CASPT 2018 Full Paper Driver chedule efficiency v. public tranport robutne: A framework to quantify thi trade-off baed on paive data Menno Yap Niel van Oort Abtract More complex, efficient driver chedule reduce operator cot during undirupted operation, but increae the diruption impact for paenger and operator once a diruption occur. We develop an integrated framework to quantify the paenger and operator cot of diruption explicitly a function of different driver chedule cheme. Since the trade-off between driver chedule efficiency and robutne can be quantified, thi upport operator in their deciion-making. Keyword: Diruption Driver cheduling Paenger perpective Paive data Public Tranport Robutne 1 Introduction The Driver Scheduling Problem (DSP) for public tranport network i a well-tudied topic in operation reearch (e.g. Kroon and Fichetti, 2001; Huiman et al. 2005; Portugal et al. 2009; De Leone and Feta, 2011). Reearch development and the availability of advanced driver cheduling oftware (uch a HASTUS) have reulted in the development and implementation of more complex driver chedule, which can improve operator efficiency and reduce operating cot. Where a driver duty traditionally conited of tak on one vehicle only, a duty now often conit of tak on different vehicle during one hift. Thi i implemented by ingle-line multivehicle cheduling a driver change vehicle during a hift, but remain operating one and the ame line or multi-line multi-vehicle cheduling. In the latter cae, a more complicated driver chedule i applied where driver tak are cheduled on different vehicle a well a on different line during one hift. Thi allow vehicle to operate with a different driver during a driver break, and can reduce the total required fleet ize and number of driver hour the operator require on a network level. Menno Yap Department of Tranport and Planning, Delft Univerity of Technology Delft, the Netherland Email: M.D.Yap@TUDelft.nl Niel van Oort Department of Tranport and Planning, Delft Univerity of Technology / Goudappel Coffeng conultant Delft, the Netherland Email: N.vanOort@TUDelft.nl
There i however a trade-off between driver chedule complexity and public tranport robutne: albeit a more complex driver chedule reduce operator cot during undirupted operation, it increae the impact of diruption for paenger and operator in cae a diruption occur. More complex chedule reult in longer ervice recovery time once the incident ha been reolved, and in more complicated and le effective recheduling: there i a rik of delay propagation over the network if a driver i not able to arrive in time for the next tak on another line. Robut driver cheduling tudie mainly incorporate minor recurrent delay by adding lack in the timetable (e.g. Laplagne 2008), but do not conider robutne related to large non-recurrent diruption. On the other hand, tudie aiming to quantify the paenger impact of urban public tranport diruption (e.g. Van Oort et al. 2015b; Jeneliu and Cat 2015; Cat et al. 2016, Yap et al. 2018c) do not incorporate driver chedule complexity. In our tudy we develop an integrated framework in which paenger diruption impact i explicitly quantified a function of different level of driver chedule complexity. For operator to balance chedule efficiency and robutne, quantification of the operator impact of diruption for different type of driver chedule i explicitly incorporated in thi framework. 2 Methodology Table 1 how the notation ued in our framework. Table 1 Indice and et, parameter and variable Indice and et, S top index, et l, L line index, et S l et of top on line l, S l S l line l i defined a ordered equence of top = { l,1, l,2,, l, l } r, R run index, et R l et of run on line l, R l R i index for diruption h hourly time period Parameter β 1 weight of perceived paenger waiting time β 2 operator revenue for average paenger journey β 3 operator cot for each hour of peronnel overtime β 4 operator fine for run with too early departure β 5 operator fine for run with too late departure β 6 operator fine for cancelled run β 7 operator fine for unavailable infratructure per hour E d demand elaticity VoT Value-of-Time γ crowding in-vehicle time multiplier γ crowding in-vehicle time multiplier at eat capacity γ c crowding in-vehicle time multiplier at cruh capacity φ r eat capacity of run r
