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Stochastic modelling of train delays and delay propagation in stations

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(60) !B;JN?L  'HNLI>O=NCIH.

(61) . . '0-;1; 7=<416-. 2BCM M?=NCIH JLIPC>?M ;H IONFCH? I@ NBCM NB?MCM 2B? NB?MCM MNLO=NOL? CM MBIQH CH $CAOL? . Chapter 1. Introduction. Chapter 2. State-of-the-art of railway operations and scheduling. Chapter 3. Statistical analysis of train operations. Chapter 4. Statistical distributions of train event and process times. Chapter 5. Probability model of train delay propagation. Chapter 6. Improving station capacity utilization and timetable design. Chapter 7. Conclusions and recommendations 1/=:-

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(67). %)14?)A +)8)+1<A )6, +)8)+1<A =<141B)<176. 0;CFQ;S =;J;=CNS CM MNO>C?> NI P;FC>;N? NB? @?;MC<CFCNS I@ M=B?>OF?> NCG?N;<F?M CH ;H ?R CMNCHA L;CFQ;S H?NQILE NI ?P;FO;N? NB? H?=?MMCNS I@ ?RN?H>CHA NB? NL;=E CH@L;MNLO=NOL? ;H> .

(68) . 20'* 2B?MCM M?LC?M. GI>?LHCTCHA NB? MCAH;FFCHA MSMN?G ;H> NI JLIPC>? ;MMCMN;H=? @IL >?MCAHCHA ; H?Q L;CFQ;S H?NQILE CH IL>?L NI M;NCM@S NB? ?RJ?=N?> @ONOL? NL;@= >?G;H> .;=BF .  HINB?L GINCP;NCIH I@ L;CFQ;S =;J;=CNS L?M?;L=B L?MOFNM @LIG NB? M?J;L;NCIH I@ L;CFQ;S CH@L;MNLO= NOL? G;H;A?G?HN ;H> NL;CH IJ?L;NCIHM ;H> NB? CHNLI>O=NCIH I@ L;CFQ;S =;J;=CNS =B;LA?M NI NL;CH IJ?L;NILM 2I ?HMOL? @;CL NL;=E ;==?MM ;H> =IHA?MNCIH =B;LA?M NB? ;H;FSMCM ;H> GI>?FFCHA I@ NB? L?F;NCIHMBCJ <?NQ??H =;J;=CNS ONCFCT;NCIH ;H> NL;CH J?L@ILG;H=? CM HIQ <?CHA J;C> GO=B ;NN?HNCIH NI CH #OLIJ?;H =IOHNLC?M %C<MIH ?N ;F  3'! .  5BCF? NB? N?LG =;J;=CNS CM Q?FF EHIQH CN CM HIN ?;MCFS >?H?> IL KO;HNC?> 2B? =;LLS CHA =;J;=CNS I@ ; L;CFQ;S NL;HMCN MSMN?G ?RJL?MM?> <S NB? HOG<?L I@ J;MM?HA?L MJ;=?M J?L NCG? J?LCI> CM >?N?LGCH?