Wybrane zagadnienia optymalizacji organizacji ruchu kolejowego w celu minimalizacji kosztów zużycia energii elektrycznej Some aspects of optimization of rail traffic organization in order to minimize the costs of electricity consumption

Pełen tekst

(1)35$&(1$8.2:(32/,7(&+1,.,:$56=$:6.,(- ]. . 7UDQVSRUW. . 0DULDQQD-DF\QD 3ROLWHFKQLND:DUV]DZVND:\G]LDá7UDQVSRUWX. 0LFKDá8UEDQLDN. 3ROLWHFKQLND*GDĔVND:\G]LDá,QĪ\QLHULL/ąGRZHMLĝURGRZLVND. . :<%5$1(=$*$'1,(1,$237<0$/,=$&-, 25*$1,=$&-,58&+8.2/(-2:(*2:&(/8 0,1,0$/,=$&-,.26=7Ï:=8ĩ<&,$(1(5*,, (/(.75<&=1(- . 5ĊNRSLVGRVWDUF]RQRVW\F]HĔ. . 6WUHV]F]HQLH:DUW\NXOHSU]HGVWDZLRQRSRG]LDáNRV]WyZZWUDQVSRUFLHNROHMRZ\P]XZ]JOĊGQLHQLHP NRV]WyZ ZHZQĊWU]Q\FK SU]HGVLĊELRUVWZD GR NWyU\FK ]DOLF]DMą VLĊ PLĊG]\ LQQ\PL NRV]W\ GRVWĊSX GRLQIUDVWUXNWXU\F]\NRV]W\HQHUJLL6WZLHUG]RQRĪHSU]\RGSRZLHGQLHMRUJDQL]DFMLUXFKXSRFLąJyZ QD VLHFL NROHMRZHM EH] SRQRV]HQLD GRGDWNRZ\FK QDNáDGyZ QD LQIUDVWUXNWXUĊ L VSHFMDOLVW\F]QH XU]ą G]HQLDPRĪQD]QDF]QLHRJUDQLF]\ü]XĪ\FLHHQHUJLLDFR]DW\PLG]LHNRV]W\]QLą]ZLą]DQH3U]\WR F]RQR VWRVRZDQH UR]ZLą]DQLD SROHJDMąFH QD PRQLWRURZDQLX HQHUJHW\NL SU]HMD]GX L GąĪHQLX GR MDN QDMPQLHM HQHUJRFKáRQQ\FK F\NOL MD]G\ RUD] SU]HGVWDZLRQR GRNáDGQLHM LGHĊ RSW\PDOQHM VWUDWHJLL SUR ZDG]HQLDSRMD]GXV]\QRZHJRZFHOX]DRV]F]ĊG]HQLDHQHUJLL 'RGDWNRZR]DSURSRQRZDQRXZ]JOĊGQLHQLHSU]\SURFHVDFKRSW\PDOL]DFMLRUJDQL]DFMLUXFKXSRMD]GyZ QDVLHFLNROHMRZHMNU\WHULXPHIHNW\ZQRĞFLWUDQVIHUXHQHUJLLSRFKRG]ąFHM]UHNXSHUDFMLPLĊG]\SRMD] GDPL =ZUyFRQR XZDJĊ QD F]\QQLNL VSU]\MDMąFH WDNLHM NRRSHUDFML RGOHJáRĞü PLĊG]\ SRMD]GDPL SR NU\ZDQLH VLĊ F]DVyZ KDPRZDQLD L UR]UXFKX L LQQH

(2) DOH WDNĪH SUREOHP\ WHFKQLF]QH L RUJDQL]DF\MQH ]W\P]ZLą]DQH 3U]HGVWDZLRQ\ SU]HJOąG UR]ZLą]DĔ RUJDQL]DF\MQ\FK SR]ZDOD VWZLHUG]Lü ĪH X ZLĊNV]RĞFL SROVNLFK SU]HZRĨQLNyZ NROHMRZ\FK LVWQLHMH GXĪ\ SRWHQFMDá RJUDQLF]HQLD NRV]WyZ WUDQVSRUWRZ\FK SU]HGVLĊ ELRUVWZ0RĪOLZRĞFL Z W\P]DNUHVLHGDMHRGSRZLHGQLHRUJDQL]RZDQLHSU]HZR]yZ Z W\P WZRU]HQLH ]RSW\PDOL]RZDQ\FK UR]NáDGyZ MD]G\ ] XZ]JOĊGQLHQLHP NU\WHULXP PLQLPDOL]DFML NRV]WyZ ]XĪ\FLD HQHUJLL 3U]HGVWDZLRQH UR]ZLą]DQLH GDMH V]DQVĊ SHáQLHMV]HJR Z\NRU]\VWDQLD ZGUDĪDQ\FK WHFKQRORJLL LRJUDQLF]HQLD]XĪ\FLDHQHUJLL 6áRZDNOXF]RZHWUDQVSRUWNROHMRZ\RUJDQL]DFMDUXFKXRSW\PDOL]DFMDNRV]W\WUDQVSRUWX. . :67ĉ3. =DJDGQLHQLH RUJDQL]DFML UXFKX NROHMRZHJR REHMPXMH ZLHOH VNáDGRZ\FK 6ą QLPL SODQRZDQLH SU]HELHJX WUDV NRQVWUXNFMD UR]NáDGyZ MD]G\ Z SRVWDFL Z\NUHVyZ UXFKX.