Variable φ r c t r a t r d a t r td r tivt rl ivt,p t rl twtt p t i j t i t o ci o h f l cruh capacity of run r cheduled arrival time of run r at top cheduled departure time of run r from top arrival time of run r at top departure time of run r from top paenger in-vehicle time of run r from top l to l+1 perceived paenger in-vehicle time of run r from top l to l+1 paenger waiting time at top generalized paenger travel time for journey from top i to top j duration of diruption peronnel overtime hour per diruption operator cot of diruption frequency of line l during hour h d r headway between run r and ubequent run r + q r paenger load on-board run r between top and ubequent top in number of paenger boarding run r at top q r To quantify the cot of a public tranport diruption we develop a framework a hown in Figure 1. Fig. 1 Framework to quantify diruption cot compared to driver chedule cot
Cot are divided into paenger cot and operator cot, which both conit of everal component. The (ocietal) diruption cot for paenger conit of the additional in-vehicle time, waiting time and perceived in-vehicle time due to crowding, all expreed in monetary term. The additional in-vehicle time equal the delay of each run r R due to thi diruption, multiplied by the paenger flow q r travelling over the dirupted link between l and l+1 (Eq.1). t ivt a = (((t rl+1 r R a t r l+1 ) (t d rl t r d l )) q rl ) VoT (1) The additional waiting time i quantified by comparing the cheduled and realized headway, incorporating the Percentage Regularity Deviation Mean (PRDM) a meaure for irregularity for each ervice hour (Van Oort & Van Ne 2009) (Eq.2). Given our focu on urban, high frequent public tranport ervice, a random paenger arrival pattern i aumed reulting in the quantification of additional waiting time due to irregularity a hown in Eq.3. d r h h d r r h R h d PRDM h = r 60 h 2 f h (2) t wtt = (( 60 2 f ) h (1 + 60 (PRDMh2 )) ( )) h β 1 VoT l 2 f l h H (3) Since large diruption can reult in ervice cancellation and more irregular ervice headway, the average crowding level on the remaining run i expected to increae. A crowding reult in a higher perceived in-vehicle time, thi component i quantified a well (Eq.4). For the public tranport line directly affected by the diruption, a well a parallel line ued a alternative route by paenger, for each run and each link the average crowding level i compared between an average undirupted day and during the diruption, thereby correcting for eaonal effect and day of the week. Baed on the vehicle eat capacity φ r and cruh capacity φ r c and their correponding crowding multiplier γ r and γ rc, the realized in-vehicle time i multiplied by a crowding multiplier γ r. In line with e.g. Wardman and Whelan (2011) and Yap et al. (2018a), γ r i aumed to be a linear piecewie function between 50% eat occupancy, eat capacity and cruh capacity (Eq.5). t ivt,p i = ((q r l,1 l, l a (t r+1 t d r ) γ r ) (q j i a r (t r+1 t d r ) γ r ) VoT r h R h (4)
γ r = { 0.95 if q r 0.5 φ r 0.95 + ( q r 0.5 φ r 0.5 φ r ) (γ r 0.95) if0.5 φ r < q r < φ r γ r + ( q r φ r φ r c φ r ) (γ r c γ r ) if q r > φ r (5) One component of operator diruption cot i the lot revenue following a lo of public tranport demand due to the impact of diruption. Although long-term riderhip impact from diruption are difficult to predict, we ued a imple elaticitybaed approach a applied by Van Oort et al. (2015a), uing parameter calibrated for planned diruption baed on mart card data (Yap et al. 2018b). For a given time period T, the generalized travel time i calculated for the dirupted and undirupted cenario (Eq.6). The generalized cot equal the weighted um for the dirupted cenario i and undirupted cenario j i, a ratio of the duration of a diruption t i compared to T, and i compared to a cenario with no diruption during T (Eq.7). ((t wtt ivt,p t p i S i j S j i β 1 + t i, j ) q i, j ) = qi,j i S i j S j (6) q = (E d ( t pi t i +(t pj i (T t i )) t pj i T 1) + 1) i S i j S j q i, j (7) The demand lo i quantified in Eq.8 by multiplication of q with the average paenger revenue. Due to the unannounced and relatively heavy impact of unplanned diruption compared to planned diruption, thi cot component can be conidered a lower bound. For each diruption the extra overtime hour for peronnel, the number of early run (departure before cheduled departure time), late run (departure later than cheduled departure time plu threhold ) or cancelled run, and the time the infratructure i not available, are multiplied with their correponding cot parameter (Eq.8). For the latter four component, the value of the cot parameter are uually pecified in the contract between operator and authority, indicating the fine for each early, late or cancelled run, or for each hour that no PT ervice can be provided on a link reulting from infratructure unavailability. c oi = β 2 q + β 3 t+β 4 r e + β 5 r l + β 6 r c + β 7 t i with r e { 1 ift r d 0 if t d r 3 Cae tudy d < t r t r r R d d, re { 1 ift r 0 if t d r > t r d t r r R r R + d +, 1 ifrun ha been cancelled rc { 0 if run i not cancelled (8)
