Estmated Tme of Arrval (ETA) Based Elevator Group Control Algorthm wth More Accurate Estmaton Ayng Rong Unversty of Turu, Department of Informaton Technology, Lemmnäsenatu 14 A, FIN-20520 Turu, Fnland Henr Haonen Unversty of Turu, Department of Informaton Technology, Lemmnäsenatu 14 A, FIN-20520 Turu, Fnland Rsto Lahdelma Unversty of Turu, Department of Informaton Technology, Lemmnäsenatu 14 A, FIN-20520 Turu, Fnland Turu Centre for Computer Scence TUCS Techncal Report No 584 December 2003 ISBN 952-12-1289-6 ISSN 1239-1891
Abstract We develop ETA (Estmated Tme of Arrval) based elevator group control algorthms wth more accurate estmatons to mnmze the average watng tme of the passengers. Followng the prncple of ETA estmatons, the algorthms not only estmate the attendng tme of the new hall call, but also the delay that servng t wll cause to successve unattended passengers that have been allocated to the same elevator. To ncrease the accuracy of ths estmaton we try to consder the number of extra stops caused by the new hall call and apply the three-passage concept to determne the servce order of the hall calls: passage one (P1) hall calls are those that can be served by the elevator along ts current travel drecton, passage two (P2) hall calls requre reversng the drecton once, and passage three (P3) hall calls requre two reversals. We propose two varants of the algorthm: a basc varant and a reallocaton varant. The basc varant s based on the mmedate allocaton polcy. The reallocaton varant s based on coordnaton between the basc varant and a heurstc reallocaton mechansm. The tme complexty of both algorthms s O(MN), where M s the number of the elevators and N s the number of floors n the buldng. We have performed test runs wth traffc data generated from realstc buldngs rangng from 9 to 40 floors and wth 3 to 8 shafts for typcal traffc patterns. Our basc ETA algorthm reduces the average watng tme by 16 % and reduces the percentage of passengers who wat for more than 60 seconds by more than 3 % ponts when compared wth the ETA algorthm of the commercally avalable Elevate smulator. Our reallocaton varant further reduces the average watng tme by 7 % and the percentage of the passengers who wat for more than 60 seconds by more than 2 % ponts as compared wth our basc algorthm. Keywords: Elevator Group Control, Estmated Tme of Arrval, Three- Passage Concept, Immedate Allocaton Polcy.
1. Introducton A large number of modern elevator systems consst of multple elevators that transport the passengers to ther destnatons on the desred floors n the buldng. To mae an elevator system operate safely and effcently on passengers behalf, some automatc controls are employed. The coordnaton of a group of elevators n the elevator systems for satsfyng the demands of passengers s called the elevator group control. In the tradtonal up/down hall call button elevator systems, two events trgger the acton of the elevator group controller. One s the hall call button on the floors and the other s the car call button nsde the elevator. The basc functon of the elevator group control s to assgn approprate elevators to occurred hall calls to qucly attend them. The usual performance crteron to be optmzed s the average watng tme (AWT) of all the passengers n the system. The watng tme s the tme perod from the moment a passenger arrves to the moment when he boards some elevator. The elevator group control problem s of nherently stochastc nature. The stream of arrvng passengers s a stochastc process. Each passenger ntroduces three random varables: arrval tme, arrval floor and desred destnaton floor. In addton, the number of passengers s also unnown behnd each hall call n real elevator systems. All of these random sources must be consdered when the decson s made about the approprate elevator to serve the new hall call. Therefore, the elevator group control can be vewed as a combnaton of on-lne schedulng, resource allocaton and stochastc optmal control problem. The elevator group control problem has receved extensve attenton because of ts theoretcal mportance and practcal sgnfcance (Sutton & Barto 1998). Two allocaton polces are wdely used n assgnng elevators to serve hall calls: mmedate allocaton polcy and contnuous allocaton polcy. In the mmedate allocaton polcy, new hall calls are allocated to an elevator as soon as they appear, remanng fxed once made. That s, the system tells the passenger mmedately whch elevator to use when the passenger maes a hall call. Japan typcally adopts ths polcy and the destnaton-based control system (DCS) follows ths assgnment polcy. In the contnuous allocaton polcy, each elevator s allocated a maxmum of one hall call, and some hall calls can reman unallocated. The unattended hall calls are contnuously reevaluated to decde the approprate elevator. Ths mode of the operaton s typcal of western countres. The advantage of the mmedate allocaton s to shorten the psychologcal watng tme of the passengers. However, the early allocaton may lose ts optmalty as the future traffc events change the stuaton. The advantage of contnuous allocaton s that the best elevator to serve a hall call can be updated as new calls are ntroduced nto the system. However, elaborately desgned contnuous reallocaton algorthms must n prncple consder an exponental number of dfferent calls-to-car assgnments. Therefore, t s computatonally expensve. In ths paper we develop Estmated Tme of Arrval (ETA) based elevator group control algorthms wth more accurate estmatons to mnmze the average watng tme of the passengers. Followng the prncple of ETA estmaton, the algorthms not only estmate 1
