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2 Transportaton Research Part C 30 (013) Contents lsts avalable at ScVerse ScenceDrect Transportaton Research Part C journal homepage: An adaptve control algorthm for traffc-actuated sgnals ng Zheng a,, Wll Recker b a Chongqng Transport Plannng Insttute, No. 1, Yangheercun, Jangbe Dstrct, Chongqng 40000, Chna b Insttute of Transportaton Studes, Unversty of Calforna at Irvne, Irvne, CA 9697, USA artcle nfo abstract Artcle hstory: Receved 15 March 011 Receved n revsed form 17 February 013 Accepted 17 February 013 Keywords: Actuated control Adaptve control Optmzaton Mcroscopc smulaton A real-tme, on-lne control algorthm s proposed that ams to mantan the adaptve functonalty of actuated controllers whle mprovng the performance of traffc-actuated sgnal control system. To be consstent wth the operaton logc of exstng sgnal control devces, only those four basc control parameters that can be found n modern actuated controllers are consdered: phase sequence, mnmum green, unt extenson and maxmum green. Mcroscopc smulaton s used to test and evaluate the proposed control algorthm comparng wth free-mode actuated, actuated-coordnated and volume densty control n a calbrated sgnalzed network. Smulaton results ndcate that the proposed algorthm has the potental to mprove the performance of the network at dfferent traffc demand levels. Ó 013 Elsever Ltd. All rghts reserved. 1. Introducton Tradtonally, traffc sgnals at a sgnalzed ntersecton operate n one of two dfferent control modes: ether pre-tmed or traffc-actuated (both sem-actuated and full-actuated). In pre-tmed control, all of the control parameters, ncludng cycle length, phase splts and phase sequence, are preset offlne based on an assumed determnstc demand level at dfferent tme perods of day. Ths control mode has only a lmted ablty to accommodate the traffc fluctuatons that are commonly found n realty. In traffc-actuated control, cycle length, phase splts and even phase sequence can be changed n response to the real-tme vehcle actuatons regstered at loop detectors or other traffc sensors, but these changes are stll subject to a set of predefned, fxed control parameters (e.g., mnmum green, unt extenson and maxmum green, etc.) that are not accordngly responsve to the varyng traffc condton. Alternatvely, an on-lne control algorthm that decdes real-tme sgnal operaton parameters offers a potental mprovement to actuated control. Exstng on-lne control algorthms that have been deployed are typfed by the so-called thrdgeneraton urban traffc control systems (UTCS), whch can be further categorzed nto centralzed traffc-responsve systems and dstrbuted traffc-adaptve systems. In the centralzed system, such as SCATS (Sms and Dobnson, 1979; Lowre, 199) and SCOOT (Hunt et al., 191; Robertson and Bretherton, 1991), a master computer s used to adjust the cycle lengths, offsets and splts of all sgnals on a cycle-by-cycle bass, such that a best tmng plan can be found for the operaton of the entre network. In the dstrbuted system, such as OPAC (Gartner, 193) and RHODES (Head et al., 199; Mrchandan and Head, 001), separate calculatons are taken to determne the phase sequences and duratons of each sgnal, wth an attempt to optmze the performance of each local ntersecton. To some extent, actuated controllers are themselves adaptve n vew of ther ablty to vary the same set of outcomes as n adaptve control, but as mentoned prevously, ths adaptablty s restrcted by a set of predefned, fxed control parameters that are not adaptve to current condtons. To acheve the functonalty of truly adaptve controllers, a set of onlne optmzed phasng and tmng parameters are needed. Correspondng author. E-mal addresses: xngzheng190@gmal.com (. Zheng), wwrecker@uc.edu (W. Recker) /$ - see front matter Ó 013 Elsever Ltd. All rghts reserved.