(3) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. . SU]\G]LDá NUDZĊG]L SHURQRZ\FK QDSRVWHUXQNDFK UXFKX SODQRZDQLH RELHJyZ WDERUX DWDNĪHSUDF]HVSRáyZREVáXJXMąF\FKSRFLąJL.DĪGD]W\FKVNáDGRZ\FK PDPQLHMV]\OXE ZLĊNV]\ ZSá\Z QD NRV]W\ SRQRV]RQH SU]H] SU]HZRĨQLNyZ NROHMRZ\FK 2SW\PDOL]DFMD RUJDQL]DFML UXFKX PD QD FHOX Z\EyU QDMOHSV]HJR ] PRĪOLZ\FK ZDULDQWyZ QDNDĪG\P V]F]HEOX RUJDQL]DF\MQ\P 1DMZDĪQLHMV]ą VNáDGRZąSURFHVX RUJDQL]DFML UXFKX NROHMRZHJR MHVW HWDS IL]\F]QHM NRQVWUXNFML UR]NáDGyZ MD]G\ SRFLąJyZ >@ 2SW\PDOL]DFMD UR]NáDGX MD]G\ MHVW GąĪHQLHP GR RVLąJQLĊFLD PDNV\PDOQHM HIHNW\ZQRĞFL Z\NRU]\VWDQLD ĞURGNyZ ILQDQVRZ\FKWHFKQLF]Q\FKLORJLVW\F]Q\FKSRVLDGDQ\FKSU]H]NROHM0DWRQDFHOX]DSHZ QLHQLHSRĪąGDQHMF]ĊVWRWOLZRĞFLNXUVyZNWyUHZ\QLNDMą]]DSRWU]HERZDQLDSRGUyĪQ\FK 2SW\PDOL]DFMD RUJDQL]DFML UXFKX NROHMRZHJR ZHGáXJ NU\WHULXP PLQLPXP NRV]WyZ REHMPXMH>@ RSW\PDOL]RZDQLH UXFKX SRFLąJyZ Z F]DVLH U]HF]\ZLVW\P ]XZ]JOĊGQLHQLHP RV]F]ĊGQRĞFL]XĪ\FLDHQHUJLLRUD]PLQLPDOL]RZDQLDRSyĨQLHĔLFKSU]HMD]GyZ RSW\PDOL]RZDQLHWHFKQLNMD]G\GODPDV]\QLVWyZZUXFKXWRZDURZ\P RSW\PDOL]DFMĊOLF]E\VNáDGyZREVáXJXMąF\FKSRáąF]HQLDZDVSHNFLHNRV]WyZSXVW\FK SU]HELHJyZ RSW\PDOL]DFMĊ SODQX SUDF\ ]DáyJ NRQGXNWRUVNLFK L REVáXJL SRFLąJyZ ] XZ]JOĊGQLH QLHPNRV]WyZLFKXWU]\PDQLD : ]ZLą]NX ] W\P ĪH NRV]W\ SU]HZR]yZ Z GXĪHM PLHU]H ZSá\ZDMą QD UHQWRZQRĞü LSHUVSHNW\ZĊ UR]ZRMX SU]HGVLĊELRUVWZD WUDQVSRUWRZHJR QDOHĪ\ ]QDOHĨü RGSRZLHGĨ QD S\WDQLH MDNLH ĞURGNL RUJDQL]DF\MQH ]ZLą]DQH ]SURZDG]HQLHP UXFKX SRMD]GyZ V]\QRZ\FK PRJąSU]\F]\QLüVLĊGRRV]F]ĊGQRĞFLZ\QLNDMąF\FK]RJUDQLF]DQLDSRQRV]RQ\FKNRV]WyZ 1LH]Z\NOH LVWRWQ\P HIHNWHP GRERUX RGSRZLHGQLFK NU\WHULyZ GR DOJRU\WPX XVSUDZQLDQLDRUJDQL]DFMLSU]HZR]yZNROHMRZ\FKPRĪHVLĊRND]DüRJUDQLF]HQLH SRĞUHGQLH L EH]SRĞUHGQLH

(4) HPLVML JD]yZ FLHSODUQLDQ\FK Z W\P &2 GR DWPRVIHU\ > @ 2SW\PDOL]DFMD UXFKX SRFLąJyZ SRG NąWHP RJUDQLF]DQLD ]XĪ\FLD HQHUJLL DOHUyZQLHĪ WHFKQLF]Q\FKPRĪOLZRĞFLMHMRG]\VNXZSURFHVLHKDPRZDQLDZSLVXMHVLĊGRVNRQDOHZLGHĊ RJUDQLF]DQLD HQHUJRFKáRQQRĞFL WUDQVSRUWX NROHMRZHJR >@ QD NWyUą MHVW NáDG]LRQ\ V]F]H JyOQ\QDFLVNZSROLW\FH8QLL(XURSHMVNLHM . .26=7<:75$16325&,(.2/(-2:<0 . =$à2ĩ(1,$2*Ï/1(. 3RMĊFLH SRQRV]HQLD NRV]WyZ Z ZLĊNV]RĞFL SU]\SDGNyZ ZLąĪH VLĊ EH]SRĞUHGQLR ]SHZQą ZLHONRĞFLąĞURGNyZSLHQLĊĪQ\FKF]ĊVWRZ\QLNDMąFą]IL]\F]QHJREąGĨQDWXUDOQHJR]XĪ\FLH ĞURGNyZWUZDá\FK&]ĊVWRXWRĪVDPLDQHMHVWUyZQLHĪ]FHQą]DXVáXJĊOXERSáDFDQLHPSUDF\ OXG]NLHMZFHOXX]\VNDQLD]DPLHU]RQ\FKNRU]\ĞFL3U]HGVWDZLRQHXMĊFLHMHVWMHGQDNPRFQR ]DZĊĪRQH L QLH RGGDMH Z SHáQL DVSHNWX NRV]WyZ WUDQVSRUWX NROHMRZHJR DRJUDQLF]D VLĊ MHG\QLH GRRNUHĞORQHM MHGQRVWNL SU]HGVLĊELRUVWZD L MHM NRV]WyZ ZáDVQ\FK : SU]\SDGNX NRV]WyZ WUDQVSRUWX ]DUyZQR NROHMRZHJR GURJRZHJR ORWQLF]HJR MDN L LQQ\FK JDáĊ]L

(5) .