the attendng tme of the new hall call, but also the delay that servng t wll cause to successve unattended passengers that have been allocated to the same elevator. To ncrease the accuracy of ETA estmaton we try to consder the number of extra stops caused by the new hall call and apply the three-passage concept (Cho et al. 1999, Gagov et al. 2001) to determne the servce order of the hall calls: passage one (P1) hall calls are those that can be served by the elevator along ts current travel drecton, passage two (P2) hall calls requre reversng the drecton once, and passage three (P3) hall calls requre two reversals. We propose two varants of the enhanced ETA allocaton algorthm. The basc varant adopts the mmedate allocaton polcy. The reallocaton varant s based on coordnaton between the basc varant and a heurstc reallocaton mechansm. Each tme only a fnte number of carefully selected hall calls enter the reallocaton cycle and they are reevaluated usng the basc allocaton algorthm. Therefore our reallocaton varant s computatonally effcent as compared wth the contnuous call allocaton based group control algorthm. The rest of ths paper s organzed as follows: Secton 2 brefly revews the group control algorthms from the vewponts of dealng wth the uncertanty n the system, Secton 3 gves the smplfed elevator system model, Secton 4 presents the basc ETA estmaton based on the three-passage concept, Secton 5 dscusses the coordnaton between basc ETA allocaton algorthm and the reallocaton mechansm, and Secton 6 presents the results on test runs. 2. Revew on elevator group control algorthms The nsurmountable combnatoral complexty and stochastc nature of the elevator group control problem has been attractng the attenton of both researchers and practtoners to mae ther effort n ths area. The elevator group control algorthms span from ad hoc approxmatons and heurstcs to AI plannng (Fujno et al. 1997, Km et al. 1998, Sonen 1997a) and decson-theoretc plannng (Novs & Brand 2003a, 2003b). The oldest elevator controllers used the prncple of collectve control n that elevators always stops at the nearest calls n ther runnng drecton. Ths nd of allocaton strategy s not desgned to deal wth randomness. The drawbac of ths algorthm s bunchng, where several elevators move close to each other and compete for the same hall call. Ths may result n the stuaton that elevators arrve at the same floor at about the same tme. Generally only one elevator pcs up the passengers and all other elevators waste tme n mang an extra stop, thus delayng the servce tme to other passengers. Pure up-pea and down-pea traffc patterns can be analyzed from a theoretcal vewpont (Gamse & Newell 1982a, 1982b, Gandh & Cassandras 1996). Specalpurpose group control algorthms based on such traffc patterns have provably optmal solutons. The threshold based dynamc programmng method (Pepyne & Cassandras 1997) provdes an optmal soluton durng up-pea traffc. Dynamc zonng (Chan et al. 1997) can mae the controller adapt to up-pea and down-pea traffc to obtan the optmal soluton. However, snce these nds of algorthms were derved for specal 2
stuatons, they perform well durng partcular traffc patterns but fal to adapt to other traffc patterns. To address the dffculty of the elevator group control problem, AI technques have also found ther way n the elevator area. Crtes & Barto (1996) developed renforcement learnng (RL) algorthms that approxmate dynamc programmng (DP) on an ncremental bass. It s computatonally tractable n theory and guaranteed to converge to an optmal polcy. However, the RL algorthm requred 60,000 hours of smulated elevator operaton to converge for one specfc down-pea scenaro. So t s not practcal for real elevator systems. Genetc algorthms (GAs) represent the possble solutons to the problem by chromosomes. They use a ftness functon to evaluate the performance crteron correspondng to ndvdual chromosomes and mprove the chromosomes by genetc operators such as selecton, crossover and mutaton. Whle GAs are good for fndng hgh qualty solutons, they are slow and neffcent n the use of computatonal resources. Therefore, GAs are dffcult to use when the tme avalable to acheve a soluton s lmted (Tyn & Ylnen 1999). More rgorously motvated methods use approxmatons of the desred performance crteron that are computable n reasonable tme. Estmated Tme to Destnaton (ETD) and Estmated Tme of Arrval (ETA) algorthms belong to ths category. ETA and ETD attempt to treat each passenger n the system equally. When a new passenger s allocated to the elevator, the algorthms consder both the attendng tme of the new passenger and the delay that the new passenger wll cause to the passengers that have already been allocated to ths very elevator. The basc logc of allocaton s same for ETA and ETD, but they use dfferent optmzaton crtera. ETA mnmzes the average watng tme of the passengers