3 94. Zheng, W. Recker / Transportaton Research Part C 30 (013) In general, three ssues must be addressed n formulatng an on-lne optmal control problem: (1) development of a mathematcal model that represents the current, or expected, traffc condton of the controlled system; () specfcaton of the real-tme control objectve that can be expressed as a certan performance ndex; and (3) desgn of an approprate optmzaton technque such that the controlled system meets the specfed crtera. Mathematcal models that represent the traffc condton of the controlled system, whch n ths research corresponds to the sgnalzed ntersectons, can be classfed nto the followng three generalzed categores (Pavls and Recker, 004): (1) store-and-forward models (e.g., Gazs and Potts, 1963); () dsperson-and-store models (e.g., Pacey, 1956; Robertson, 1969); and (3) knematc wave models (e.g., Stephanedes and Chang, 1993; Lo, 001). The most common objectve for real-tme sgnal control strateges s to desgn a sgnal tmng plan that mnmzes total (or, average) ntersecton control delay, whch serves as the prmary performance ndcator of level of servce at sgnalzed ntersectons. Exstng ntersecton control delay models are summarzed nto four categores (Don et al., 004): (1) determnstc queung models (e.g., Cox and Smth, 1961), () shock wave models (e.g., Rorbech, 196; Stephanopoulos and Mchalopoulos, 1979; Mchalopoulos et al., 190), (3) steady-state stochastc models (e.g., Webster, 195; Newell, 1960, 1965; McNel, 196; Hedemann, 1994), and (4) tme-dependent stochastc models (e.g., Akcelk, 191, 19; Brlon and Wu, 1990; Akcelk and Rouphal, 1993; Fambro and Rouphal, 1997). Two fundamental approaches are commonly used for on-lne optmzatons (Ln and Vjayakumar, 19): bnary choce approach and sequencng approach. In bnary choce approach, tme s dvded nto successve small ntervals ( 4 s) and a decson s made n each nterval ether to extend or to termnate the current sgnal phase. Examples of ths approach nclude Mller s algorthm (Mller, 1963), Traffc Optmzaton Logc (TOL) (Bang, 1976), Modernzed Optmzed Vehcle Actuaton strategy (MOVA) (Vncent and Young, 196), and Stepwse Adjustment of Sgnal Tmng (SAST) (Ln et al., 197). In sequencng approach, the decson-makng nterval s relatvely longer and usually long-term optmal settngs, such as phase splts and phase swtchng ponts, are specfed. Typcal of ths approach s the Optmzaton Polces for Adaptve Control (OPAC) (Gartner, 193), whch ncorporates a rollng horzon scheme to determne optmal sgnal swtchng sequences for a future tmng perod. Addtonally, the development and adopton of on-lne control procedures have been hampered by two fundamental mpedments to ther successful mplementaton: (1) the theoretcally-sound algorthms generally are specfed n terms of those parameters and control optons that are not smply wthn the lexcon of control devces and typcally nvolve complex programmng formulatons (e.g., mxed-nteger and/or pece-wse functons) that do not lend themselves to real-tme soluton, and () the practcally feasble algorthms that do manpulate those parameters employed n modern control devces almost unversally are formulated based on hghly smplfed approxmatons and assumptons (e.g., steady-state condton) to both control response and traffc measurement. In consderaton of these aspects, ths paper, as an extenson of the prevous work (Zheng et al., 010), ntroduces an on-lne control algorthm that ams to mantan the adaptve functonalty of actuated controllers whle mprovng the performance of traffc-actuated sgnal control system. In the nterest of facltatng deployment, ths algorthm s developed based on the tmng protocol of the standard NEMA (Natonal Electrcal Manufacturers Assocaton) eght-phase full-actuated dual-rng controller (ITE, 001). In formulatng the optmal control problem, a flow predcton model s developed to estmate the future vehcle arrvals at the target ntersecton, the traffc condton at the target ntersecton s descrbed as over-saturated through the whole tmng process, and the optmzaton objectve s specfed as to mnmze total cumulatve vehcle queue as an equvalent to mnmzng total ntersecton control delay. Accordng to the mplct tmng features of actuated control, a modfed rollng horzon scheme s devsed to optmze the values of four basc control parameters phase sequence, mnmum green, unt extenson and maxmum green based on the future flow estmaton, and these optmzed parameters serve as avalable sgnal tmng data for further optmzatons. Ths dynamcally recursve optmzaton procedure properly reflects the functonalty of truly adaptve controllers. In the followng secton, we wll address how the general ssues regardng onlne optmal control are consdered n ths research. Then, an onlne optmzaton procedure that corresponds to the proposed adaptve control algorthm s ntroduced n detal. Next, mcroscopc smulaton s used to test and evaluate the performance of the proposed algorthm n a calbrated network consstng of thrty-eght sgnals. Last, conclusons and potental future works are presented. The notatons used n the model formulaton appear n the Appendx.. Consderaton of the general ssues regardng onlne optmal control.1. Modelng the traffc condton at sgnalzed ntersectons Generally, the operatonal state of a sgnal control phase vares alternatvely between n servce and not n servce wthn the complete tmng perod. Each n-servce perod s defned as phase splt, and each not-n-servce perod defned as the red duraton, whch s actually the n-servce perod for those conflctng phases wthn the same rng. From another vewpont, the phase state changes alternatvely between effectve green and effectve red. Effectve green refers to the perod from the end of start-up lost tme to the begnnng of clearance lost tme wthn the same phase, and effectve red refers to the perod precedng effectve green, whch conssts of total lost tme and red duraton. The relatonshps between these tmng perods are shown n Fg. 1, and can be expressed by

4 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Effectve Red Effectve Green l R l 1 g e l Tme Not-In-Servce Perod In-Servce Perod (Phase Splt) Fg. 1. Phase state. r e ¼ l þ R þ l 1 ¼ R þ L G ¼ l 1 þ g e þ l ¼ g e þ L ð1þ ðþ R ¼ 0 G 0 ð3þ where 0 s the ndex of the precedng phases that conflct wth phase wthn the same rng. Based on the defntons of effectve green and effectve red, the traffc condton for each phase, both under-saturated and over-saturated, can be llustrated wth the queue formaton and dsspaton process as shown n Fg.. A (t) and D (t) are two general (smooth) functons of tme that represent the cumulatve number of vehcle arrvals and departures respectvely for phase. (Here, smooth functons are adopted to use dfferental calculus n the optmzaton process.) The vertcal dstance between the arrval and departure curves represents the number of vehcle queue at tme t and equals to A (t) D (t). By extendng ths approach, a combned arrval departure curve pattern can be developed to llustrate the real-tme traffc condton of the entre ntersecton. Fg. 3 shows an example of the combned queue accumulaton curves wthn a sgnal Cumulatve Vehcles Arrval Curve A (t) Departure Curve D (t) Cumulatve Vehcles Arrval Curve A (t) Departure Curve D (t) Effectve Red Effectve Green Tme Effectve Red Effectve Green Tme (a) Under-saturated condton (b) Over-saturated condton Fg.. Queue accumulaton curves. Fg. 3. Combned queue accumulaton curves.

5 96. Zheng, W. Recker / Transportaton Research Part C 30 (013) control cycle. (Note that a sgnal control cycle s comprsed of two barrer groups and, n actuated control, both barrer groups and the cycle length are varable.) P A ðtþ and P D ðtþ are two general functons of tme that represent the total cumulatve number of vehcle arrvals and departures respectvely for all eght phases ( = 1,,..., ). The vertcal dstance between the combned arrval and departure curves represents the total number of vehcle queue at the ntersecton at tme t and equals to P A ðtþ P D ðtþ. Theoretcally speakng, snce only two phases can be n servce at a tme (e.g., Dt), the combned departure curve wll never ntersect the combned arrval curve as long as conflctng phases have an arrval flow rate greater than zero. (In practce, the combned departure curve wll fnally meet the combned arrval curve when no conflctng phase s actuated and the sgnal stays n green for current phases.) Therefore, t s safe to presume that the sgnalzed ntersecton s over-saturated through the whole tmng process (.e., P A ðtþ P D ðtþ > 0Þ... Specfyng the real-tme control objectve In ths research, only one objectve s consdered for optmzaton to mnmze total ntersecton control delay. Dfferent from other well-known delay expressons, heren the delay experenced by each phase s consdered smultaneously. Based on the combned queue accumulaton curves as shown n Fg. 3, the total ntersecton control delay durng a certan perod, W total, s equvalent to the area between P A ðtþ and P D ðtþ over ths perod, whch can be determned by W total ¼ Z t t 1 " A ðtþ # D ðtþ dt ð4þ where t 1 s the start moment of the target perod and t s the end moment of the target perod. Then, the control objectve can be expressed by Z t mn W total ¼ mn t 1 " A ðtþ # D ðtþ dt ð5þ.3. Desgnng the on-lne optmzaton technque Snce the advent of Mller s algorthm (Mller, 1963), rollng horzon scheme (or, varatons of t) has become ncreasngly attractve regardng on-lne control procedures (e.g., Robertson and Bretherton, 1974; Gartner, 193; Bell, 1990; Heydecker, 1990). In ths scheme, a project horzon s predetermned whch generally conssts of N tme ntervals, as shown n Fg. 4. Flow data are measured for the frst H ntervals (head porton) and are estmated from a model for the next N H ntervals (tal porton). Optmal phase splts and/or phase swtchng ponts are specfed based on these data so as to mnmze the total delay (or, optmze other performance ndces) over an upcomng target perod (e.g., a length of tme equal to the horzon). Then, the project horzon s shfted nto the future by R ntervals (roll perod) and the same process repeats for the next teraton. Usually, the roll perod s equal to the length of the head porton, and t can be as small as one tme nterval (say, 4 s). Wthout dstortng the prncple, n ths secton we ntroduce a modfed rollng horzon scheme that s developed based on the mplct tmng features of actuated control (refer to Fg. 5 for example): Fg. 4. Rollng horzon scheme.