(6) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . QDOHĪ\ ]D]QDF]\ü ĪHLVWQLHMą NRV]W\ GRGDWNRZH REFLąĪDMąFH LQQH MHGQRVWNL RUJDQL]DF\MQH L VSRáHF]QH QLH]ZLą]DQH EH]SRĞUHGQLR ] SU]HGVLĊELRUVWZDPL NROHMRZ\PL 0RĪQD ]DWHP Z\UyĪQLüGZLHSRGVWDZRZHJUXS\NRV]WyZ NRV]W\ZHZQĊWU]QHZDVSHNFLHIXQNFMRQRZDQLDSU]HGVLĊELRUVWZDWUDQVSRUWX NROHMRZHJR NRV]W\]HZQĊWU]QHRGZRáXMąFHVLĊGRMHGQRVWHNQLH]ZLą]DQ\FKEH]SRĞUHGQLR] WUDQVSRUWHPNROHMRZ\PQDWRPLDVWSRQRV]RQ\PSU]H]RWRF]HQLHOXERJyá VSRáHF]HĔVWZD 3RG]LDáNRV]WyZZWUDQVSRUFLHNROHMRZ\PSU]HGVWDZLDU\VXQHNQDWRPLDVWZGDOV]HM F]ĊĞFL DUW\NXáXJáyZQą XZDJĊ VNXSLRQR QD NRV]WDFK ZHZQĊWU]\FK EH]SRĞUHGQLR SRQRV]RQ\FK SU]H] SU]HGVLĊELRUVWZR NROHMRZH NWyUH PRĪQD RJUDQLF]\ü SRSU]H] RGSRZLHGQLąRUJDQL]DFMĊUXFKXNROHMRZHJR. 5\V6WUXNWXUDNRV]WyZWUDQVSRUWXNROHMRZHJR & ' [26]. . . :ĞUyGNRV]WyZZáDVQ\FKSU]HGVLĊELRUVWZPRĪQDGRGDWNRZRZ\UyĪQLü NRV]W\VWDáHNWyUHVąSRQRV]RQHQLH]DOHĪQLHRGSURZDG]HQLDZGDQ\PRNUHVLH G]LDáDOQRĞFLWUDQVSRUWRZHMLPRJąE\ü]ZLą]DQHQS]OHDVLQJLHPĞURGNyZWUZDá\FK NRV]W\]PLHQQHXOHJDMąFH]ZLĊNV]HQLXOXE]PQLHMV]HQLXZ]DOHĪQRĞFL RGLQWHQV\ZQRĞFLRUD]RUJDQL]DFMLG]LDáDOQRĞFLSU]HZR]RZHMLPRJąE\üQLPLQD SU]\NáDGNRV]W\]XĪ\FLDHQHUJLL>@ . .26=7'267ĉ38'2,1)5$6758.785<.2/(-2:(-. %DUG]R ZDĪQ\P HOHPHQWHP ZSá\ZDMąF\P QD FHQ\ XVáXJ Z WUDQVSRUFLH NROHMRZ\P VąNRV]W\GRVWĊSXGRLQIUDVWUXNWXU\:3ROVFHJáyZQ\P]DU]ąGFąLQIUDVWUXNWXU\NROHMRZHM Vą3.33ROVNLH/LQLH.ROHMRZH6$ 3.33/.6$

(7) NWyUHRGSRZLDGDMąPLĊG]\LQQ\PL.

(8) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. . ]D RSUDFRZ\ZDQLH RUD] DNWXDOL]RZDQLH UR]NáDGyZ MD]G\ RUD] XWU]\PDQLH GREUHM MDNRĞFL SDĔVWZRZHMLQIUDVWUXNWXU\NROHMRZHM-DNR]DU]ąGFDSDĔVWZRZHJRPLHQLD3.33/.6$ PDRERZLą]HNXVWDOHQLD VWDZHN ]D XĪ\WNRZDQLH LQIUDVWUXNWXU\SU]H]SU]HZRĨQLNyZNROH MRZ\FK.RV]W\GRVWĊSXGRLQIUDVWUXNWXU\VąXVWDODQHZRSDUFLXRSU]HSLV\8VWDZ\]GQLD PDUFD U R 7UDQVSRUFLH .ROHMRZ\P ']8 ] U QU SR] ]SyĨQLHMV]\PL]PLDQDPL

(9) RUD]5R]SRU]ąG]HQLH0LQLVWUD,QIUDVWUXNWXU\]OXWHJRU Z6SUDZLH:DUXQNyZ'RVWĊSXL.RU]\VWDQLD],QIUDVWUXNWXU\.ROHMRZHM ']8]U QUSR]

(10) >@ $NWXDOQ\Z\ND]VWDZHNMHGQRVWNRZ\FKRSáDW]DNRU]\VWDQLH]LQIUDVWUXNWXU\NROHMRZHM ]DU]ąG]DQHM SU]H] 3.3 3/. 6$ RERZLą]XMąF\ RG JUXGQLD URNX ]DZLHUD WDNLH SR]\FMHMDN>@ VWDZNLMHGQRVWNRZHRSáDW\SRGVWDZRZHM VWDZNLMHGQRVWNRZH RSáDW\ SRGVWDZRZHM ]D PLQLPDOQ\ GRVWĊS GRLQIUDVWUXNWXU\ NROHMRZHMZ\UDĪRQHZ]áSRFNP VWDZNL MHGQRVWNRZH RSáDW\ SRGVWDZRZHM ]D GRVWĊS GR XU]ąG]HĔ ]ZLą]DQ\FK ]REVáXJąSRFLąJyZNWyU\PLVąXU]ąG]HQLD]DRSDWU]HQLDZSDOLZR>]áNPSU]H MD]GX@ VWDFMH L SU]\VWDQNL >]áZDJRQ OXE ]áSRVWyM WHUPLQDOH WRZDURZH >]áNP SU]HMD]GX@ JyUNL UR]U]ąGRZH >]áUR]U]ąG]RQ\ZDJRQ@ XU]ąG]HQLD GR IRUPRZD QLDVNáDGyZSRFLąJyZ>]áSRFLąJ@WRU\SRVWRMRZHRUD]WRU\SU]\UDPSDFKLSOD FDFKáDGXQNRZH>]áJRG]WRU@ VWDZNL MHGQRVWNRZH RSáDW GRGDWNRZ\FK GR NWyU\FK ]DOLF]D VLĊ XG]LHODQLH SR PRF\ ZSURZDG]HQLX SRFLąJyZ QDG]Z\F]DMQ\FK GRVWDUF]DQLH LQIRUPDFML X]X SHáQLDMąF\FKRSU]HMHĨG]LHSRFLąJXSU]\G]LHODQLHLSU]\JRWRZDQLHWUDV\SRFLąJX SR]D URF]Q\P UR]NáDGHP MD]G\ XGRVWĊSQLDQLH UHJXODPLQX RUD] Z\ND]X VWDFML NROHMRZ\FK L SXQNWyZ KDQGORZ\FK Z IRUPLH Z\GUXNX D WDNĪH XGRVWĊSQLDQLH Z\FLąJyZ ] UHJXODPLQyZ L LQQ\FK GRNXPHQWyZ Z\PDJDMąF\FK SRQLHVLHQLD NRV]WyZSU]H]3.33/.6$ :DUWR ]ZUyFLü XZDJĊ ĪH NRV]W GRVWĊSX GR OLQLL NROHMRZ\FK QD NWyU\FK Vą GRVWĊSQH XU]ąG]HQLDWUDNFMLHOHNWU\F]QHMMHVWZ\ĪV]\ĞUHGQLRRRN Z]DOHĪQRĞFLRGNDWHJRULL OLQLL

(11) >@ . .26=7=8ĩ<&,$(1(5*,,. : WUDQVSRUFLH NROHMRZ\P GR ]DVLODQLD SRMD]GyZ Vą REHFQLH Z\NRU]\VW\ZDQH GZD SRGVWDZRZH URG]DMH WUDNFML VSDOLQRZD RUD] HOHNWU\F]QD 3RQLHZDĪ FKDUDNWHU\VW\ND SRUyZQDZF]D W\FK GZyFK UyĪQ\FK WUDNFML Z\PDJD GRGDWNRZR GRJáĊEQHM DQDOL]\ ZDUW\NXOHVNXSLRQRVLĊW\ONRQD]DVLODQLXHQHUJLąHOHNWU\F]QąLNRV]WDPL]QLą]ZLą]DQ\PL *áyZQ\P SRGPLRWHP Z\VSHFMDOL]RZDQ\P Z GRVWDUF]DQLX HQHUJLL WUDNF\MQHM LQLHWUDNF\MQHM QD SROVNLHM VLHFL NROHMRZHM MHVW 3.3 (QHUJHW\ND 6$ 'R MHM JáyZQ\FK ]DGDĔ QDOHĪą REUyW L G\VWU\EXFMD HQHUJL HOHNWU\F]QHM RUD] ĞZLDGF]HQLH XVáXJ HQHUJRHOHNWU\F]Q\FKGRNWyU\FKPRĪQD]DOLF]\üF]\QQRĞFLXWU]\PDQLDPRGHUQL]DFMLRUD] RGWZDU]DQLD XU]ąG]HĔ WUDNF\MQ\FK >@ 6]F]HJyáRZH ]DVDG\ G\VWU\EXFMLL VSRVREX UR]OLF]DQLD L NRV]W\ MHGQRVWNRZH HQHUJLL WUDNF\MQHM ]RVWDá\ SU]HGVWDZLRQH Z 7DU\ILH GOD.

(12) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . HQHUJLLHOHNWU\F]QHM>@ 'RQLHGDZQDMHG\Q\PV\VWHPHPUR]OLF]HQLRZ\PQD3.3E\áV\VWHPU\F]DáWRZ\F]\OL XPRZQDRSáDWD]DXVáXJĊZ\OLF]DQDQDSRGVWDZLHVWRVRZQ\FKDOJRU\WPyZX]DOHĪQLRQ\FK RGZLHONRĞFLSU]HZR]yZ1LHZSá\QĊáRWRSR]\W\ZQLHQDVWRVRZDQLHHQHUJRRV]F]ĊGQ\FK WHFKQRORJLL ']LĊNL XZROQLHQLX U\QNX HQHUJHW\NL WUDNF\MQHM QD NROHL RUD] ZSURZD G]HQLX WHFKQRORJLL XPRĪOLZLDMąF\FK PLHU]HQLH U]HF]\ZLVWHJR]XĪ\FLD HQHUJLL SU]H] SRMD]G\VWDáRVLĊPRĪOLZHVWRVRZDQLHNRU]\VWQLHMV]HJRGODSU]HZRĨQLNyZNRU]\VWDMąF\FK ]HQHUJRRV]F]ĊGQ\FKWHFKQRORJLLUR]OLF]HQLD]DHQHUJLĊU]HF]\ZLVWą:3ROVFH]DZLRGąFą VSyáNĊ ZUR]OLF]HQLX U]HF]\ZLVWHJR ]XĪ\FLD HQHUJLL HOHNWU\F]QHM QD FHOH WUDNF\MQH PRĪQD X]QDü.ROHMH0D]RZLHFNLH .0

(13) NWyUHNRU]\VWDMą]QLHJRRGURNX>@-DNZ\QLND ] WDEOLF\ MXĪ ZSLHUZV]\P URNX QRZHJR V\VWHPX UR]OLF]HQLD XGDáR VLĊ ]DRV]F]ĊG]Lü WHM VSyáFHPOQ]áZVWRVXQNXGRURNXSRSU]HG]DMąFHJR 7DE =HVWDZLHQLHSRUyZQDZF]HNRV]WyZ]XĪ\FLDHQHUJLLWUDNF\MQHMZ.ROHMDFK0D]RZLHFNLFK SU]\UR]OLF]HQLXU\F]DáWRZ\PLOLF]QLNRZ\P 3UDFDSU]HZR]RZD (QHUJLDUR]OLF]RQD .RV]WHQHUJLL &HQDMHGQRVWNRZD >POQSRFNP@ >POQN:K@ >POQ]á@ HQHUJLL>]áN:K@. 7\SUR]OLF]HQLD. 5RN. 5R]OLF]HQLH U\F]DáWRZH. . . . . . . . . . . . . . . . 5R]OLF]HQLH OLF]QLNRZH. & 'opracowanie [21]. :NRQWHNĞFLHRSW\PDOL]DFMLNRV]WyZHQHUJLLWUDNF\MQHMZSU]HGVLĊELRUVWZLHNROHMRZ\P W\ONR UR]OLF]HQLH OLF]QLNRZH WDEOLFD

(14) PD ILQDQVRZH X]DVDGQLHQLH 3R]ZDOD RQR QD SHáQH Z\NRU]\VWDQLH QDMQRZV]HJR WDERUX WHFKQRORJLL RUD] UR]ZLą]DĔ RUJDQL]DF\MQ\FK RJUDQLF]DMąF\FK ]XĪ\FLH HQHUJLL HOHNWU\F]QHM SU]\ RG]ZLHUFLHGOHQLX LFK VWRVRZDQLD ZQLĪV]\FKNRV]WDFK. 25*$1,=$&-$58&+8 .2/(-2:(*2$.26=7<=8ĩ<&,$(1(5*,, (/(.75<&=1(- ,6727$237<0$/,=$&-,:,(/2.5<7(5,$/1(- $QDOL]XMąFSURFHVSRGHMPRZDQLDGHF\]MLPRĪQD]DXZDĪ\üĪHSU]\Z\ERU]HRSW\PDOQ\FK GHF\]MLGHF\GHQWSRVáXJXMHVLĊQDRJyáQLHMHGQ\POHF]ZLHORPDNU\WHULDPLMHGQRF]HĞQLH 8Z]JOĊGQLDMąF Z ]DJDGQLHQLDFK RSW\PDOL]DFML ZLHORNU\WHULDOQHM IXQNFMĊ NU\WHULXP.

(15) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. ]áRĪRQą ] ZLHOX F]ąVWNRZ\FK IXQNFML FHOX PRĪQD PRGHORZDü U]HF]\ZLVWH SUREOHP\ WUDQVSRUWRZHNWyUHXZ]JOĊGQLDMąUyĪQHFHOH>@ 3RGVWDZRZD WUXGQRĞü Z SUDNW\F]QHM UHDOL]DFML NRQFHSFML XZ]JOĊGQLDMąFHM ZLHOH NU\WHULyZF]ąVWNRZ\FK]DUyZQRZEDGDQLDFKQDXNRZ\FKMDNLG]LDáDOQRĞFLJRVSRGDUF]HM SROHJD QD W\P ĪH W\ONR Z Z\MąWNRZ\FK SU]\SDGNDFK PDP\ GR F]\QLHQLD ] GHF\]Mą ]DSHZQLDMąFą Z]DMHPQą ]JRGQRĞü HNVWUHPDOQ\FK ZDUWRĞFL F]ąVWNRZ\FK IXQNFML FHOX =UHJXá\ XZ]JOĊGQLHQLH Z PRGHOX ZLĊFHM QLĪ MHGQHM IXQNFML FHOX QLH SURZDG]L GRMHGQR]QDF]QLH QDMOHSV]HJR UR]ZLą]DQLD WM WDNLHJR NWyUH ]DSHZQLDáRE\ RSWLPXP GOD ZV]\VWNLFK F]ąVWNRZ\FK NU\WHULyZ RSW\PDOL]DFML MHGQRF]HĞQLH :DULDQW RSW\PDOQ\ ]SXQNWX ZLG]HQLD NU\WHULXP F]ąVWNRZHJR PRĪH E\ü JRUV]\ ] SXQNWX ZLG]HQLD LQQ\FK NU\WHULyZ FR SU]\ LFK F]ĊVWR UyZQRU]ĊGQ\P FKDUDNWHU]H XWUXGQLD GRNRQ\ZDQLH Z\ERUX UR]ZLą]DQLDRSW\PDOQHJR 2JyOQLH ]DGDQLH RSW\PDOL]DFML ZLHORNU\WHULDOQHM PRĪQD VIRUPXáRZDü QDVWĊSXMąFR > @ SU]\VSHáQLHQLXRJUDQLF]HĔ