We apply our framework to the urban public tranport network of The Hague, the Netherland, which conit of 12 light rail / tram line and 8 urban bu line. One large diruption on the light rail track i conidered a cae tudy (Figure 2), which occurred Wedneday January 6 th, 2016 due to a witch failure between 11:22h and 14:33h. At 19:38h all ervice were running according to chedule again. The diruption reulted in plitting light rail ervice 3 and 4, normally operating between the city of The Hague and the atellite city Zoetermeer (Figure 2 purple and orange, repectively) in a wetern and eatern part and cancellation of ome ervice due to turning capacity contraint. The Hague Fig. 2 Urban public tranport cae tudy network The Hague Zoetermeer To demontrate our propoed framework, we compare the diruption cot and driver chedule cot for two different driver chedule cenario for thi diruption. Scenario 1: multi-line multi-vehicle chedule with punctuality-baed recheduling Thi cenario decribe the ituation a currently applied by the operator of the cae tudy, namely applying a multi-line multi-vehicle driver chedule. A punctualitybaed recheduling approach i applied, aiming to let the remaining ervice depart according to chedule where poible. Although headway-baed control i preferred from a paenger perpective, interview with public tranport controller indicate that the complexity of the multi-line multi-vehicle chedule require punctualitybaed control. By trying to keep departure time of remaining ervice cloe to chedule, delay propagation to other line reulting from driver arriving earlier or later than cheduled for the next tak of their hift on another line i aimed to be reduced. The operator doe not ue recheduling oftware which allow for headwaybaed control when thi relatively complex multi-line multi-vehicle chedule i applied. The component of our framework related to paenger diruption cot are quantified directly uing realized Automated Fare Collection (AFC) and Automated Vehicle Location (AVL) data for the Wedneday the diruption occurred, and three other Wedneday of the ame month without diruption, o that particularly the diruption impact on crowding can be compared to regular, undirupted day. AVL data i alo ued to quantify the number of early, late and cancelled ervice. Baed on AVL data, log-file and information provided by public tranport cheduler, the number of peronnel overtime hour and the time the infratructure wa unavailable for PT
ervice are determined for thi cenario. Parameter value for operator fine β 3 to β 7 are determined from the contractual agreement between PT operator and authority. Scenario 2 ingle-line multi-vehicle chedule with headway-baed recheduling We contrat the diruption cot of cenario 1 with cenario 2, a cenario which evaluate the paenger and operator diruption cot in cae a ingle-line multivehicle driver chedule would be applied. In thi cae, driver only hift between vehicle of the ame line during one duty. Thi ha two effect. Firt, headway-baed control can be applied to remaining ervice, ince there i no rik of delay propagation to other line (HTM, 2015). Second, thi le complex driver chedule reduce the recovery time of PT ervice from the diruption, which reduce both the paenger diruption cot, and the peronnel overtime hour. Since thi cenario i currently not applied by the cae tudy operator, the diruption cot cannot be inferred directly from AFC, AVL and log-data in thi cae. Value for thi cenario can be obtained by combining quantitative and qualitative ource. Baed on realized AFC and AVL data when applying punctuality-baed control, we can imulate the diruption impact on paenger in-vehicle time, waiting time and crowding if all remaining ervice would be upplied with an equal headway in cae of headway-baed control. When applying our framework, headway-baed control affect the additional waiting time. We calculated the PRDM for an average undirupted day baed on AVL data (which equal 0.2 for our cae tudy ervice), and contrained the PRDM for each diruption hour to thi value to quantify the reduced additional waiting time. Baed on the remaining ervice and the PRDM being capped at a value of 0.2, the perceived ervice frequency can be calculated (Van Oort and Van Ne 2009). By dividing the hourly paenger load equally by the perceived ervice frequency, the expected occupancy for each run i calculated, reulting in monetized additional perceived in-vehicle time due to crowding for thi cenario. The generalized travel time during diruption i updated a conequence, adjuting the expected revenue lo from demand reduction. Peronnel overtime hour are expected to decreae linearly with the ervice recovery time reduction (HTM, 2015). Baed on calculation of the impact of different driver chedule type on ervice recovery time performed by the cae tudy operator, and interview held with public tranport cheduler and controller, the