6 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Target Perod Target Perod Target Perod Barrer Group 1 Barrer Group Barrer Group 1 Barrer Group Barrer Group 1 Barrer Group Iteraton 1 Head Tal Iteraton Roll Perod Head Tal Iteraton 3 Roll Perod Head Tal Fg. 5. Modfed rollng horzon scheme. Step 1: The head porton of the project horzon s set equal to the summed length of any two consecutve barrer groups (whch can be vewed as a floatng cycle and s also varable), durng whch the sgnal tmng data that nclude phase splts and parameter settngs (.e., phase sequence, mn green, max green and unt extenson) are fully exploted to obtan the vehcle arrval flow for each actuated phase. Step : Based on the flow data obtaned from step 1, a flow predcton model s used to estmate the future vehcle arrval flow for each sgnal phase (and thus the total arrval flow for the entre ntersecton) over the tal porton. The tal porton s denoted the target perod and equal to the floatng cycle that follows the head porton. Step 3: Based on the flow estmaton obtaned from step, a new sgnal tmng plan s specfed wth an objectve to mnmze the total ntersecton control delay (as expressed n Secton.) over the tal porton. Ths new plan ncludes the optmal phase sequence for the tal porton, and the optmal mn green, unt extenson and max green for each sgnal phase. Step 4: The project horzon s shfted nto the future by a tme perod that s equal to the length of one barrer group (.e., roll perod), and then the optmzaton process repeats from step 1. As can be realzed, ths modfed rollng horzon scheme features the followng three major dfferences: (1) The head porton, tal porton (.e., target perod) and roll perod are all tme-varant snce they are actually determned by the phase splts, whch n essence are determned by the sgnal tmng plan and real-tme vehcle actuatons. () Optmal control parameters are all determned based on flow estmatons, whch may degrade the performance of the optmzaton procedure. However, these optmzed control parameters that are used n the upcomng perod wll serve to be a feed-back mechansm (especally the unt extenson and max green) that has the ablty to adjust sgnal tmng n response to real-tme vehcle actuatons. (3) Snce the roll perod s equal to the length of one barrer group, the optmzaton frequency becomes once per floatng cycle and the parameter specfcatons are only mplemented n one (.e., the upcomng) barrer group. 3. Methodology 3.1. Overvew Based on the dscusson n Secton, an on-lne optmal control algorthm s proposed here that, together wth sgnal control prncples, consttutes a dynamcally recursve optmzaton procedure, as shown n Fg. 6. Ths procedure conssts of four major modules: Data Processng, Flow Predcton, Parameter Optmzaton and Sgnal Control. The frst three modules correspond to the frst three steps of the modfed rollng horzon scheme, except that vehcle spllover (of each phase) s also obtaned from step 1 and used as another nput for step 3. The fourth module corresponds to the sgnal control system that employs the optmzed control parameters output from step 3. The resultng phase splts, as well as those parameters that have been appled, wll be used as nputs for step 1 n the next teraton, whch begns a roll perod later as stated n step 4. Snce ths research focuses on mantanng the adaptve functonalty of actuated controllers whle mprovng the performance of traffc-actuated sgnal control system, whch manly apples to solated ntersectons, t s assumed for smplcty that the vehcle arrval pattern assocated wth each vehcle movement conforms to Posson process. (Strctly speakng, ths assumpton lmts the applcaton of ths algorthm to non-congested perods of operaton.) Under other condtons, such as

7 9. Zheng, W. Recker / Transportaton Research Part C 30 (013) Vehcle Arrval Flow Flow Predcton Future Vehcle Arrval Flow Proposed Onlne Control Algorthm Data Processng Vehcle Spllover Parameter Optmzaton Sgnal Control Phase Sequence Maxmum Green Phase Splts Mnmum Green Unt Extenson Fgure 6 Recursve optmzaton procedure Traffc-Actuated Control System Fg. 6. Recursve optmzaton procedure. the sgnalzed network n urban areas, the concepts of control developed n ths paper may stll apply, for example, va replacng the Posson-related arrval pattern by other approprate dstrbutons (e.g., the well-known Robertson s dsperson model). Besdes, the proposed control algorthm s formulated based on the basc operaton logc of full-actuated controllers. Other actuated control modes, such as sem-actuated and volume densty, are not consdered. A few more assumptons and explcatons are addressed below: 1. The sgnal tmng process for each actuated phase reles on the basc gap-seekng logc. Specal operaton parameters, such as recall, are not consdered.. The sgnal tmng of each cycle (or, floatng cycle) reles on the basc dual-rng control process. Specal operaton functons, such as dual-entry, smultaneous gap-out and condtonal servce, are not consdered. 3. The vehcle arrval flow rate for each sgnal phase s assumed to be constant wthn each cycle (or, floatng cycle). The saturaton flow rate for each sgnal phase s assumed to be constant durng the whole tmng process. The vehcle arrval flow rate s assumed to be strctly less than the saturaton flow rate. 4. The effectve green tme for each sgnal phase s assumed to be equal to the actual dsplayed green nterval. The total lost tme for each sgnal phase s assumed to be constant and equal to the sum of yellow change and all clearance ntervals (whch are pre-set and constant). 5. Vehcles are assumed to be equvalently dstrbuted on each lane of mult-lane approaches, and queue vertcally at the stop lne for both through and left-turn movement phases. 6. Rght-turn movements are assumed to be servced on exclusve rght-turn lanes and have neglgble effect on the sgnal operaton. U-turn movements are not consdered. 7. All tmng-related varables take expected or average values. 3.. Data processng Accordng to Hghway Capacty Manual (TRB, 000), effectve green can be broken nto queue servce tme and green extenson perod (refer to Fg. 7). Durng the queue servce tme, vehcles dscharge at saturaton flow rate untl the queue dsspates. The total number of these vehcles s equal to the sum of ntal queue, f any, plus those vehcles that arrve durng the effectve red and queue servce tme. Therefore, S G q ¼ Q þ k ðr þ L Þþk G q ð6þ Then, the queue servce tme can be expressed by G q ¼½Q þ k ðr þ L ÞŠ=ðS k Þ ð7þ Durng the green extenson perod, arrvng vehcles travel through the ntersecton freely untl the current phase termnates by gap-out control the green nterval termnates when no vehcles actuate the extenson detector wthn a unt extenson perod,.e., when the vehcle headway (n tme) larger than the unt extenson occurs. Accordng to Posson process, vehcle