(16) . ; ; dop 1DOHĪ\Z\]QDF]\üZHNWRU]PLHQQ\FKGHF\]\MQ\FK ; g ;

(17). ; GODNWyUHJR. extr g n ;

(18) n k.

(19) . JG]LH ;±UR]ZLą]DQLH]DGDQLDRSW\PDOL]DF\MQHJR ;dop±]ELyUUR]ZLą]DĔGRSXV]F]DOQ\FK ; ± ZHNWRUUR]ZLą]DĔ k±OLF]EDIXQNFMLFHOX. :LHORNU\WHULDOQHSUREOHP\GHF\]\MQHPRĪQDSRG]LHOLüQDF]WHU\JUXS\>@ SUREOHP\ZLHORNU\WHULDOQHJRZ\ERUXZNWyU\FKSUREOHPGHF\]\MQ\SROHJDQDRNUH ĞOHQLXMHGQHJRZDULDQWXVSRĞUyG]ELRUXZDULDQWyZ SUREOHP\ ZLHORNU\WHULDOQHJR SRU]ąGNRZDQLD Z NWyU\FK SUREOHP GHF\]\MQ\ SROHJD QDXSRU]ąGNRZDQLX]ELRUXZDULDQWyZ SUREOHP\ZLHORNU\WHULDOQHMNODV\ILNDFMLSROHJDMąFHQD]GHILQLRZDQLXNODVRUD]SU]\ G]LHOHQLXSRV]F]HJyOQ\FKZDULDQWyZGRW\FKNODV SUREOHP\ZLHORNU\WHULDOQHJRRSLVX :LHORNU\WHULDOQH SUREOHP\ RSW\PDOL]DF\MQH FKDUDNWHU\]XMą VLĊ GZRPD SRGVWDZRZ\PL HOHPHQWDPLWMRSLVHP]ELRUXUR]ZLą]DĔGRSXV]F]DOQ\FKRUD]]ELRUHPIXQNFML NU\WHULyZ

(20) RGZ]RURZXMąF\FK]ELyUUR]ZLą]DĔZ]ELyURFHQMDNRĞFL QDRJyáZ]ELyUOLF]EU]HF]\ZL VW\FK

(21) :]DOHĪQRĞFLRGSRVWDFLDQDOLW\F]QHMSRV]F]HJyOQ\FKIXQNFMLNU\WHULXPRUD]RJUD QLF]HĔ PRĪQD PyZLü R UyĪQ\FK URG]DMDFK ZLHORNU\WHULDOQHJR SURJUDPRZDQLD PDWHPD W\F]QHJR =DLQWHUHVRZDQLH PHWRGDPL ZLHORNU\WHULDOQHJR SURJUDPRZDQLD Z\QLND SU]HGH ZV]\VW NLP ] LFK SU]\GDWQRĞFL SUDNW\F]QHM 3R]ZDODMą RQH XZ]JOĊGQLü ZLHOH SU]HFLZVWDZQ\FK F]ĊVWRSXQNWyZZLG]HQLD NU\WHULyZ

(22) 1LHMHVWWREH]]QDF]HQLDZSU]\SDGNXSRGHMPRZD.

(23) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . QLDGHF\]MLRGQRĞQLHSU]HGVLĊZ]LĊüLQZHVW\F\MQ\FK]ZáDV]F]DGRW\F]ąF\FKUR]ZRMXLQIUD VWUXNWXU\V\VWHPXWUDQVSRUWRZHJRF]\]PLDQ\RUJDQL]DFMLUXFKXQDVLHFLQSNROHMRZHM :LHORNU\WHULDOQHSUREOHP\GHF\]\MQHRSLHUDMąVLĊQDGZyFKSRGVWDZRZ\FKSRVWXODWDFK WM SRVWXODW GRPLQDFML±MHĪHOL PDP\ GZLH SURSR]\FMH GRSXV]F]DOQ\FK UR]ZLą]DĔ LX]QDMHP\ ĪH MHGQD ] QLFK MHVW SU]\QDMPQLHM ]H Z]JOĊGX QD MHGQR NU\WHULXP NR U]\VWQLHMV]DQLĪGUXJDDSRGNDĪG\PLQQ\PZ]JOĊGHPQLHMHVWRGQLHMJRUV]DWRSR ZLQQLĞP\SLHUZV]ą]QLFKX]QDü]DOHSV]ą SRVWXODWSU]HFKRGQLRĞFLGRPLQDFML SU]\VSRVRELRQ\ ] WHRULL RF]HNLZDQHM XĪ\WHF]QR ĞFL>@

