. 4. E.B. ieberman and J.. Woo. SGOP : Program to Calclate Optimal Cycle-Based Traffic Signal Timing Patterns--Volme : User's Manal. KD ssociates, nc., ntington Station, N.Y., Oct. 1978. 5. D.. Robertson. TRNSYT: Network Stdy Tool. Report R 253. Road Research aboratory, Crowthorne, Berkshire, England, 1969. 6. R.. Vincent,.. Mitchell, and D.. Robertson. User Gide to TRNSYT, Version 8. Report 888. Transport and Road Research aboratory, Crowthorne, Berkshire, England, 1980. 7. C.E. Wallace and K.G. Corage. rterial Progression--New Design pproach. n Transportation Research Record 881, TRB, National Research Concil, Washington, D.C., 1982, pp. 53-59. 8. C.E. Wallace. Development of a Forward ink Opportnities Model for Optimization of Traffic Signal Progression on rterial ighways. Ph.D. dissertation. University of Florida, Gainesville, 1979. 9. K.G. Corage, C.E. Wallace, and D.P. Reaves. rterial nalysis Package (P), User's Manal. Transportation Research Center, University of Florida, Gainesville, 1982. ::.o. K.G. Corage. Signal Progression nalysis (SPN), McTrans Volme 1. Transportation Research Center, University of Florida, Gainesville, 1980. 11. Bandwidth sn't the End (BTE), User's Manal. Microtrans ssociates, nc., 1983. 12. K.G. Corage. Compter Graphics: New ook at Signal Progression. ~ Compendim of Technical Papers, 43rd nnal Meeting of TE, Sept. 1973. Pblication of this paper sponsored by Committee on Traffic Signal Systems. nalysis of Parking 1n Urban Centers: Eqilibrim ssignment pproach YEUD J. GUR and EDWRD. BEMBORN BSTRCT Parking policies and spply play a major role in the management of transportation systems in dense rban areas. method for representing and analyzing parking is described. nclded in the procedre are calclations of parking impedance for each destination point in a stdy area and the determination level of se of each parking location in the area, inclding illegal parking. n the model the amont of time spent looking or waiting for a parking space is an increasing fnction of the tilization level of the parking area. With this relationship it is possible to describe and analyze the parking process in the framework of ser-optimized eqilibrim assignment. ll of the major factors that affect parking behavior in rban areas are acconted for, inclding walk to destination, parking fees, parking reglations, intensity of enforcement, and spply-demand relationships. The model and its testing in a dense section of the city of aifa, srael, are described. n this test case parking behavior is examined as it varies with vale of walk time, parking cost, parking fines, enforcement policies, and level of travel demand. n densely developed sections of rban areas sch as the central bsiness district (CBD), parking constittes a large part of the total travel impedance of travelers who se private atomobiles. Parking management can be an effective tool for controlling the nmber and natre of atomobile arrivals. Sch control can be realized in a nmber of ways, from individal changes in modal split or trip schedling to overall changes in the level of activity of an area. Possibly one of the most important qestions in the management of transportation in rban centers is the determination of a level of parking spply that encorages arrival by pblic transportation, while at the same time prevents loss of activity becase of parking shortages. Becase of the fear of potential bsiness loss throgh rigid parking control, managers are nwilling to experiment with changes in parking policy as an element in the management of transportation systems. model that analyzes parking in dense rban areas is described. The model is designed to serve as part of a modeling system for the analysis of the impact of integrated transportation system management (TSM) strategies in city centers. The parking model has also proved to be an effective independent tool for parking design, and it will be presented here as sch. The prpose of the model is to simlate parking choice and to provide the following information: