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that the boundaries put pressure on the Operating Sate (OS) is added textually with the term ‘gradient’ and A;GE! 9;G9B! BH?K! :HG! $+! dFIY! O?I95@D! OFG! :?! BH9LL?K! A;9O5G@:B=! -HGBG! A;9O5G@:B! 9;G! ?C! 5@:G;GB:D! B5@<G! :HGE! ;GY;GBG@:!:HG!5@:G;@9L!Y;GBBF;G!?@!:HG!$+!9@O!I9E!5@O5;G<:LE!NG!IG9BF;GO!9@O!<9@!HGLY!GhYL95@!:HG!;GB5L5G@<G! ?C! :HG! BEB:GI! KHG@! :HG! $+! 5B! L?<9:GO! 9:! 9! BYG<5C5<! Y?B5:5?@=! PHG@! 9! A;9O5G@:! 5B! L9;AG! 5:! ;GY;GBG@:B! BEB:GI! ;GB5L5G@<G!9A95@B:!Gh:G;@9L!YG;:F;N9:5?@BD!KH5LG!BH9LL?K@GBB!;GY;GBG@:B!N;5::LG@GBB=!-H5B!A;9O5G@:!<9@!NG!I9OG! GhYL5<5:! NE! 9OO5@A! 9! OGY:H! O5IG@B5?@! :?! #9BIFBBG@B! I?OGL! 9B! 5C! 5:! 5B! 45GKGO! C;?I! 9N?4G! 5@! 9! L9@OB<9YG! ?C! 49LLGEB! 9B! OGB<;5NGO! NE! P??OB! G:! 9L=! aV88^bD! KH?! ;GL9:GO! :HG! K?;M! ?C! P9LMG;! X! .?LL5@A! aV88_b! :?! :H9:! ?C! #9BIFBBG@!a6^^Ub. The slope (α) of the valley (see figure 1 section II) describes the internal force gradient or #GB5L5G@<G!&@A5@GG;5@A! 9B! <9LLGO! NE! P9LMG;D! 9<:5@A! ?@! :HG!$YG;9:5@A! +:9:G! a$+b! KH5LG! :HG! 4G<:?;!

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–*3$,*'"#($*;,"*"#(&*%,-'(3$*#$9*3$,*"#(&*'"#-4*;,"*%2('-6* PHG@!Y9BB5@A!9!;GO!B5A@9LD!<?II?@LE!M@?K@!9B!9!+5A@9L!"9BBGO!9:!'9@AG;!?;!+"/'!a.?LLEKGLLD!V88,bD!!B9CG:E!5B! 9:!B:9MG!9@O!:HG!I?;G!C;GSFG@:LE!:H5B!?<<F;BD!:HG!H5AHG;!:HG!Y;?N9N5L5:E!?C!9@!9<<5OG@:=!-HG!@FING;!?C!+"/'B! I9E! NG! FBGO! :?! GhY;GBB! :HG! 9I?F@:! ?C! B9CG:E! Y;GBBF;G=! .?KG4G;D! :H5B! <9@! NG! Gh:G@OGO! NE! IG9BF;5@A! :HG! @FING;!?C!EGLL?K!B5A@9L!Y9BB9AGB!9@O!G4G@!NE!:HG!@FING;!?C!;GO!9@O!EGLL?K!B5A@9L!9YY;?9<HGB=!-HG!L9::G;!5B! dFB:5C5GO!NE!C?LL?K5@A!:HG!B9CG:E!BGSFG@<GD!9@O!:HG!OG459:5?@!C;?I!:HG!?Y:5Ial safe “green!wave”. In the “green wave” the train has only green signals, until it gets to its station7B:?YD!9@O!O?GB!@?:!@GGO!:?!OG<GLG;9:G!F@:5L! then. With the “green wave” as reference, the pressure of the safety boundary can be expressed as a function ?C!;GO!9@O!EGLL?K!B5A@9L!9YY;?9<HGB!9@O!Y9BB9AGB=!-HGBG!49;59NLGB!<9@!NG!Gh:G@OGO!NE!:HG!@FING;!?C!5@H5N5:GO! ;95L7Y9:HBD!OFG!:?!?<<FY9:5?@!?C!BK5:<HGB!NE!9@?:HG;!;95L!Y9:H=!!

-HFBm!

α+!p!C+a@?=!?Cm!!+"/'BD!EGLL?K!B5A@9L!Y9BB9AGBD!EGLL?Kg;GO!B5A@9L!9YY;?9<HGBD!BK5:<H!!5@H5N5:GO!;95L7Y9:HBb!