(24) ±MHĪHOLZZ\QLNXSRUyZQDĔX]QDP\ĪHZDULDQW$MHVWOHSV]\QLĪ%D]NR OHL%]DOHSV]\QLĪ&WRNRQVHNZHQWQLHSRZLQQLĞP\X]QDüĪHZDULDQW$MHVWOHSV]\ QLĪ& 3RZ\ĪV]HR]QDF]DNRQLHF]QRĞüSU]HVWU]HJDQLDZRSW\PDOL]DFMLZLHORNU\WHULDOQHMUD]SU]\ MĊWHJRV\VWHPXZDUWRĞFLRZDQLD : GDOV]HM F]ĊĞFL EDGDĔ ]RVWDQą SU]HDQDOL]RZDQH WDNLH JUXS\ NU\WHULyZ F]ąVWNRZ\FK MDN PLQLPDOL]DFMDF]DVXSRMHG\QF]HJRSU]HMD]GX PLQLPDOL]DFMD F]DVyZ SU]HMD]GyZ ZV]\VWNLFK SRFLąJyZ SRUXV]DMąF\FK VLĊ SRDQDOL]RZDQ\PRGFLQNX]XZ]JOĊGQLHQLHPLFKZDJ ZDĪQRĞFL

(25) PLQLPDOL]DFMD ]XĪ\FLD HQHUJLL WUDNF\MQHM UyZQR]QDF]QD ] PLQLPDOL]DFMą NRV]WyZ HQHUJLLWUDNF\MQHM PDNV\PDOL]DFMDZLHONRĞFLHQHUJLLRG]\VNDQHM]SURFHVXKDPRZDQLDHQHUJLL PLQLPDOL]DFMD F]DVyZ RF]HNLZDQLD QD SU]HVLDGNĊ SU]\ SU]HMD]GDFK Z\PDJDMąF\FK VNRPXQLNRZDQLD. 675$7(*,(-$='<237<0$/1(- 3RGVWDZRZH ]DáRĪHQLD GOD HQHUJRRV]F]ĊGQHM MD]G\ ]RVWDá\ VIRUPXáRZDQR Z OLWHUDWXU]H SU]HGPLRWX MXĪ Z ODWDFK V]HĞüG]LHVLąW\FK ;; ZLHNX>@ D QDVWĊSQH SRGDQR Z ODWDFK RVLHPG]LHVLąW\FK PLĊG]\ LQQ\PL Z > @ : FHOX QDMHIHNW\ZQLHMV]HJR HQHUJHW\F]QLH SURZDG]HQLDSRMD]GXV]\QRZHJR]DVLODQHJRWUDNFMąHOHNWU\F]QąQDOHĪ\ SU]HSURZDG]LüUR]UXFKSRMD]GX]QDMZ\ĪV]\PGRSXV]F]DOQ\PSU]\VSLHV]HQLHPF]\ OLQDVW\NXSU]\F]HSQRĞFLRĞURGNyZNRáR±V]\QDDĪGRX]\VNDQLD]DNáDGDQHMSUĊG NRĞFLHNVSORDWDF\MQHM PRĪOLZLHMDNQDMGáXĪHMNRQW\QXRZDüMD]GĊQDWDN ]ZDQ\P Z\ELHJX WR ]QDF]\ MHĨ G]LHVLáąUR]SĊGXEH]SRELHUDQLDHQHUJLL]VLHFLWUDNF\MQHM SU]HSURZDG]Lü PRĪOLZLH MDN QDMSyĨQLHM KDPRZDQLH ] Z\NRU]\VWDQLHP MDN QDMZLĊN V]HMZDUWRĞFLRSyĨQLHQLD 3RZ\ĪV]H ]DVDG\ UyĪQLą VLĊRG SRVWXORZDQ\FK ]DOHFHĔ W]Z HFR±GULYLQJX SU]\ SURZDG]HQLX SRMD]GyZ JáyZQLH GURJRZ\FK

(26) ]DVLODQ\FK VLOQLNDPL VSDOLQRZ\PL : W\P SU]\SDGNX Z FHOX REQLĪHQLD ]XĪ\FLD SDOLZD ZVND]DQH MHVW V]\ENLH DOH L Sá\QQH SU]\VSLHV]DQLH ZUD] ]H ]PLDQą ELHJyZ QD Z\ĪV]H 8QLND VLĊ W\P VDP\P ZFKRG]HQLD.

(27) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. QDZ\VRNLHREURW\VLOQLNDDFR]DW\PLG]LHX]\VNLZDQLDZ\VRNLFKPRF\L]ZLĊNV]RQHJR ]XĪ\FLD SDOLZD +DPRZDQLH UyZQLHĪ RGPLHQQLH QLĪ GOD HOHNWU\F]Q\FK SRMD]GyZ WUDNF\MQ\FK QDVWĊSXMH VWRSQLRZR SRSU]H] UHGXNRZDQLH ELHJyZ L GRSLHUR ZNRĔFRZ\P HWDSLHMD]G\áDJRGQH]DWU]\PDQLHSRMD]GX>@. 5\V=HVWDZLHQLHSRUyZQDZF]HY W

(28) RUD]3 W

(29) GODGZyFKUyĪQ\FKW\SyZSURZDG]HQLDHOHNWU\F] QHJRSRMD]GXWUDNF\MQHJR & ' *30]. 1D U\VXQNX SU]HGVWDZLRQR SU]\EOLĪRQH ]HVWDZLHQLH SRUyZQDZF]H GZyFK UyĪQ\FK VSRVREyZ SURZDG]HQLD HOHNWU\F]QHJR SRMD]GX WUDNF\MQHJR ]D SRPRFą IXQNFML Y W