> <S NB? NL;HMJILN =;J;=CNS I@ NB? L;CFQ;S CH@L;MNLO=NOL? CH N?LGM I@ NL;CH NBLIOABJON NB? HOG<?L I@ =;LLC;A?M CH ; NL;CH ;H> NB? =;J;=CNS I@ NB? =;LLC;A?M 'H NBCM NB?MCM Q? @I=OM IH NB? L;CFQ;S =;J;=CNS QBC=B >?J?H>M IH NB? JBSMC=;F =B;L;= N?LCMNC=M I@ NB? CH@L;MNLO=NOL? CNM?F@ ;H> IH NB? NCG?N;<F? 2B?M? =B;L;=N?LCMNC=M CH=FO>? NB? HOG<?L I@ NL;=EM <?NQ??H MN;NCIHM IH?Q;S IL NQIQ;S IJ?L;NCIHM IH NB? NL;=EM NB? HOG <?L I@ JF;N@ILGM QCNBCH MN;NCIHM NB? HOG<?L I@ F?P?F =LIMMCHAM ;H> G?LACHAM>CP?LACHAM <?NQ??H >C@@?L?HN L;CFQ;S FCH?M ;FCAHG?HN ;H> MFIJ? I@ NB? NL;=EM NL;CH B?N?LIA?H?CNS IH NB? L;CFQ;S LION? ;H> =IHH?=NCIHM I@ NL;CHM CH MN;NCIHM 2B? >2I:>F> 42A24:EJ ?RJL?MM?> CH N?LGM I@ NB? G;RCGOG HOG<?L I@ NL;CHM CH ; L;CFQ;S FCH? =;H IHFS <? ;=BC?P?> CH C>?;F =IH>CNCIHM 'H NBCM =;M? NB? M=B?>OF?> B?;>Q;S <?NQ??H ?;=B J;CL I@ MO==?MMCP? NL;CHM QIOF> H??> NI <? ?KO;F NI NB? GCHCGOG B?;>Q;S QBC=B CM KOCN? OHL?;FCMNC= 2B? GCHCGOG B?;>Q;S IH ; FCH? >?J?H>M IH NB? MI=;FF?> 3=@4<:?8 E:>6D .;=BF . I@ ;HS M=B?>OF?> J;CL I@ NL;CHM 2B? <FI=ECHA NCG? CM NB? NCG? CHN?LP;F CH QBC=B ; M?=NCIH I@ ; NL;=E OMO;FFS ; <FI=E M?=NCIH CM ?R=FOMCP?FS ;FFI=;N?> NI ; NL;CH ;N CNM M=B?>OF?> MJ??> ;H> <FI=E?> @IL ;HS INB?L NL;CH 2BOM NB? <FI=ECHA NCG? F;MNM @LIG CMMOCHA ; GIP?G?HN ;ONBILCNS C? <S =F?;LCHA ; <FI=E MCAH;F OHNCF NB? JIMMC<CFCNS I@ CMMOCHA ; GIP?G?HN ;ONBILCNS NI ;HINB?L NL;CH NI ?HN?L NB? M;G? M?=NCIH 2B? <FI=ECHA NCG? I@ ; MCAH;F <FI=E CM OMO;FFS GO=B FIHA?L NB;H NB? NCG? NB? NL;CH I==OJC?M NB? <FI=E JBSMC=;FFS 'H ; N?LLCNILS QCNB FCH?MC>? R?> MCAH;FM NB? <FI=ECHA NCG? I@ ; <FI=E M?=NCIH =IHMCMNM I@ NB? @IFFIQCHA NCG? CHN?LP;FM $CAOL?    NB? NCG? @IL =F?;LCHA NB? MCAH;F  ; =?LN;CH NCG? @IL NB? >LCP?L NI PC?Q NB? =F?;L ;MJ?=N I@ NB? MCAH;F NB;N ACP?M NB? ;JJLI;=B CH>C=;NCIH NI NB? MCAH;F ;N NB? ?HNL;H=? I@ NB? <FI=E M?=NCIH NBCM =;H <? NB? JL?=?>CHA <FI=E MCAH;F IL ; M?J;L;N? ;JJLI;=B MCAH;F.  NB? ;JJLI;=BCHA NCG? <?NQ??H NB? MCAH;F NB;N JLIPC>?M NB? ;JJLI;=B CH>C=;NCIH ;H> NB? MCAH;F ;N NB? ?HNL;H=? I@ NB? <FI=E M?=NCIH  NB? LOHHCHA NCG? <?NQ??H NB? <FI=E MCAH;FM  NB? =F?;LCHA NCG? NI =F?;L NB? <FI=E M?=NCIH ;H> C@ L?KOCL?> NB? IP?LF;J QCNB NB? @OFF F?HANB I@ NB? NL;CH  NB? L?F?;M? NCG? NI :OHFI=E NB? <FI=ECHA MSMN?G "L;QCHA NB? <FI=ECHA NCG?M I@ ;FF <FI=E M?=NCIHM NB;N ; NL;CH J;MM?M CHNI ; NCG?>CMN;H=? >C;AL;G SC?F>M NB? MI=;FF?> 3=@4<:?8 E:>6 DE2:CH2J $CAOL?   2B? <FI=ECHA NCG?M.