8 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Fg. 7. Queue accumulaton dagram. headways have a negatve exponental dstrbuton and the number (n) of headways untl the frst one that nvokes gap-out (.e., larger than b) has a geometrc dstrbuton. Therefore, P robablty ðnumber of headways untl the frst one larger than b occursþ ¼½1 expð k b ÞŠ n 1 expð k b Þ M ean ðnumber of headways untl the frst one larger than b occursþ ¼expðk b Þ Durng the e kb vehcle headways, a total of (e kb 1) vehcles are servced. Thus, the green extenson perod can be expressed by G e ¼½expðk b Þ 1Š=k ðþ It should be noted here that the green-tme estmaton model mentoned by HCM s formulated based on two ndefensble assumptons: (1) the extenson detectors are placed at the stop lne and so the green extenson perod starts tmng rght after the queue servce tme expres, and () the phase defntely termnates by gap-out control. In real feld stuatons, however, the extenson detectors, especally those for through-movement phases, are set back a certan dstance (e.g., 300 ft) from the stop lne, and max-out control materalzes frequently when the traffc demand reaches a relatvely hgher level. In addton, accordng to the tmng logc of actuated control phases, the green extenson perod starts tmng exactly when mnmum green expres, so t s possble that the phase termnates whle the vehcle queue has not yet dsspated. To avod all these shortcomngs, heren we take nto account both the gap-out/max-out nformaton and the sgnal tmng data that ncludes phase splt, mn green, max green and unt extenson to determne the effectve green tme for each actuated phase. Furthermore, the vehcle arrval flow rate and spllover are also determned. Specfcally, t s assumed here that when mnmum green expres, the vehcle queue length has been decreased to be shorter than the dstance from the tralng edge of the extenson detector to the stop lne. (1) Gap-out stuaton When a sgnal phase termnates by gap-out control, the green extenson perod,.e., the perod from the end of mnmum green to the end of green nterval, can stll be expressed by Eq. () unless the arrval pattern changes. Therefore, the effectve green tme s equal to the mnmum green plus green extenson perod,.e., g e ¼ G mn þ G e ¼ G mn þ½expðk b Þ 1Š=k ð9þ Then, accordng to Eq. (), the phase splt can be expressed by G ¼ G mn þ½expðk b Þ 1Š=k þ L ð10þ In Eq. (10), all varables except k are known sgnal tmng data obtaned from phase, and thus the vehcle arrval flow rate, k, can be determned by solvng the nonlnear nverse functon F 1 (k ),.e., k ¼ F 1 ðk Þ; where Fðk Þ¼G mn þ½expðk b Þ 1Š=k þ L G ¼ 0 ð11þ To determne the vehcle spllover, the followng three cases that descrbe dfferent gap-out stuatons need to be consdered (refer to Fg. ): 1. G q 6 G mn ; :e:; ½Q þ k ðr þ L ÞŠ=ðS k Þ 6 G mn ; or k 6 ðs G mn Q Þ=ðR þ L þ G mn Þ ð1þ

9 100. Zheng, W. Recker / Transportaton Research Part C 30 (013) Fg.. Gap-out stuatons.. G mn < G q 6 g e ; :e:; G mn < ½Q þ k ðr þ L ÞŠ=ðS k Þ 6 G L ; or ðs G mn Q Þ=ðR þ L þ G mn Þ < k 6 ½S ðg L Þ Q Š=ðR þ G Þ ð13þ

10 . Zheng, W. Recker / Transportaton Research Part C 30 (013) g e < G q ; :e:; G L < ½Q þ k ðr þ L ÞŠ=ðS k Þ; or k > ½S ðg L Þ Q Š=ðR þ G Þ ð14þ As can be seen, three consecutve, non-overlapped numercal ntervals regardng the value of k are llustrated by nequaltes (1) (14), whch are also expressed n terms of known tmng data. Based on the k determned by Eq. (11), only one nequalty (.e., only one case) s true. Therefore, the vehcle spllover can be determned by one of the followng equatons correspondng to the true case. Case 1; : spll Q ¼ 0; Case 3 : spll Q ¼ Q þ k ðr þ G Þ S ðg L Þ ð15þ () Max-out stuaton When a sgnal phase termnates by max-out control, the green extenson perod,.e., the perod from the end of mnmum green to the end of green nterval, s determned by G e ¼ G max G mn ð16þ And, the effectve green s equal to maxmum green,.e., g e ¼ G max ð17þ Then, the phase splt s expressed by G ¼ G max þ L ð1þ Unlke Eq. (10), although the varables n Eq. (1) are also known sgnal tmng data obtaned from phase, the vehcle arrval flow rate, k, cannot be determned. However, consderng that, after the mnmum green expres, arrvng vehcles keep actuatng the extenson detector untl the maxmum green lmt s reached, t s safe to presume that the expected tme for the frst headway larger than b to occur, as determned by Eq. (), s greater than the green extenson perod as determned by Eq. (16),.e., ½expðk b Þ 1Š=k > G max G mn ð19þ Note that the term (e kb 1)/k n nequalty (19) s a monotone ncreasng functon of k, so the mnmum value of k, denoted by k mn here, can be acheved by solvng another nonlnear nverse functon F 1 (k ),.e, k mn ¼ F 1 ðk Þ; where Fðk Þ¼½expðk b Þ 1Š=k ðg max G mn Þ¼0 ð0þ Specfcally, snce the vehcle arrval flow rate s strctly less than the saturaton flow rate, we assume here that k s approxmately equal to the mean of k mn and S,.e., k ¼ðk mn þ S Þ= ð1þ Agan, to determne the vehcle spllover, the followng three cases that descrbe dfferent max-out stuatons need to be consdered (refer to Fg. 9): 1. G q 6 G mn ; :e:; ½Q þ k ðr þ L ÞŠ=ðS k Þ 6 G mn ; or k 6 ðs G mn Q Þ=ðR þ L þ G mn Þ ðþ. G mn < G q 6 g e ; :e:; G mn < ½Q þ k ðr þ L ÞŠ=ðS k Þ 6 G max ; or ðs G mn Q Þ=ðR þ L þ G mn Þ < k 6 ðs G max Q Þ=ðR þ L þ G max Þ ð3þ 3. g e < G q ; :e:; G max < ½Q þ k ðr þ L ÞŠ=ðS k Þ; or k > ðs G max Q Þ=ðR þ L þ G max Þ ð4þ Smlarly, three consecutve, non-overlapped numercal ntervals regardng the value of k are llustrated by nequaltes () (4), whch are also expressed n terms of known tmng data. Based on the k determned by Eq. (1), only one nequal-