/! B9CG:E! #+! <9@! NG! OGC5@GO! KHG@! :HG! BL?YG! OG<;G9BG! 5B! L9;AG;! :H9@! 9! Y;GOGC5@GO! :H;GBH?LOD! -H;GBH?LO7#++D! 5@O5<9:5@A! :H9:! :HG! 5@:G;@9L! BEB:GI! 5B! NG<?I5@A! LGBB! ;GB5L5G@:! 9B! BGG@! 5@! 35AF;G67(((9=! PHG@! 9BBFI5@A! 9! I?@?:?@5<!CF@<:5?@D!:HG!change of the slope Δα+!<9@!NG!GB:5I9:GO!NE!:HG!<FIFL9:54G!KG5AH:GO!<H9@AGB!?C!:HG! CF@<:5?@!49;59NLGBm!

Δα+!p! ! J6+(Δ SPADs) + KV+(Δ yellow7Y9BB9AGBb! „! JZ+(Δ red79YY;?9<HGBb! „! J_+(Δ yellow7! ! 9YY;?9<HGBb! „! J,+(Δ BK5:<H7inhibits); Safety RS: Δα+!!•!-H;GBH?LO7#++!!•!!8!KHG;G!:HG!KG5AH:B!J6+D!JV+D!JZ+D!J_+D!J,+!9@O!-H;GBH?LO7#++!! @GGOB!CF;:HG;!GIY5;5<9L!5@4GB:5A9:5?@=!

(4)

6^_!

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α;'p!C"(Driven km’s/km track, delays, km infrastructure withdrawal)!

+5I5L9;! :?! :HG! B9CG:E! #+D! 9! <9Y9<5:E! #+! <9@! NG! OGC5@GO! KHG@! :HG! BL?YG! OG<;G9BG! 5B! L9;AG;! :H9@! 9! Y;GOGC5@GO! :H;GBH?LOD!-H;GBH?LO7#+". The change of the slope Δα"!<9@!NG!GB:5I9:GO!NE!:HG!<FIFL9:54G!KG5AH:GO!<H9@AGB! ?C!:HG!CF@<:5?@!49;59NLGBm!

Δα"!p!!J6"(Δ driven km’s/km track) + KV"(Δ km infrastructure withdrawal) + KZ"(Δ delays)! Performance RS: Δα"!!•!-H;GBH?LO7#+"!!•!!8! -HG!OGL9E!IG9BF;GIG@:!5B!9!<?IYLGh!?@G!B:5LL!:?!NG!:9<MLGO!5@!:HG!9YY;?Y;59:G!<?@:Gh:=!-HG!KG5AH:B!J6"D!JV"D!JZ"! 9@O!-H;GBH?LO7#+"!@GGO!CF;:HG;!GIY5;5<9L!5@4GB:5A9:5?@!9B!KGLL=! 7[7' /"E]@"DH' -HG!I95@!O;54G;!C?;!I9@9A5@A!:HG!;95L!?YG;9:5?@!5B!:HG!Y;GY9;GO!L?A5B:5<!YL9@=!PHG@!@?!OG459:5?@!?<<F;B!C;?I! :H5B!YL9@D!:HG!BEB:GI!<9@!Y;9<:5<9LLE!NG!;F@!9F:?I9:5<9LLE!9@O!<9FBGB!K?;M!F@OG;7L?9O=!PHG@!OG459:5?@B!?<<F;D! :HG! YL9@! 5B! FYO9:GO! ?;! O5;G<:! <?II9@OB! :?! :HG! 5@C;9B:;F<:F;G! 9;G! GhG<F:GO=! -HG! K?;ML?9O!<9@! NG! GB:5I9:GO! :H;?FAH! :HGBG! IG9BF;9NLG! BEB:GI! 9<:545:5GB=! )GG;5@<h! aV88Zb! Y;?Y?BGO! 9! I?OGL! :?! IG9BF;G! :HG! K?;ML?9O! OF;5@A!?YG;9:5?@BD!9B!9!CF@<:5?@!?C!:H;GG!49;59NLGBm!:9BM!BK5:<HGBD!:9BM!:5IG!OF;9:5?@!9@O!:9BM!<?IYLGh5:E=!&9<H! ?C!:HG!9N?4G!BEB:GI!9<:545:5GB!<?FLO!NG!BGG@!9B!Y9;:!?C!9!:9BM!BGSFG@<G!Y;?45O5@A!:HG!Y?BB5N5L5:E!:?!<?F@:!:HG! :9BM! BK5:<HGB! 9@O! :9BM! OF;9:5?@=! %?IYLGh5:E! 5@! :H5B! I?OGL!5B! OGC5@GO! NE!#9BIFBBG@B! +#J7LG4GLB! a#9BIFBBG@D! 6^[Qb=!&9<H!<H9@AG!?C!:HG!YL9@!@GGOB!;G9B?@5@A!9@O!5B!9:!LG9B:!;FLG7N9BGO!NF:!I?B:LE!M@?KLGOAG!N9BGO=!-H5B! I?OGL5@A! I9MGB! 5:! Y?BB5NLG! :?! GB:5I9:G! :HG! K?;ML?9O! K5:H! 5@O5;G<:! IG9BF;GIG@:B! 9@O! <9@! NG! GhY;GBBGO! 9B! C?LL?KBm!