(69) !B;JN?L  1N;N?I@NB?;LN I@ L;CFQ;S IJ?L;NCIHM ;H> M=B?>OFCHA. . Distance Minimum headway (as distance) of following trains. Time Sighting distance. 11. Block section. Clearing point. Block section 13. 15 Train length. Time for clearing signal Signal watching time. Approaching time. a) Train without stop. Blocking time of block section 13-15 Running time between block signals Clearing time Release time. 11. 13. 15 Train length. Time for clearing signal Signal watching time. b) Train with stop. Running time between block signals. Blocking time of block section 13-15. Clearing time Release time. 1/=:-

(70)  FI=ECHA NCG? I@ ; <FI=E M?=NCIH 1IOL=? .;=BF . >CL?=NFS ?MN;<FCMB NB? MCAH;F B?;>Q;S ;M NB? NCG? CHN?LP;F <?NQ??H NQI MO==?MMCP? NL;CHM CH ?;=B <FI=E M?=NCIH 2B? GCHCGOG FCH? B?;>Q;S CM NB? B?;>Q;S <?NQ??H NQI NL;CHM HIN IHFS =IHMC>?LCHA IH? <FI=E M?=NCIH <ON NB? QBIF? <FI=ECHA NCG? MN;CLQ;SM I@ NB? FCH? 'H NBCM =;M? NB? <FI=ECHA NCG? MN;CLQ;SM I@ NQI @IFFIQCHA NL;CHM DOMN NIO=B ?;=B INB?L CH ;N F?;MN IH? <FI=E M?=NCIH ;H> ;N NBCM =LCNC=;F <FI=E M?=NCIH NB?L? CM HI 3F776C E:>6 ;P;CF;<F? <?NQ??H NB? <FI=ECHA NCG? MN;CLQ;SM I@ NB? NQI MO==?MMCP? NL;CHM 2B? <O@@?L NCG? CM >?H?> ;M NB? NCG? >C@@?L?H=? <?NQ??H NB? ?H> I@ NB? <FI=ECHA NCG? I@ NB? LMN NL;CH ;H> NB? MN;LN I@ NB? <FI=ECHA NCG? I@ NB? M?=IH> NL;CH ;N NB? =LCNC=;F <FI=E M?=NCIH 0;CFQ;S =;J;=CNS >?J?H>M IH NB? NCG?N;<F? NII 2I ;=BC?P? NB? G;RCGOG =;J;=CNS I@ ; L;CFQ;S LION? NB? MJ??> I@ ;FF NL;CHM GOMN <? M=B?>OF?> ?KO;FFS &IQ?P?L MO=B ; M=B?>OF? =;H IHFS <? @IOH> IH LION?M >?>C=;N?> NI HI GIL? NB;H IH? NSJ? I@ NL;@= ?A G?NLI FCH?M -H L;CFQ;S LION?M ; P;LC?NS I@ NL;CH NSJ?M QCNB >C@@?L?HN MNIJJCHA J;NN?LHM ;H> LOHHCHA MJ??>M ;L? A?H?L;FFS IJ?L;N?> 2BCM B;M F?> NI NB? N?LGCHIFIAS I@ E:>6E23=6 42A24:EJ .;=BF . NB? G;RCGOG HOG<?L I@ B?N?LIA?H?IOM NL;CH J;NBM NCG?>CMN;H=? =OLP?M. NB;N =IOF> <? M=B?>OF?> QCNBION =IHMC>?LCHA ;HS <O@@?L NCG? 2B? >C@@?L?H=? <?NQ??H NB? NCG?N;<F? =;J;=CNS ;H> NB? G;RCGOG =;J;=CNS I@ ; FCH? CM ; L?M?LP? =;J;=CNS CH IL>?L NI KOC=EFS L?>O=? KO?O?M CH =;M? I@ J?LNOL<;NCIHM <S N?GJIL;LCFS ?KO;FCTCHA NB? MJ??> >C@@?L?H=?M NI ?H;<F? ; BCAB?L IONJON NB;H M=B?>OF?> >IJNCHA MO=B ; L?M?LP? B?FJM NI JL?P?HN M=B?>OF?> IJ?L;NCIHM @LIG M?P?L? =IHA?MNCIH.