n the system whle ETD mnmzes the system tme of the passengers n the system. Regular ETD and ETA address the stuatons wthout reallocaton. Novs & Brand (2003a) developed a varant of the ETA algorthm based on the evaluaton of average watng tme (AWT) by means of dynamc programmng. However, they use the queue length nformaton behnd the hall call that would not be avalable n a real elevator system. Smth & Peters (2002) demonstrated the use of the ETD algorthm n the full DCS. 3. Smplfed elevator system model An elevator group control system conssts of M elevators delverng passengers from ther respectve arrval floors to ther destnaton floors n the N-floor buldng. The objectve s to mnmze the average watng tme of all the passengers n the system. The elevator system model s smlar to that n (Haonen, 2002). The followng tradtonal constrants on the behavor of the elevator are mposed: (a) The elevator must not pass a floor at whch a passenger wshes to get off; (b) The elevator must fulfll ts current commtment and not reverse drecton wth passengers n elevator; (c) An empty elevator can stop, go up or go down. 3
The followng assumptons are made throughout the paper. (1) The arrval process follows the Posson dstrbuton. (2) Both the acceleraton and maxmum speed of the elevator are constant. Thus, travelng tme between any two floors can be fully determned by the dstance between floors. The elapsed tme snce the elevator left mmedate prevous floor can be used to calculate the nearest floor at whch the elevator can stop and the tme to any floor. It s unnecessary for the controller to now the absolute poston and velocty of the elevator explctly. Therefore, the nearest floor and the travel drecton are used to determne the elevator dynamcs. If the elevator s not n moton, the nearest floor s ts current floor. (3) The bypass load of the elevator s 80 %. The movng elevator wll not stop to respond a hall call when ts load s equal to or greater than 80 % of ts rated capacty. (4) Each elevator follows the followng servce routes n attendng the hall calls assgned to t: P1 hall calls P2 hall calls P3 hall calls, whle the elevator capacty constrant s satsfed. If the elevator can not serve all of the passengers behnd a hall call, the remanng passengers ntate a new hall call. Next we wll dscuss detals of our ETA based group control algorthms. To mae the prncple of ETA estmaton clear, we ntroduce the number of passengers behnd the hall call. However, we do not use ths nformaton n the algorthms. 4. Basc ETA estmaton Our basc ETA algorthm follows the prncple of ETA estmaton and s based on the three-passage concept, estmatng the number of extra stops caused by the hall call besdes the mandatory stops at occurred floor and the most lely reversal floor of the elevator. 4.1 Prncple of ETA estmaton ETA attempts to treat each hall call (or passenger) equally by ntroducng the system degrade factor (SDF) to fnd the approprate elevator to serve the new hall call. Not only s the attendng tme of the new hall call consdered, but also the delay t wll cause to the successve unattended hall calls that have been assgned to the same elevator. Thus, the total cost of allocatng the new hall call to elevator s gven below. t total n = j = 1 delay attendng t, j + t (1a) Here n s the number of the passengers that have been assgned to elevator and not been served yet, t delay, j ( 0) s the delay that the new hall call wll cause to passenger j, who has been assgned to elevator and not been served, t attendng ( 0) s the estmated 4
attendng tme of the new hall call. The system wll allocate the new hall call to the elevator wth the lowest total cost. That s, e canddate = arg mn t (1b) [ 1, M ] Lemma 1. The allocaton based on (1b) s the best allocaton under the mmedate allocaton polcy. Proof Let W, [1, M] denote the total watng tme of all the unattended passengers currently assgned to elevator, excludng the new hall call. Let W +, [1, M] denote the total watng tme of all the unattended passengers currently assgned to elevator, ncludng the new hall call. Let W, [1, M] denote the total watng tme of all the unattended passengers ncludng the new hall call wth the assgnng the new hall call to elevator, total W = W + + M + j= 1 j W M j = 1 j = ( W W ) + W. j (2) In formula (2), M W j j= 1 s the total watng tme of all of unattended passengers before the new hall call arrves and t cannot be changed based on the mmedate allocaton polcy. We dvde two sdes of formula (2) smultaneously by all of the unattended passengers ncludng the new arrval passenger (ths number can be vewed as fxed f we do not consder the future arrval of the passengers) and obtan the average watng tme of these passengers. Thus, mnmzng average watng tme of all of the passengers s equvalent to mnmzng W (the total watng tme of all the passengers), + total whch n turn s equvalent to mnmzng ( W W ) = t 4.2 Three-passage concept The three-passage concept s llustrated n Fg. 1. It descrbes the relatonshp between the assgned hall calls and elevator moton status characterzed by elevator drecton and poston. The elevator serves the hall calls sequentally as t reaches them. Passage one (P1) hall calls are calls supposed to be served wthout changng the elevator drecton, passage two (P2) after the changng the drecton once, and passage three (P3) hall calls after a second change of drecton. If the elevator s dle (drecton s NONE), the drecton of the elevator s frst set and then the hall call passage can be determned based on above descrpton. If the new hall call occurs at the same floor as the current floor of the elevator, the drecton of the 5