11 10. Zheng, W. Recker / Transportaton Research Part C 30 (013) Fg. 9. Max-out stuatons. ty s true. Therefore, the vehcle spllover can be determned by one of the followng equatons correspondng to the true case.

12 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Case 1; : spll Q ¼ 0; Case 3 : spll Q ¼ Q þ k ðr þ L þ G max Þ S G max ð5þ 3.3. Flow predcton Accordng to the modfed rollng horzon scheme, we here employ a dynamc exponental smoothng model to estmate the future vehcle arrval flow for each sgnal phase: Defne m k head the vehcle arrval flow rate assocated wth phase over the head porton n teraton m, whch s determned by Eq. (11) for gap-out cases or by Eq. (1) for max-out cases m the vehcle arrval flow rate assocated wth phase over the tal porton n teraton m, whch s predcted a m k tal m based on and vewed as the estmated value for k head k head the smoothng factor assocated wth phase n teraton m mþ1 Suppose the target perod s the tal porton n teraton m + 1, then mþ1 mþ1 k tal ¼ a mþ1 k head þ 1 a mþ1 k tal m; 0 < a mþ1 6 1; or mþ1 m mþ1 m k tal ¼ k tal þ a mþ1 k head k tal ; 0 < a mþ1 6 1 ð6þ The value of smoothng factor a m can be any postve decmals (61), and s usually set small for slowly evolvng condtons and large for sgnfcant transents. The propertes of exponental smoothng model can be found elsewhere (Chou, 1970). Here, the ntal value of a m s arbtrarly determned (e.g., 0.3), and, f sgnfcant errors exst, t wll be updated every floatng cycle by replacng the estmated value wth the true value,.e., Accordng to Eq. (6), we have m ¼ k tal k tal m 1 þ a m k head m k tal m 1 ; 0 < a m 6 1 If m k tal k head m 1 m > d; where d s a predetermned tolerance value; say; 0:1 k head Then, replace the frst term on the rght hand sde (k tal ) m 1 by (k head ) m, and the updated smoothng factor, a m+1, s determned by h m m. a mþ1 ¼ k tal k head m k tal k head m 1 ð7þ Partcularly noteworthy here s that, snce the head porton (and thus the tal porton) s rolled nto the future by a tme perod equal to one barrer group, n whch only up to four phases are servced, ths predcton model can only apply to those (up to four) actuated phases n the barrer group that has just expred, as only the arrval flow rates of these phases can be obtaned for the new head porton n the next teraton Parameter optmzaton Determnng optmal phase sequence The optmal phase sequence s determned along wth the specfcaton of optmal phase splts, wth the objectve to be mnmzng the total ntersecton control delay over the tal porton. (Note that these optmal phase splts are not parameter settngs but wll be used to determne the other three parameters.) Recallng Eq. (4) for the expresson of total ntersecton control delay, we then have the total delay for the tal porton expressed by W tal total ¼ Z t t 1 W tal total ¼ " A tal ðtþ # D tal ðtþ dt; or Z t t 1 A tal ðtþdt Z t t 1 D tal ðtþdt ðþ

13 104. Zheng, W. Recker / Transportaton Research Part C 30 (013) where t 1 s the start moment of the tal porton and t s the end moment of the tal porton. Based on the future vehcle arrval flow rate determned by Eq. (6), the term A tal ðtþ n Eq. () can be expressed by Therefore, A tal ðtþ ¼k tal t Z t t 1 A tal ðtþdt ¼ Z t t 1 k tal t dt ¼ k tal Z t t dt ¼ 1 t 1 t t 1 Snce t 1 s actually the start moment of the target perod, t can be set equal to zero for smplcty, and thus t refers to the length of the target perod and equals to the cycle length of the tal porton,.e., t ¼ G tal 1 þ G tal þ G tal 3 þ G tal 4 ¼ G tal 5 þ G tal 6 þ G tal 7 þ G tal ; or t ¼ 1 Then, Eq. (9) can be revsed nto Z t A tal t 1 ðtþdt ¼ 1 1 G tal! k tal! ¼ 1 k tal! G tal G tal k tal ð9þ! ð30þ To express the term D tal ðtþ n Eq. (), whch s the cumulatve number of departures at tme t assocated wth phase over the tal porton, we expect a clearance condton that, the phase green nterval wll be large enough to servce the ntal queue, f any, plus all the vehcles that arrve durng the effectve red and effectve green,.e., the phase s expected to be termnated wthout nvokng any vehcle spllovers (refer to Case 1 and Case n both gap-out and max-out stuatons). Therefore, D tal ðtþ can be expressed by >< S t; t 1 6 t < t D tal ðtþ ¼ k tal t; t 6 t < t 3 ; t 1 < t 1 < t < t 3 < t >: 0; otherwse where t 1 s the start moment of the queue servce tme (.e., G tal q ) assocated wth phase ; t s the end moment of the queue servce tme assocated wth phase, equal to t 1 þ G tal q ; and t 3 s the end moment of the effectve green assocated wth phase, equal to t 1 þ G tal L. Therefore, Z t D tal ðtþdt ¼ Z t Z! t3 S t dt þ k tal t dt ¼ Z t Z t3 Z! t S t dt þ k tal t dt k tal t dt t 1 t 1 t t 1 t 1 t 1 ¼ " Z t Z # t3 S k tal t dt þ k tal t dt ¼ 1 h S k tal t t 1 t 1 t 1 þ k tal t 3 t 1 ¼ 1 h S k tal ðt t 1 Þðt þ t 1 Þþk tal ðt 3 t 1 Þðt 3 þ t 1 Þ Recall t ¼ t 1 þ G tal q Z t D tal ðtþdt ¼ 1 t 1 þk tal G tal L Z t D tal ðtþdt ¼ 1 t 1 þ S k tal and t 3 ¼ t 1 þ G tal h G tal q S k tal t 1 þ G tal nh þ k tal L, then L S k tal G tal G tal q ; or G tal q L t 1 þ G tal q þ k tal G tal L t 1 ð31þ Recall Eq. (7) for the expresson of queue servce tme, then h. G tal q ¼ Q tal þ k tal R tal þ L S k tal ð7 0 Þ In Eq. (7 ), term Q tal refers to the ntal queue assocated wth phase over the tal porton, and equals to the vehcle spllover over the head porton, whch s determned by Eq. (15) for gap-out cases or Eq. (5) for max-out cases. Therefore Q tal ¼ spll Q head Then Eq. (7 ) can be revsed nto h G tal q ¼ spll Q head þ k tal R tal þ L = S k tal ð3þ ð7 00 Þ