(71) . 20'* 2B?MCM M?LC?M Distance Time. Blocking time Blocking time. Tra in. Minimum line headway. 1. Blocking time Blocking time. Blocking time. Blocking time. Train 2. Blocking time Blocking time. Signal headway of critical block section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

(72) !B;JN?L  1N;N?I@NB?;LN I@ L;CFQ;S IJ?L;NCIHM ;H> M=B?>OFCHA. . NL;CHM CH NB? =IHMC>?L?> NCG? QCH>IQ 89 EB CM NB? ;P?L;A? GCHCGOG FCH? B?;>Q;S 8 GCH9 ;H> EJ MN;H>M @IL NB? NCG? QCH>IQ 8 GCH9 !;J;=CNS ONCFCT;NCIH I@ ; FCH? CM NB? L?MOFN I@ NB? =IGJL?MMCIH JLI=?MM ;H> G?;MOL?> ;N NB? <?ACHHCHA I@ NB? LMN <FI=E M?=NCIH QCNBCH NB? FCH? 2B? L?G;CHCHA =;J;=CNS NB;N ?KO;FM NB? =BIM?H NCG? QCH>IQ GCHOM NB? =;J;=CNS ONCFCT;NCIH ;H> NIN;F <O@@?L NCG? CM =;FF?> F? FD65 42A24:EJ '@ H?=?MM;LS ;>>CNCIH;F NL;CH J;NBM =IOF> <? CH=ILJIL;N?> CHNI NB? ILCACH;F NCG?N;<F? ;H> ; H?Q ?MNCG;NCIH I@ =;J;=CNS ONCFCT;NCIH QIOF> NB?H <? L?KOCL?> 3MO;FFS NB? =;J;=CNS ONCFCT;NCIH L;N? CM L?=IGG?H>?> NI <? MG;FF?L NB;H ; JL?>?H?> NBL?MBIF> P;FO? QBC=B CM >?N?LGCH?> <;M?> IH LOF?M I@ NBOG< IL NB? ?RJ?=N?> L?FC;<CFCNS ;H> JOH=NO;FCNS I@ NL;CH IJ?L;NCIHM 'H IL>?L NI CHP?MNCA;N? NB? =;J;=CNS ONCFCT;NCIH I@ ; =IGJF?R H?NQILE NB? =;J;=CNS ONC FCT;NCIH L;N? MBIOF> <? =;F=OF;N?> M?J;L;N?FS @IL ?;=B J;LN 2B? BCAB?MN L;N? I@ =;J;=CNS ONCFCT;NCIH I@ ; =?LN;CH H?NQILE J;LN >?N?LGCH?M NB? =;J;=CNS ONCFCT;NCIH CH NB? QBIF? L;CF Q;S H?NQILE I@ CHN?L=IHH?=N?> FCH?M. . -<-:516)<176 7. 5)@15)4 +)8)+1<A =<141B)<176. $;=CHA ; =IHNCHOIOM ALIQNB I@ NL;@= >?G;H> ;H> =IHM?KO?HNFS H??>?> ;>>CNCIH;F NL;CH M?LPC=?M GIMN L;CFQ;S CH@L;MNLO=NOL? G;H;A?LM MNLCP? NI ONCFCT? NB? ?RCMNCHA =;J;=CNS ;M GO=B ;M JIMMC<F? &IQ?P?L C@ NB? ONCFCT;NCIH L;N? I@ L;CFQ;S =;J;=CNS CM >?MCAH?