elevator becomes the same as that of the hall call. If the hall call occurs at the floor above (below) the current floor of the elevator, then the drecton of the elevator becomes UP (DOWN). To smplfy the presentaton, we only derve the relatonshp when the elevator s movng up. The formulas are symmetrc when the elevator s movng down. Hghest floor P3 Hall calls Nearest floor Elevator P2 Hall calls Hall call Elevator Drecton (Hall call or Elevator) Lowest floor Fg. 1. Three Passage Concept. The followng notatons are used. M Number of elevators n the system N Number of floors wth the lobby floor ndexed 0 and the top floor ndexed by N 1. nearest f The nearest floor of the th elevator. d d H The drecton of the th elevator, ether UP or DOWN. If d s NONE (the elevator s not n moton n ths case), d can be set frst based on above descrpton. The drecton of the new hall call, ether UP or DOWN. The floor of the new hall call. Set of hall calls assgned to the th elevator. 6
(1) H Set of P1 hall calls assgned to the th elevator. (2) H Set of P2 hall calls assgned to the th elevator. (3) H Set of P3 hall calls assgned to the th elevator. We have nearest H = { < d > H d = d and f } (1) (3) (2), (3) H = { < d > H d } 7 d, (4) nearest H = { < d > H d = d and < f }, (5) (1) (2) (3) It s obvous that H = H H H, that s, the three-passage hall calls cover all the hall calls assgned to the elevator. Moreover, t s easy to extend the three-passage concept to descrbe the relatonshp between any hall call and any elevator n the system. In the followng, we wll concentrate on mplementaton of the ETA estmaton. 4.3 Implementaton of ETA estmaton Formula (1a) provdes the general gudelne on how to evaluate the total cost of allocatng the hall call to the elevator. The concrete mplementaton vares. For example, Novs & Brand (2003a) employed dynamc programmng to estmate the total cost based on the assumpton that the number of people that get off at the ongong floors follow the bnomnal dstrbuton. They dd not explctly nclude the stop cost. Here we ntroduce stop cost explctly. t total s estmated based on the passage relatonshp between hall calls and the elevator, the expected number of extra stops caused by the hall calls besdes the mandatory stop at the occurred floor and the estmated elevator reversal floor. Before we descrbe ETA calculaton, we brefly dscuss the components of stop cost, the method of estmatng the expected number of stops and estmated farthest floor of the hall call. 4.3.1 Expected extra stops and expected farthest floor Stop cost s assocated wth the tme delay caused by the elevator n servng the hall calls or car calls at the occurred floor. It conssts of the followng components: (a) opendoor tme, (b) close-door tme, (c) photocell tme (the tme delay between the moment when the last passenger enters the elevator and the moment elevator starts closng the door), (d) entrance tme (the tme requred for one passenger to enter the elevator), (e) ext tme (the tme requred for one passenger to ext the elevator) and (f) acceleraton/deceleraton tme (tme lost due to acceleraton and deceleraton). The mpact of hall calls and car calls on elevator dynamcs s dfferent. Each car call only causes one mandatory stop but each hall call can cause a number of extra stops on the ongong floors besdes the mandatory stop at the occurred floor. The actual number of extra stops caused by the hall call vares based on the current assgnment of the
elevator ncludng the car calls and assgned hall calls. In pure up-pea traffc the stuaton s greatly smplfed. Hall calls wll arrve only at the lobby floor, and the elevators attendng them wll be empty. Next, we descrbe calculaton of the expected number of extra stops and the expected farthest floor that the current hall call can reach. We extend the method by Sonen (1997b) for dealng wth the up-pea traffc pattern to any traffc stuaton. The followng notatons are ntroduced. d The drecton of the new hall call, ether UP or DOWN. The floor of the new hall call. pass n Number of passengers behnd the hall call. f Number of floors to move to reach the farthest floor n the current drecton. net l Expected net dstance to the farthest floor. s Expected number of stops for ongong f floors caused by the new hall call <,d> under the condton that the assgnment of elevator s empty. extra s, j Actual extra number of stops caused by the new hall call <,d> before t arrves at the j th floor. mandatory s, j Number of mandatory stops between floor and floor j (excludng floor and floor j). C,j Set of car calls between floor and floor j (excludng floor and floor j). H,j Set of assgned hall calls between floor and j (excludng floor and floor j) that should be attended before the elevator arrves at floor j. farthest f Expected farthest floor that the current hall call can reach. P Probablty that none of the passengers that board on floor wth travel drecton d get off at each ongong floor To mae the estmaton smple, we assume that the passengers boardng on floor have an equal probablty to get off at the ongong f floors. We have Thus, pass 1 1/ f f n = 1 P =. (6) pass pass n / f f n > 1 e and s = f (1 P ) (7) 8