14 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Substtutng Eq. (7 ) nto Eq. (31) yelds Z t D tal ðtþdt ¼ 1 >< h spll Q head >: t 1 ¼ h spll Q head þ k tal þ k tal R tal R tal þ G tal þ G tal h spll Q head þ k tal R tal þ L t 1 þ S k tal h t 1 þ 1 >< spll Q head þ k tal R tal þ L >: S k tal Thus, by substtutng Eqs. (30) and (33) nto Eq. (), we have!! W tal total ¼ 1 k tal G tal h spll Q head þ k tal R tal þ G tal t 1 h 9 1 >< spll Q head þ k tal R tal þ L >= þ k tal S k tal G tal L >: >; þ k tal 9 >= G tal L >; 9 >= G tal L >; þ k tal ð33þ ð34þ Note that n Eq. (34), the expresson of term R tal depends on the two phase sequences over both the head and tal portons, ether of whch can be any one of the 3 possble phase orders as shown n Fg. 10. As an example, here we suppose the phase sequence over the head porton s order #1 (whch s known) and the phase sequence over the tal porton s gong to be order #; then, referrng to Fg. 11, we have R tal 1 ¼ G head þ G head 3 þ G head 4 R tal ¼ G head 3 þ G head 4 þ G tal 1 R tal 3 ¼ G head 4 þ G tal 1 þ G tal R tal 4 ¼ G tal 1 þ G tal þ G tal 3 R tal 5 ¼ G head 6 þ G head 7 þ G head R tal 6 ¼ G head 7 þ G head þ G tal 5 R tal 7 ¼ G tal 5 þ G tal 6 þ G tal R tal ¼ G tal 5 þ G tal 6 The expresson for term t 1 depends on the phase sequence over the tal porton. Agan, referrng to Fg. 11, for example, we have t 11 ¼ 0 t 1 ¼ G tal 1 t 31 ¼ G tal 1 þ G tal t 41 ¼ G tal 1 þ G tal þ G tal 3 t 51 ¼ 0 t 61 ¼ G tal 5 t 71 ¼ G tal 5 þ G tal 6 þ G tal t 1 ¼ G tal 5 þ G tal 6 Note here that the start moment of queue servce tme s assumed to be equvalent to the start moment of phase splt. As can be realzed, both R tal and t 1 can also be expressed n terms of the phase splt G tal, and of course, there are a total of 3 possble expressons due to the 3 possble phase order numbers. Here we defne k W tal total k G tal k R tal k t 1 the total ntersecton control delay over the tal porton correspondng to phase order k, where k the phase splt assocated wth phase over the tal porton correspondng to phase order k the red duraton assocated wth phase over the tal porton correspondng to phase order k the start moment of phase over the tal porton correspondng to phase order k 1,,..., 3 as specfed n Fg. 10

15 106. Zheng, W. Recker / Transportaton Research Part C 30 (013) Fg. 10. Phase sequence. R 3 tal R 4 tal R 1 tal R tal Head (phase order #1) Tal (phase order #) R 5 tal R 6 tal R 7 tal R tal Fg. 11. Expresson of red duraton.

16 . Zheng, W. Recker / Transportaton Research Part C 30 (013) Then, Eq. (34) can be revsed nto!! k W tal total ¼ 1 k tal k G tal h h 1 >< spll Q head þ k tal k R tal þ L >: S k tal spll Q head þ k tal þ k tal k R tal þ k G tal 9 >= k G tal L >; k t 1 ð35þ Snce the objectve s specfed as mnmzaton of total ntersecton control delay, the objectve functon can be expressed by mn k W tal total ; where k ¼ 1; ;...; 3 Obvously, there s a specfc value of mnmzed total delay that corresponds to the phase order k. Here, of the thrty-two possble values of mnmzed delay, we take the mnmum as the optmal result,.e., h W optmal ¼ mn mn k W tal total ; where k ¼ 1; ;...; 3 Addtonally, three constrants are consdered n formulatng the optmzaton problem: (1) Barrer condton. Accordng to the concept of dual-rng sgnal control, the tmng perod n rng A should be equal to the tmng perod n rng B on ether sde of the barrer, therefore, G tal 1 þ G tal ¼ G tal 5 þ G tal 6 G tal 3 þ G tal 4 ¼ G tal 7 þ G tal () Clearance condton. As mentoned prevously, ths constrant ndcates that the phase green nterval s expected to be large enough to servce the ntal queue, f any, plus all the vehcles that arrve durng the effectve red and effectve green, and fnally termnate wth no vehcle spllover. Therefore, G tal L P G tal q Substtutng Eq. (7 ) yelds h G tal L P spll Q head þ k tal R tal þ L = S k tal (3) Storage condton. It s assumed here that each lnk between sgnalzed ntersectons and each left-turn bay has a fnte storage capacty. The storage capacty can ether be defned as maxmum allowable queue length f vehcles are assumed to queue horzontally along the approach, or defned as maxmum allowable queue sze f vehcles are assumed to queue vertcally at the stop lne. In ths research, the storage capacty s equvalent to maxmum allowable queue sze based on the assumpton n Secton 3.1, and t s expected that the maxmum vehcle queue sze of each phase, whch forms at the start moment of effectve green, cannot exceed the storage capacty, therefore, spll Q head þ k tal R tal þ L < Q max Therefore, the complete optmzaton problem can now be expressed by h W optmal ¼ mn mn k W tal total ; where k ¼ 1; ;...; 3 ð36þ subject to k W tal total ¼ 1 k tal! k G tal! h spll Q head h 1 >< spll Q head þ k tal k R tal þ L >: S k tal þ k tal þ k tal k G tal k R tal þ k G tal 9 >= L k t 1 ; ¼ 1; ;...; >; k G tal 1 þ k G tal ¼ k G tal 5 þ k G tal 6 k G tal 3 þ k G tal 4 ¼ k G tal 7 þ k G tal k G tal spll Q head h L P spll Q head þ k tal k R tal þ L = S k tal þ k tal R tal þ L < Q max ; ¼ 1; ;...; ; ¼ 1; ;...;