ervice recovery time i expected to reduce by 50% (De Bont and Wageman, 2015). Thi allow quantification of the reduced cot from peronnel overtime, a well a the hortened paenger impact of the diruption. Service are now aumed to operate according to an undirupted day 2.5 hour after the diruption ha been reolved (at 17:00h), intead of the ervice recovery time of 5 hour which i currently the cae. Multiplication of the diruption cot by the yearly number of diruption baed on log-data allow for the quantification of yearly paenger and operator cot for different driver chedule cenario. The reduced diruption cot reulting from a le complex driver chedule can then be compared to the increaed driver chedule cot, o that the trade-off between diruption and chedule cot can be monetized. 4 Reult
4.1 Reult From Figure 3 we can conclude that one non-recurrent diruption on the conidered light rail network currently (cenario 1: multi-line multi-vehicle cheduling with punctuality-baed control) cot 65,000, coniting of 36,000 paenger cot and 29,000 operator cot. The additional waiting time cot and long-term revenue lo are the mot important cot component. Fig. 3 Cot per diruption per component for different driver chedule type When cenario 2 ingle-line multi-vehicle cheduling with headway-baed control would be applied, total diruption cot are expected to decreae by 45% to 36,000 per diruption. Thi i epecially caued by le additional waiting time and lower additional perceived in-vehicle time, due to the improved regularity between ervice and horter ervice recovery time. Thi, in turn, reduce revenue loe from long-term paenger demand decreae. When extrapolating thee cot to yearly cot baed on the frequency of non-recurrent diruption, one can conclude from Figure 4 that yearly diruption cot are expected to be equal to 1.1 million and 0.6 million for cenario 1 and cenario 2, repectively.
Fig. 4 Yearly paenger and operator diruption cot for different driver chedule type In Figure 5 the trade-off between diruption cot and driver chedule cot i quantified for ingle-line multi-vehicle cheduling (cenario 2) compared to the current multi-line multi-vehicle cheduling (cenario 1) applied to the cae tudy network. A le complex and le efficient driver chedule without hift between different line increae the direct driver chedule cot by 300,000 (HTM, 2015), but reduce the total diruption cot by 500,000 and i beneficial from a ocietal perpective. The operator diruption cot are reduced by 200,000, howing that purely the financial robutne benefit of thi le complex driver chedule do not outweigh the cot. Fig. 5 Cot-Benefit Analyi for trade-off between diruption and driver chedule cot 4.2 Senitivity analyi A enitivity analyi i performed to the two mot uncertain parameter: the demand elaticity and the impact of ingle-line multi-vehicle cheduling on ervice recovery time reduction. We experimented with value of -0.3 and -0.7 for demand elaticity, compared to the default value of -0.5 [-40%,+40%]. For the reduction in ervice recovery time, a reduction of 30% and 70% wa teted next to the default value of 50% [-40%,+40%].
Fig. 6 Senitivity analyi to demand elaticity (-0.3: upper left / -0.7 (lower left) and ervice recovery time reduction (30%: upper right / 70%: lower right) Figure 6 how that a 40% le negative demand elaticity parameter of -0.3 reduce the operator robutne benefit of Scenario 2 by 50,000, howing a relatively limited enitivity of the output to thi parameter value. If ervice recovery time reduction i 40% le than aumed, operator robutne benefit reduce by almot 100,000, wherea total robutne benefit reduce by 300,000. Reult how to be epecially enitive to thi parameter, indicating that more in-depth reearch to thi value i recommended. 5 Concluion In thi tudy we develop a framework to quantify the paenger and operator cot of diruption explicitly a function of different driver chedule cheme. Thi upport operator in their deciion-making, ince the trade-off between driver chedule complexity and efficiency on the one hand, and robutne on the other hand, can be quantified. We tet our propoed framework for one large, non-recurrent diruption on the cae tudy network of The Hague, the Netherland. Reult for thi cae tudy how that when applying a le complex, ingle-line multi-vehicle driver chedule, total monetized paenger and operator robutne benefit outweigh the increaed driver chedule cot. The financial robutne benefit for the operator olely are however maller than the increaed operator cot reulting from a le efficient driver chedule. We recommend particularly more in-depth reearch to the impact of different type of driver chedule on (the reduction of) ervice recovery time from a diruption.
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