After l net net l 0 f l = f P = 2 j= f l+ 1 f f f f = 1. (8) > 1 has been calculated, t s trval to obtan the expected farthest floor. farthest f = the actual farthest floor - l net (9) The number of mandatory stops and extra stops are then estmated by and s madatory, j, j, j, j, j = C + H C H (10) extra mandatory s, j = s ( j 1 s, j )/ f. (11) 4.3.2 Total tme t total estmaton (1) Attendng tme t attendng estmaton t s Stop tme of one full stop. It s the sum of 6 components descrbed at the begnnng of ths subsecton. C Set of car calls currently n the th elevator. Set of hall calls assgned to the th elevator. H before C Set of car calls to be attended before the hall call <,d>. after C Set of car calls to be attended after the hall call <,d>. before H Set of hall calls to be attended before the hall call <,d>. after H Set of hall calls to be attended after the hall call <,d>. t, Nonstop travel tme to floor based on current moton status of the elevator. nonstop Then t attendng s estmated as follows. (a) If <,d> s a P1 hall call, then t attendng nonstop before before before before = t, + ( C + H C H + s, ) t (12) (b) If <,d> s a P2 hall call, then () If no P1 hall calls and car calls exst n elevator, t attendng usng the same logc as (12) extra before H s can be estmated 9
() Otherwse, t attendng can be decomposed nto two parts: The frst part s the tme to fnsh servng all of car calls and P1 hall calls f they exst, then the elevator reverses the drecton. The second part s the tme to attend <,d> s a from the reversal floor. The reversal floor can be calculated by combnaton of the estmated farthest floors of H hall calls based on (9) and C (set of car (1) calls currently n elevator ). Two parts of tme can be estmated separately usng the same logc as n (12). (c) If <,d> s a P3 hall call, then t attendng can be decomposed nto three parts: The frst part s the tme to fnsh servng all of car calls and P1 hall calls f they exst, then the elevator reverses the drecton. The second part s the tme to fnsh servng all the P2 hall calls f they exst, then the elevator reverses the drecton for the second tme, the last part s the tme to attend <,d> from the second reversal floor. The frst reversal floor can be calculated by combnaton (1) of the estmated farthest floors of H hall calls based on (9) and C and the second reversal floor can be determned smlarly based on the farthest floors of (2) H. Three parts of tme can be estmated separately usng the same logc as n (12). In some cases, ether the frst part or second part tme does not exst, but the estmaton logc remans unchanged. (2) SDF t delay estmaton. The delay tme t delay, j that the new hall call <,d> wll cause to passenger j assocated wth s made up of three parts: after H (a) One mandatory stop at the occurred floor of the evaluated hall call f there s no commtted car call at the very floor. In other words, f the floor of the hall call concdes wth the car call n the rght drecton, ths stop tme can be gnored because the elevator has to stop at ths floor for lettng off the passenger(s) regardless of the occurrence of the hall call; (b) The expected number of extra stops on the ongong floors caused by the hall call and (c) Addtonal travel tme f the hall call wll affect the reversal floor. For regular SDF estmaton where delay pass t = t, n (13) delay j after j H pass n j s the number of passengers behnd the hall call. 4.4 Basc ETA allocaton algorthm In vew of the fact that the queue length nformaton behnd the hall call s unnown n the real elevator system, we tae the number of passengers behnd the hall call as one when we mplement the algorthms. The estmaton based on Secton 4.3 s stll vald. The procedures for the basc ETA allocaton algorthm are summarzed as follows 10 j
Step 1. For all of the elevators Step 1.1 Determne the passage of the new hall call <,d> wth respect to each elevator [1,M]. Step 1.2 Calculate the total cost t total that s the cost of assgnng the <,d> hall call to elevator based on the formula descrbed n Secton 4.3 dependng on the passage of <,d>. Step 2. Choose the best allocaton for the new hall call <,d> based on (1b) The tme complexty of the basc ETA allocaton algorthm s O(MN). 5. Reallocaton varant ETA allocaton algorthm The basc ETA allocaton algorthm employs the mmedate allocaton polcy. Some early-allocated hall call may lose optmalty as future events appear n the system. Our reallocaton varant of the ETA algorthm s based on the coordnaton between the basc ETA algorthm and a heurstc reallocaton mechansm to mprove the performance of the allocaton algorthm further. 5.1 Canddates for hall call reallocaton Three categores of hall calls wll be consdered for reallocaton. (1) The oldest call n the system. (2) Some hall calls of the elevator that s about to leave the current floor: (a) The oldest hall call f the number of hall calls assgned to the elevator exceeds a certan lmt. (b) The hall call whose attendng tme can be severely affected. Ths category ncludes the last hall call n the servce sequence f t belongs to the P2 or P3 passage. (c) The hall calls whose attendng tme s relatvely certan, for example, the successve hall call and the hall calls that concde wth the car calls n the rght drecton (called matched hall calls). 