17 10. Zheng, W. Recker / Transportaton Research Part C 30 (013) The soluton to ths problem are the optmal phase sequence k, and a set of optmal phase splts k G tal phase order k. correspondng to the Determnng optmal mnmum green Conventonally, the mnmum green s set equal to an ntal green tme that allows all the vehcles potentally stored between the set-back detector (e.g., extenson detector) and the stop lne to enter the ntersecton (especally for throughmovement phases). Ths settng assumes that the entre dstance between the detector and the stop lne s occuped by stored vehcles, an assumpton that may be volated under lght traffc condtons. Referrng to Fg. a and Fg. 9a for example, the requred queue servce tme s less than the mnmum green,.e., the queung vehcles (stored vehcles plus the vehcles jonng the queue) wll enter the ntersecton before mnmum green expres, and thus the mnmum green wll not be fully utlzed and the phase may termnate by gap-out control later. Ths weakness s mtgated by volume densty control, n whch the mnmum green (or, added ntal) s calculated based on the number of stored vehcles, and ths computed ntal green cannot exceed a pre-set maxmum lmt (.e., maxmum ntal). A smlar method s taken here to determne mnmum green: set mnmum green equal to queue servce tme f the queue servce tme s less than the pre-determned (.e., conventonal) mnmum green, G 0 mn, otherwse, set t equal to the pre-determned mnmum green,.e., where G tal mn ¼ G tal mn G tal q ( Gtal q G 0 mn f G tal q f G tal q h ¼ mn Gtal q ; G 0 mn h ¼ spll Q head 6 G 0 mn ; or > G 0 mn þ k tal k R tal þ L = S k tal ð37þ Determnng optmal unt extenson The optmal unt extenson s expected to be a gap tme that s large enough to nvoke gap-out control at the end of the specfed optmal phase green. Then, accordng to Eq. (10), the optmal phase splt can be expressed by k G tal h ¼ G tal mn þ exp ktal b tal 1 =k tal Then, the optmal unt extenson s determned by h b tal ¼ ln 1 þ k tal k G tal L G tal mn =k tal h Note that the natural logarthm n Eq. (39) requres that clearance condton, we have þ L ð3þ 1 þ k tal ð k G tal L G tal mn Þ ð39þ be greater than 0. Accordng to the Thus, k G tal L P G tal q k G tal L G tal mn P Gtal q G tal mn Accordng to Eq. (37), we have k G tal k G tal L G tal mn P Gtal q G tal q f G tal q 6 G 0 mn ; or L G tal mn P Gtal q G 0 mn f G tal q > G 0 mn Then, k G tal k G tal L G tal mn P 0fGtal q 6 G 0 mn L G tal mn > 0fGtal q > G 0 mn 1 þ k tal k G tal L G tal mn 1 þ k tal k G tal L G tal mn P 1fG tal q > 1fG tal q 6 G 0 mn > G 0 mn ð40þ The requrement of natural logarthm s satsfed. Furthermore, substtutng nequalty (40) nto Eq. (39), we have b tal P 0 f G tal q 6 G 0 mn b tal > 0 f G tal q > G 0 mn ð41þ

18 . Zheng, W. Recker / Transportaton Research Part C 30 (013) where G tal q h ¼ spll Q head þ k tal k R tal þ L = S k tal Determnng optmal maxmum green When the optmal unt extenson fals to termnate the phase by gap-out control at the end of the optmzed phase green nterval, the maxmum green lmt s needed. Recallng Eq. (3) for the expresson of the optmzed phase splt, we have k G tal k g tal e h. L ¼ G tal mn þ exp ktal b tal 1 k tal ; or h. ¼ G tal mn þ exp ktal b tal 1 k tal As can be realzed, gven that G tal mn s determned by Eq. (37) and btal determned by Eq. (39), the effectve green over the tal porton, g tal e, s a monotone ncreasng functon of k tal. Specfcally, we assume here that g tal e reaches ts maxmum lmt (.e., maxmum green tme G tal max Þ as ktal ncreases to a value that s equal to the mean of k tal and the saturaton flow rate S. Therefore, h.. k G tal max ¼ Gtal mn þ exp k0tal b tal 1 k 0tal ; where k 0tal ¼ k tal þ S ; or "! #, k G tal max ¼ Gtal mn þ exp btal ktal þ S ð43þ 1 k tal þ S ð4þ 4. Testng and evaluaton The proposed adaptve control algorthm s tested and evaluated usng the scalable, hgh-performance mcroscopc smulaton package, PARAMICS (Cameron and Duncan, 1996). PARAMICS has been wdely used n the testng and evaluaton of varous Intellgent Transportaton System (ITS) strateges because of ts powerful Applcaton Programmng Interfaces (API). Users can access the core functons provded n PARAMICS through API to customze and extend many features of the underlyng smulaton model wthout havng to deal wth the propretary source codes. For the purpose of testng and evaluaton n ths paper, the proposed algorthm s developed as a plug-n through API programmng and appled to a calbrated sgnalzed network n PARAMICS. Ths network conssts of 3 sgnals that are ndvdually controlled by the free-mode traffc-actuated strategy and, for more detaled performance comparson, these sgnals are further coded under actuated-coordnated and volume densty control wth properly tuned parameters (whch are also programmed nto PARAMICS plug-ns through API). The study network s as shown n Fg. 1, whch s so-called the Irvne Trangle located n southern Calforna. Ths network ncludes a 6-mle secton of freeway I-405, a 3-mle secton of freeway I-5, a 3-mle secton of freeway SR-133 and several adjacent surface streets, ncludng two streets parallel to I-405 (.e. Alton Parkway and Barranca Parkway), one street parallel to I-5 (.e., Irvne Center Drve), and three crossng streets to I-405 (.e. Culver Drve, Jeffery Road, and Sand Canyon Avenue). A total of thrty-eght sgnals under free-mode traffc-actuated control are ncluded n the network. A prevous study has calbrated ths network for the mornng peak perod from 6 AM to 10 AM, and calbraton results have properly reflected exstng traffc condtons (Chu et al., 004). In the proposed control algorthm, the saturaton flow rate, S, s assumed to be 1900 veh/h/lane for each through movement phase, and 100 veh/h/lane for each left-turn movement phase. If the optmzed mn green s extremely short (e.g., <4 s), t s set to be 4 s n order to roughly cover the start-up lost tme. If the optmzed unt extenson s not greater than 1/S, whch may cause premature gap-out rght after the mn green expres, t s set equal to 1/S s. The unt extenson needs to be further adjusted for those phases (especally through movement phases) that have relatvely dstant set-back extenson detectors. Fg. 13 shows an example where the extenson detectors for the through movement phase are placed beyond the left-turn bay. In ths case, the unt extenson for the through phase s adjusted by b 0tal h. ¼ ln 1 þ k 0tal m G tal L G tal mn k 0tal where k 0tal s the the approachng flow rate over the tal porton. Three traffc demand scenaros are set up for the smulaton: 1. Exstng demand scenaro: ths scenaro corresponds to the traffc condton for the mornng peak perod and the traffc demands are obtaned drectly from the calbrated smulaton model;. Medum demand scenaro: the traffc demands are equvalent to 75% of the exstng demand scenaro; 3. Low demand scenaro: the traffc demands are equvalent to 50% of the exstng demand scenaro. Smulatons are conducted for a perod of 4 h and 15 mn for each scenaro under each control mode. The frst 15 mn are consdered to be the warm-up perod for vehcles to fll n the network, n order to represent the typcal (free-flow) traffc ð44þ