· α/'p!CPaYL9@!9O9Y:9:5?@BD!O5;G<:!9<:5?@B!?@!:HG!5@C;9bo!!

· ΔαP!p!!J6P(Δ plan adaptations) + KVP(Δ direct actions on the infra); ! · Workload RS: ΔαP!!•!-H;GBH?LO7#+P!!•!!8! -HG!K?;ML?9O!<H9@AG!<9@!NG!GB:5I9:GO!NE!:HG!<H9@AG!?C!YL9@!9O9Y:9:5?@B!9@O!:HG!@FING;!?C!9<:5?@B!?@!:HG! 5@C;9B:;F<:F;G=!-HG!K?;ML?9O!#+!<9@!NG!OGC5@GO!KHG@!:HG!BL?YG!OG<;G9BG!5B!L9;AG;!:H9@!9!Y;GOGC5@GO!:H;GBH?LOD! -H;GBH?LO7#+P=!-HG!KG5AH:GO!;GL9:5?@B!J6PD!JVP!9@O!-H;GBH?LO7#+P!@GGO!:?!NG!K?;MGO!?F:!GIY5;5<9LLE=!

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N[T' !"EE%@D$?"#'F%$L%%#'D'&DK%$='+:'D#H'&DK%$='E?&]'''

$@G!?C!:HG!9BBFIY:5?@B!?C!:HG!B9CG:E!B5A@9L!I?OGLD!K?;MGO!?F:!5@!:HG!Y;G45?FB!Y9;9A;9YHD!5B!:H9:!9!A;?K5@A! @FING;! ?C! +"/'B! 5@O5<9:GB! 9! A;?K5@A! B9CG:E! Y;GBBF;G=! -H5B! 9BBFIY:5?@D! 9I?@A! ?:HG;BD! @GGOB! :?! NG! Y;?4G@! GIY5;5<9LLED!B5@<G!9!+"/'!O?GB!@?:!9LK9EB!<;G9:G!9!H5AH!;5BM!B5:F9:5?@=!3?;!Gh9IYLGD!5C!@?!:;95@!5B!5@!:HG!NL?<M! NGH5@O!9!;GO!B5A@9L!:HG!Y;?N9N5L5:E!?C!9!<?LL5B5?@!5B!4G;E!L?K=!-HG!9BYG<:!?C!O5CCG;G@:59:5@A!NG:KGG@!9!+"/'!K5:H! 9!H5AH!?;!L?K!;5BM!H9B!NGG@!K?;MGO!?F:!NE!:HG!'F:<H!15@5B:;E!?C!(@C;9B:;F<:F;G!9@O!&@45;?@IG@:!aV866b!:H9:! :;9<MB!9@O!;GY?;:B!EG9;LE!?@!:HG!B:9:FB!?C!+"/'B=!(:!FBGB!C?;!G9<H!+"/'!:HG!+"/'!#5BM!;9@M5@A!IG:H?O?L?AED!9! B:9@O9;O! ?C! :HG! #++]!a#95L! B9CG:E! 9@O! B:9@O9;OB! N?9;ObD! KH5<H! :9MGB! 5@:?! 9<<?F@:! 9I?@A! ?:HG;B! :HG!;GL9:54G! Y?B5:5?@BD!4GL?<5:5GBD!5@C;9!BG::5@AD!G:<=!:?!<9L<FL9:G!:HG!;5BM!?C!9!BG;5?FB!9<<5OG@:=!-HGBG!C5AF;GBD!:HG!@FING;!?C! EG9;LE!+"/'B!K5:H!9!H5AH!;5BMD!H94G!NGG@!Gh:;9<:GO!C;?I!:HG!;GY?;:!9B!KGLL!9B!:HG!:?:9L!@FING;!?C!EG9;LE!+"/'BD! 9@O!YL?::GO!9A95@B:!G9<H!?:HG;=!-HG!;GBFL:!C?;!:HG!YG;5?O!V88U7V866!BH?KB!:H9:!:HG!:K?!49;59NLGB!9;G!H5AHLE! <?;;GL9:GO!a"G9;B?@! ;! p! 8D^[bD! dFB:5CE5@A! :HG!5@:F5:54G! B9CG:E! #+! I?OGL! 9BBFIY:5?@! :H9:! 9! A;?K5@A! @FING;! ?C!

(5)

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