5.2 The reallocaton mechansm To reduce the computatonal effort, the canddates for reallocaton hall calls are reevaluated serally. Before reallocaton, all of the hall calls are assgned to the elevator based on the basc ETA allocaton algorthm. Each tme only one hall call s consdered for reallocaton, but a fnte number of hall calls may be reevaluated n sequence for one reallocaton slot. The followng tme slots are chosen as the reallocaton ponts. (1) Every tme when a new hall call arrves, the basc ETA allocaton algorthm fnds the approprate elevator for the new hall call and then the oldest call n the system (f t exsts) s consdered for reallocaton. (2) When the elevator s about to leave the current floor. Frst, the oldest hall call n the system s consdered for reallocaton. Then, the hall calls of ths elevator (ntroduced n 11
secton 5.1) are consdered for reassgnment. If there s overlap among these hall calls, reallocaton s consdered just once for the same hall call. 5.3 Coordnaton between dfferent categores of reallocaton hall calls It s necessary to coordnate between dfferent categores of hall calls so that ther aggregate effect moves toward mprovng the performance of algorthm. Tmng s mportant. We ntroduce threshold n reallocaton. That s, the reallocaton s executed only when the hall calls stay n the system for a suffcent perod of tme n terms of the oldest hall call, the last hall call to be served and the oldest call of the elevator. There s no such restrcton on the matched hall calls. 5.4 Reallocaton varant ETA allocaton algorthm The reallocaton varant of the ETA algorthm can be vewed as nteracton between trggerng hall calls and the basc ETA allocaton algorthm n secton 4.4 at the approprate moment. The reallocaton ETA group control algorthm framewor s llustrated n Fg. 2. Obvously, the tme complexty of the reallocaton ETA allocaton algorthm s stll O(MN). Introducng the reallocaton mechansm based on secton 5 does not affect the tme complexty because the number of reallocaton hall calls for each relocaton slot s fnte. The practcal computaton tme should be -fold ( 1) of the computaton tme of the basc ETA allocaton algorthm dependng on how many hall calls enter the reallocaton for each reallocaton slot. New hall call s ntated New hall call Elevator s about to leave the current floor Reallocaton hall calls Oldest hall call n system Lowest servce prorty hall call of ths elevator Immedate next hall call of ths elevator Matched hall calls Basc ETA Allocaton Algorthm Fg. 2 Reallocaton varant ETA Group Control Algorthm Framewor 12
6. Test runs Our basc ETA allocaton algorthm (wthout reallocaton) and ts reallocaton varant were tested through smulaton. To verfy the estmaton accuracy of the basc ETA allocaton algorthm, we benchmared t aganst the commercally avalable ETA allocaton algorthm on Elevate developed by Peters Research Ltd. (2002). The reallocaton varant ETA was compared wth the basc ETA allocaton algorthm to verfy the effect of the reallocaton mechansm. Three performance crtera were used n the comparsons: average watng tme (AWT), average journey tme (AJT) and the percentage of passengers that wat longer than 60 seconds (P > 60s). - AWT: The average watng tme of all the passengers. Passenger watng tme s defned as the actual tme a prospectve wats after regsterng a landng call (or enterng the watng queue f a call has already been regstered) untl the passenger has entered the elevator. - AJT: The average journey tme of all the passengers. Passenger journey tme begns when the watng tme begns and ends when passenger has exted the elevator. Elevate defnes the watng tme as startng from the passenger arrval and endng at the elevator arrval at the orgn floor. Journey tme s from the passenger arrval to the elevator arrval at the target floor. Therefore the events of each passenger n Elevate were reconstructed to compute the watng tmes and journey tmes accordng to our defntons. The benchmar ETA allocaton algorthm s the group control algorthm wthout reallocaton. The followng notatons are used to dstngush between the dfferent varants of ETA allocaton algorthms. ETA-E: Benchmar ETA algorthm on Elevate ETA-U: Basc ETA algorthm wthout reallocaton n ths paper on our smulator ETA-R: Reallocaton varant ETA algorthm n ths paper on our smulator 6.1 Test problem To be representatve for a wde range of practcal stuatons, we have generated the test problems based on the actual buldngs by consderng buldng types, elevator confguratons and traffc scenaros. Table 1 shows the buldng parameters and related elevator confguratons. The number of floors ranges from 9 to 40 and the number of elevators from 3 to 8. Buldng B has two entrance floors. The elevator group of buldng C serves the upper zone and elevators do not stop at floors 1-24. The bottom floor s ndexed 0. Passenger traffc n the buldng can be descrbed as combnatons of the three basc components: Incomng, outgong and nter-floor traffc. - Incomng passenger arrves at entrance floor and travels up to the populated floor n the buldng. - Outgong passenger arrves at populated floor and travels down to the entrance floor. 13