19 110. Zheng, W. Recker / Transportaton Research Part C 30 (013) Fg. 1. Study network. Call Only Detectors Extenson Detectors Stop Lne Call and Extenson Detectors Fg. 13. Set-back extenson detector confguraton. condton at the start tme of smulaton (.e., 6 AM) t takes less than 10 mn for a vehcle to fnsh the longest trp n the network n the real world. It should be noted here that the man objectve of smulaton s to evaluate f the proposed algorthm has the ablty to mprove the performance of the network under exstng traffc condtons; therefore, the setup of only scenaro 1 pertans drectly to ths end. However, scenaro and 3 are set up to further evaluate f ths algorthm also has the ablty to mprove the performance under the condtons of lower demand levels, whch may reflect non-congested or off-peak stuatons. And, snce scenaro 1 already reflects a relatvely hgh demand level, the condton of an even hgher demand level s not consdered. Two groups of measure of performance are specfed as the major smulaton results for analyss: (1) For the whole network: Average Travel Tme and Average Vehcle Speed; and () for local ntersectons: Maxmum Queue Length and Vehcle Travel Delay. Snce ths research focuses on the sgnal control at ntersectons, the measure of performance regardng the freeway are not ncluded n the results. These measures of performance are compared between these four control modes for each scenaro as defned above. Snce PARAMICS s a stochastc smulaton model that ntroduces random effects n varous processes durng smulaton, the results of several smulaton runs usng dfferent seed numbers are needed to reflect the general traffc condton for a specfc scenaro. The method used to determne the number of requred runs s explaned as follows (Chu et al., 004). Frst, fve smulaton runs are conducted; then, Eq. (45), whch specfes the requred number of runs, s used to determne f fve runs satsfy the crteron. If not, one addtonal run s conducted and then the requred number s calculated agan. Ths process contnues untl the crteron s satsfed, at whch pont the results for the current number of runs are averaged for performance analyss. ð45þ N ¼ t a= r l e

20 . Zheng, W. Recker / Transportaton Research Part C 30 (013) where N s the requred number of smulaton runs; l, r s the mean and standard devaton of a measure of performance based on conducted smulaton runs; e s the allowable error specfed as a fracton of the mean l; and t a/ s the crtcal value of the t-dstrbuton at the sgnfcance level a. In ths study, e = % and a = The smulaton results of the network are shown n Table 1. The correspondng mprovements compared wth the freemode actuated control, whch are represented as postve percentages, are also ncluded. It s found that the network under ether of the actuated-coordnated, volume densty and proposed control performs better than the free-mode actuated control n all scenaros drvers spend less tme n the network wth mproved travelng speed. Specfcally, these better control modes have ganed the most mprovement n scenaro 1 (.e., 6.3%, 6.9%,.7% decrease n Average Travel Tme, and 6.5%, 7.1%, 9.0% ncrease n Average Vehcle Speed), whle the least mprovement n scenaro 3 (.e., 0.%, 0.6%, 0.7% decrease n Average Travel Tme, 0.%, 0.7%, 0.7% ncrease n Average Vehcle Speed). One possble reason underlyng ths result s that the low flow-level traffc may behave freely n the network wthout beng affected by the change of control strategy. Furthermore, the network under the proposed algorthm has ganed the best performance, whch ndcates that the adaptve functonalty ncorporated n ths algorthm may provde more effcency than the other actuated control strateges. A T-ntersecton s selected to demonstrate the performance at the ntersecton level. Ths ntersecton corresponds to the juncton of Irvne Center Drve and the Off Ramp from Southbound I-405, as shown n Fg. 14. Phases and 6 are assgned to the through movements and operate as mn-recall phases, and phase 4 s assgned to the left-turn movement (plus the rghtturn movement) wthout recall. The extenson detectors ( ) for the through phases are placed 300 ft upstream from the stop lne, and the call and extenson detectors ( ) for the left-turn phase are placed rght behnd the stop lne. The operaton parameters of ths sgnal n the free-mode actuated, actuated-coordnated and volume densty control are shown respectvely n Table. For smplcty, only the smulaton results from scenaro 1 are taken for analyss, as shown n Table 3. The correspondng mprovements, whch are represented as postve percentages, are also ncluded. Smlarly, the network performs better under the actuated-coordnated, volume densty and proposed control, wth the mprovement beng 11.4%, 16.%, 17.3% decrease n Maxmum Queue Length, and 10.7%, 16.0%, 16.% decrease n Vehcle Travel Delay. Agan, the network under the proposed control algorthm has acheved the best performance. Table 1 Performance of the network. Average travel tme (s) Improvement (%) Average vehcle speed (mle/h) Improvement (%) Scenaro 1 Free-mode actuated 97.0 n/a 36.6 n/a Actuated-coordnated Volume densty Proposed adaptve Scenaro Free-mode actuated 13.3 n/a 43. n/a Actuated-coordnated Volume densty Proposed adaptve Scenaro 3 Free-mode actuated n/a 45.9 n/a Actuated-coordnated Volume densty Proposed adaptve Fg. 14. Study ntersecton.