> NII BCAB NB? NL;CH NL;@= <?=IG?M ?;MCFS J?LNOL<?> F?;>CHA NI ; FIQ?L F?P?F I@ L?FC;<CFCNS ;H> JOH=NO;FCNS I@ IJ?L;NCIHM  =IGJLIGCM? GOMN <? @IOH> NI ONCFCT? GIL? ?@=C?HNFS NB? ?RCMNCHA =;J;=CNS I@ L;CFQ;S H?NQILEM IH NB? IH? B;H> ;H> CGJLIP? NB? F?P?F I@ L?FC;<CFCNS ;H> JOH=NO;FCNS I@ IJ?L;NCIHM IH NB? INB?L B;H> 2B? >?N?LGCH;NCIH I@ NB? G;RCG;F =;J;=CNS ONCFCT;NCIH CM HIN MCGJF? ;M ; F;LA? HOG<?L I@ L?F?P;HN @;=NILM GOMN <? N;E?H CHNI ;==IOHN 3J NI HIQ NB? =;J;=CNS ONCFCT;NCIH ;JJFC?> @IL NB? JF;HHCHA I@ NL;CH M?LPC=?M B;M G;CHFS <??H <;M?> IH LOF?M I@ NBOG< 2B? L?=IG G?H>?> G;RCG;F =;J;=CNS ONCFCT;NCIH CM >?H?> <S 3'!  ;N   @IL J?;E BIOLM ;H>   @IL NB? ?HNCL? >;S CH NB? =;M? I@ GCR?> NL;@= FCH?M 2B? %?LG;H 0;CFQ;SM OM? NB? NIN;F Q;CNCHA NCG? I@ NL;CHM ;M ; <?H=BG;LE NI >?N?LGCH? NB? G;RCG;FFS ;==?JN;<F? =;J;=CNS ONCFCT;NCIH QBC=B CM <;M?> IH NB? G;RCG;F KO?O? F?HANB J?L >;S >?H?> <S 1=BQ;HB]O[?L   2BCM KO?O? F?HANB CM =B;L;=N?LCT?> <S ; MCGJF? ?RJIH?HNC;F ?KO;NCIH ;M ; @OH=NCIH I@ NB? MB;L? I@ J;MM?HA?L NL;CHM .. $ GK  6 A . . QB?L? $ GK L?JL?M?HNM NB? KO?O? F?HANB 89 A J NB? MB;L? I@ J;MM?HA?L NL;CHM ;H>   =I?@=C?HNM NB;N Q?L? =;FC<L;N?> ;M  ;H>  L?MJ?=NCP?FS @IL NB? %?LG;H 0;CFQ;SM 2BL?? >C@@?L?HN F?P?FM I@ KO;FCNS I@ IJ?L;NCIHM P?LS AII> M;NCM@;=NILS OH M;NCM@;=NILS ;L? >?N?LGCH?> <S NB? ?MNCG;N?> F?HANB I@ NB? KO?O? >CPC>?> <S NB? G;RC G;FFS ;==?JN;<F? F?HANB I@ NB? KO?O? 2B? G;RCG;F Q;CNCHA NCG? NIF?L;N?> <S NB? %?LG;H 0;CFQ;SM CM <?NQ??H  OJ NI  GCH J?L MN;NCIH J?L >;S >?J?H>CHA IH NB? MB;L? I@ J;MM?HA?L NL;CHM 2B?M? NBL?MBIF> P;FO?M I@ NB? G;RCG;F Q;CNCHA NCG? BIQ?P?L FIIE MIG?QB;N ;L<CNL;LS ;H> F;=E MO@=C?HN ?GJCLC=;F ;H> NB?IL?NC=;F ?PC>?H=?.

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