- Inter-floor passenger arrves at populated floor and travels to another populated floor. Four traffc patterns used n the smulaton test are shown n Table 2. For each traffc pattern, traffc densty was generated at two ntensty levels: full and half arrval rates respectvely as shown n Table1. Arrval rate s defned as percentage of populaton n fve mnutes. Therefore, a total of eght traffc scenaros were nvestgated: Heavy ncomng (HI), moderate ncomng (MI), heavy outgong (HO), moderate outgong (MO), heavy lunch (HL), moderate lunch (ML), heavy two-way (HT) and moderate two-way (MT). For each traffc scenaro, ten random samples of one-hour traffc were generated. Each buldng contans 80 test problems and altogether 240 test problems were generated for three buldngs. In practce, the performance n pure up-pea stuaton can be mproved greatly f elevators are returned to the entrance after they fnsh ther current commtments even f no calls are allocated to them. There are several possble methods to return elevators. Here we concentrate on the performance of allocaton algorthms and smulators are not equpped wth returner algorthms. Instead, the ncomng traffc pattern contans 5 % outgong passengers, whch return elevators to the entrance floor(s). Table 1. Buldng parameters and the related elevator confguratons. Parameter Buldng A Buldng B Buldng C Total floors 9 16 40 Elevators 3 4 8 Capacty (persons) 13 20 21 Door openng tme (s) 1.9 1.2 1.6 Door closng tme (s) 2.8 2.5 2.6 Door pre-openng (s) 0 0 0 Photocell delay (s) 0.9 0.9 0.9 Loadng tme (s) 1.2 1.0 1.0 Unloadng tme (s) 1.2 1.0 1.0 Max velocty (m/s) 1.0 2.5 4.0 Acceleraton (m/s 2 ) 0.8 1.0 1.0 Start Delay (s) 0 0 0 Floor heght (m) 3.8 3.6 3.6 Excepton heghts (m) Floor 0: 4.6 m Floor 0: 3.9 m Floor 0: 4 m Lobby floor (entrance %) Floor 0 (100%) Floor 0 (20%) Floor 0 Populaton by floors Floors 1,7,8: 30, other floors: 70 14 Floor 1 (80%) Floors 2-9: 20, floors 10-16: 16, floor 15: 2 Total populaton 440 242 1350 Full arrval % of populaton / 5 15 40 13 mn Half arrval % of populaton / 5 mn 7.5 20 6.5 (100%) Floors 25-39: 90
Table 2 Traffc patterns Traffc pattern Incomng (%) Outgong (%) Inter-floor (%) Incomng 95 5 0 Outgong 0 100 0 Lunch 40 40 20 Two-way 50 50 0 6.2 Test results Table 3. Performance comparson for dfferent varants of ETA allocaton algorthms. Buld. Traffc ETA-E ETA-U ETA-R AWT AJT P>60s AWT AJT P>60s AWT AJT P>60s HI 26.0 79.9 5.68 22.6 75.8 2.86 23.0 76.6 3.51 MI 16.2 58.7 0.25 14.9 57.3 0.05 14.9 57.4 0.03 HO 37.4 78.1 20.52 29.3 70.6 10.21 26.3 69.7 6.40 A MO 27.7 60.3 5.93 21.3 54.4 1.69 21.1 54.5 1.16 HL 38.4 79.4 23.25 34.6 75.3 18.09 31.6 73.6 14.51 ML 21.0 51.0 3.13 18.5 48.5 2.90 18.3 48.4 1.41 HT 34.5 76.5 18.41 30.8 72.3 13.62 29.4 71.9 12.69 MT 19.8 51.3 2.22 17.0 48.4 2.45 16.0 47.6 0.91 AVG 27.6 66.9 9.92 23.6 62.8 6.49 22.6 62.5 5.08 HI 19.0 76.0 1.79 16.4 72.7 1.27 15.9 72.5 0.67 MI 13.0 49.8 0.00 11.2 47.1 0.05 11.2 47.5 0.00 HO 31.5 69.9 11.91 22.5 62.6 3.52 21.3 61.8 1.70 B MO 21.0 47.2 1.43 15.2 41.6 0.17 15.1 41.8 0.05 HL 33.4 76.0 16.42 31.1 71.7 13.11 27.8 69.9 8.99 ML 15.6 39.4 0.62 12.9 36.6 0.53 12.3 36.3 0.07 HT 28.9 71.0 11.05 26.2 66.0 8.66 23.9 65.0 4.96 MT 13.6 37.5 0.15 10.9 35.0 0.38 10.6 34.7 0.02 AVG 22.0 58.4 5.42 18.3 54.2 3.46 17.3 53.7 2.06 HI 33.6 131.0 15.20 30.4 127.9 13.53 31.6 129.0 15.33 MI 17.0 104.5 0.14 14.9 104.5 0.02 14.9 104.5 0.01 HO 34.5 101.7 16.83 33.1 100.7 14.08 26.9 96.7 7.96 C MO 33.2 88.7 14.93 22.9 85.3 1.71 22.2 85.2 0.81 HL 35.3 107.8 20.58 27.3 101.4 10.53 24.8 99.9 8.31 ML 20.9 71.3 4.02 15.2 66.0 1.21 14.5 65.7 0.37 HT 33.5 108.5 17.78 28.6 104.4 10.81 22.6 100.7 6.93 MT 19.2 74.2 3.16 14.1 69.4 1.28 13.3 69.2 0.35 AVG 28.4 98.5 11.58 23.3 94.9 6.65 21.3 93.9 5.01 15
Table 3 shows the results for dfferent varants of ETA allocaton algorthms aganst 8 traffc scenaros. Based on the results, we mae the followng observatons. (1) Compared wth ETA-E, the reducton n AWT for ETA-U s n the range [4%, 31%] wth an average of 16 %. For AJT, the reducton s n the range [0.1%, 12%] wth an average of 5 %. (2) In terms of long watng percentage (P>60), the mprovement for ETA-U s n the range [-0.3%, 13%] wth an average of 3 % ponts. There s a phenomenon that ETA-U mproves the average watng tme of moderate down-pea traffc scenaro sgnfcantly as compared wth the mprovement of heavy down-pea traffc scenaro. The reason behnd t s that the performance of ETA-U s lmted by the elevator capacty. We dd not consder the capacty when the assgnment was done. The elevator passes the landng hall call when the load s equal to or greater than the bypass load. Reallocaton s a remedy. (3) As compared wth ETA-U, the reallocaton varant ETA-R can mprove the performance consstently for all the traffc scenaros except the up-pea traffc scenaro. Its overall speed-up of AWT s 7 % and the reducton of long watng percentage s 2 % ponts. Generally, reallocaton can mprove the performance of the heavy traffc scenaro more sgnfcantly. For heavy traffc patterns, t can reduce AWT by more than 10 % and the long watng percentage by more than 3 % ponts. The reason why reallocaton worsens the performance for the up-pea traffc scenaro may le n the fact that the elevators compete for one hall call and paralyze the reallocaton mechansm. On the way bac to the lobby floor, the elevator may stop halfway on the ntermedate floor because the reallocaton can transfer the lobby floor hall call from elevator to elevator and thus delay the transportaton of the passengers on the lobby floor. From Table 3, we can also see that the reallocaton can mprove the performance n the heavy up-pea traffc scenaro for buldng B. Ths s not occasonal because buldng B has two entrances that can generate hall calls n up-pea traffc scenaros, whch can mae the elevator return the lobby floors more securely and transport the passengers on the lobby floors tmely. Therefore, the strength of the reallocaton les n ts ablty to coordnate the allocaton among dfferent hall calls nstead of competng for the same hall call. (4) In terms of AWT, the effect of reallocaton s not sgnfcant. The mprovement s n the range [-1%, 4%] wth an average of 1 %. 7. Conclusons We have developed ETA based elevator group control algorthms wth more accurate estmaton. A heurstc reallocaton mechansm mproves the performance further. In the test runs wth real-lfe buldng types, elevator confguratons and typcal traffc scenaros, our basc ETA-U allocaton algorthm (wthout reallocaton) (as compared wth the benchmar ETA) reduced the watng tme by 16 % and the percentage of the passengers who wat for more than 60 seconds by 3 % ponts. In addton, ETA-U can 16
brng 5 % mprovement on the journey tme. The reallocaton varant ETA-R can enhance the performance further as compared wth ETA-U. The further mprovement n watng tme s 7 % and the reducton n the long watng percentage s 2 % ponts. References Chan W.L., So A.T.P., Lam K.C., 1997. Dynamc zonng n elevator traffc control. Elevator world, March, 136-140. Cho Y.C., Gagov Z., Kwon W.H., 1999. Tmed Petr net based approach for elevator group controls. Techncal report No. SNU-EE-TR-1999-3, School of electrcal engneerng, Seoul Natonal Unversty. Crtes R.H., Barto A.G., 1996. Improvng elevator performance usng renforcement learnng. In D.S. Touretzy, M.C. Mozer, and M.E. Hasselmo (eds.) Advances n Neural Informaton Processng Systems 8, MIT Press, Cambrdge MA, 1017-1023. Fujno A., Tobta T., Segawa K., Yoneda K., Togawa A., 1997. An Elevator group control system wth floor-attrbute control method and system optmzaton usng genetc algorthms. IEEE Transactons on Industral Electroncs, 44(4), 546-552. Gagov Z., Cho Y.C., Kwon W.H., 2001. Improved concept for dervaton of velocty profles for elevator systems. Proceedngs of the 2001 IEEE Internatonal Conference on Robotcs & Automaton, Seoul, Korea, May 21-26, 2419-2423. Gamse B., Newell G. F., 1982a. An analyss of elevator operatons n moderate hgh buldngs-i - Sngle elevator. Transportaton research-b 16(4), 303-319. Gamse B. & Newell G. F., 1982b. An analyss of Elevator Operatons n moderate hgh buldngs-ii - Multple elevators. Transportaton research-b 16(4), 321-335. Gandh A.D., Cassandras C.G., 1996. Optmal control of pollng models for transportaton applcatons. Math. Comput. Modelng 23(11/12), 1-23. Haonen H., 2003. Smulaton of buldng traffc and evacuaton by elevators. Lcentate thess, System Analyss Laboratory, Helsn Unversty of Technology. Km C.B., Seong K.A, Hyung L.K., Km J.O., 1998. Desgn and mplementaton of a fuzzy elevator group control system. IEEE Transactons on systems, Man and Cybernetcs Part A: Systems and Humans. 28(3), 277-287. Novs D., Brand M., 2003a. Decson-theoretc group elevator schedulng. 13 th Internatonal Conference on Automated Plannng and Schedulng, ICAPS 03, June 9-13, Trento, Italy. Novs D., Brand M., 2003b. Margnalzng out future passengers n group elevator control. 9 th Conference on Uncertanty n Artfcal Intellgence, UAI-2003, August 8-10, Acapulco, Mexco. Pepyne D.L., Cassandras C.G., 1998. Desgn and mplementaton of an adaptve dspatchng controller for elevator systems durng up-pea Traffc. IEEE Transactons on Control Systems Technology, 6(5), 635-650. Peters Research Ltd., 2002. Gettng started wth Elevate. 17
Sonen M.L., 1997a. Elevator group control wth artfcal ntellgence. Research reports A 67, System Analyss Laboratory, Helsn Unversty of Technology. Sonen M.L., 1997b. Customer servce n an elevator system durng up-pea. Transportaton research-b, 31(2), 127-139. Sonen M.L., Sus T., Haonen H., 2001. Passenger traffc flow smulaton n tall buldngs. Elevator world, 117-123. Smth R., Peters R., 2002. ETD algorthm wth destnaton dspatch and booster optons. Elevator world, July, 136-142. Sutton R.S., Barto A.G., 1998. Renforcement learnng: An ntroducton. MIT press. Tyn T., Ylnen J., 1999. Improvng the performance of Genetc Algorthms wth a Gene Ban. Proceedngs of EUROGEN99, Report A2/1999, Unversty of Jyväsylä, Fnland, 162-170. 18
Turu Centre for Computer Scence Lemmnäsenatu 14 FIN-20520 Turu Fnland http://www.tucs.f/ Unversty of Turu Department of Informaton Technology Department of Mathematcs Åbo Aadem Unversty Department of Computer Scence Insttute for Advanced Management Systems Research Turu School of Economcs and Busness Admnstraton Insttute of Informaton Systems Scence