(30) RUD] 3 W

(31) ,OXVWUXMH RQ MHGQR]QDF]QLH ĪHQDUHDOL]DFMĊ SU]HMD]GX ] Z\NRU]\VWDQLHP PDNV\PDOQHJRSU]\VSLHV]HQLDUR]UXFKX DUPD[

(32) RUD]PDNV\PDOQHJRRSyĨQLHQLDKDPRZDQLD DKPD[

(33) SRWU]HEQD MHVW PQLHMV]D LORĞü HOHNWU\F]QHM HQHUJLL WUDNF\MQHM QLĪ SU]\ SU]HMHĨG]LH ³%´ $OJRU\WP RSW\PDOL]DFML NRV]WyZ HQHUJLL GOD SU]HMD]GX SRMHG\QF]HJR SRFLąJX ]RVWDá SU]HGVWDZLRQ\ MXĪ PLĊG]\ LQQ\PL Z SUDF\ >@ $XWRU]\ WHM SUDF\ ]DSURSRQRZDOL DQDOL]Ċ NRV]WyZ HQHUJLL WUDNF\MQHM Z F]DVLH U]HF]\ZLVW\P SRGF]DV SU]HMD]GX RUD] RSW\PDOL]DFMĊ NLHURZDQLD SRMD]GHP ] XZ]JOĊGQLHQLHP GRGDWNRZR ZDJL ZDĪQRĞFL

(34) NU\WHULXP F]DVX SU]HMD]GX $OJRU\WP WHQ RGSRZLHGQLR SU]HOLF]D SDUDPHWU\ HQHUJHW\F]QH SU]HMD]GX LDQDOL]XMHF]\QDOHĪ\ZSURZDG]Lü]PLDQ\ZSURZDG]HQLXSRMD]GXGODRJUDQLF]HQLD]XĪ\ FLDHQHUJLL 'R ZGURĪHQLD VWUDWHJLL MD]G\ RSW\PDOQHM Z FHOX REQLĪHQLD NRV]WyZ HQHUJLL ]DUyZQR WUDNF\MQHMMDNLQLHWUDNF\MQHMGąĪą.0:GURĪRQ\ SURMHNW (FR'ULYLQJ GDMH PRĪOLZRĞFL HIHNW\ZQHJR ]DU]ąG]DQLD HQHUJLą SU]\ RJU]HZDQLX SRMD]GX DOH SU]HGH ZV]\VWNLP SU]\ RGSRZLHGQLP SURZDG]HQLX SRMD]GX 6NáDG\ WUDNF\MQH Z\SRVDĪRQH Z RGSRZLHG]QLH OLF]QLNL ]ELHUDMą GDQH QD WHPDW LORĞFL SRELHUDQHM HQHUJLL RUD] FKDUDNWHU\VW\NL MHM ]XĪ\FLD 1DVWĊSQLH Vą RQH DQDOL]RZDQH LSRUyZQ\ZDQH ] LQQ\PL SU]HMD]GDPL 0RĪOLZD MHVW G]LĊNL.

(35) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . WHPX RSW\PDOL]DFMD RUJDQL]DFML UXFKX SRMD]GyZ .0 SRSU]H] SURZDG]HQLH V]NROHĔ LLQVWUXNWDĪ\GODPDV]\QLVWyZPDMąF\FKQDFHOXSRSUDZĊHIHNW\ZQRĞFLHQHUJRRV]F]ĊGQHJR SURZDG]HQLDSRMD]GyZ>@. 675$7(*,$:<0,$1<(1(5*,,0,ĉ'=<32-$='$0, 75$.&<-1<0, (IHNW\ZQH Z\NRU]\VWDQLH HQHUJLL HOHNWU\F]QHM SRFKRG]ąFHM ] UHNXSHUDFML PRĪQD ĞFLĞOH SRZLą]Dü ]]DU]ąG]DQLHP UXFKHPZ WUDQVSRUFLH NROHMRZ\P D ĞFLĞOHM XMPXMąF ] SURFHVHP WZRU]HQLD UR]NáDGyZ MD]G\ :DĪQH MHVW WR Z SU]\SDGNXJG\ RG]\VNLZDQD HQHUJLD MHVW Z\PLHQLDQDEH]SRĞUHGQLRPLĊG]\UyĪQ\PLSRMD]GDPLQDWUDVLH5R]ZLą]DQLHWRMHVWRW\OH NRU]\VWQHZ]JOĊGHPZ\NRU]\VWDQLD]DVREQLNyZHQHUJLL SRNáDGRZ\FKOXEVWDFMRQDUQ\FK

(36) ĪH QLH Z\PDJD GRGDWNRZ\FK QDNáDGyZ ILQDQVRZ\FK QDVSHFMDOLVW\F]QH XU]ąG]HQLD LLQIUDVWUXNWXUĊ : SUDNW\FH ZLąĪH VLĊ RQR MHG\QLH ] NRQLHF]QRĞFLą RGSRZLHGQLHJR VNRRUG\QRZDQLD UXFKX SRMD]GyZ QD GDQ\P RGFLQNX ]DVLODQLD WDN DE\ PRĪOLZD E\áD NRRSHUDFMDPLĊG]\SURFHVDPLSRELHUDQLDLRGGDZDQLDHQHUJLL2GSRZLHGQLHVNRUHORZDQLH SRMD]GyZ QD VLHFL Z WDNL VSRVyE ĪHE\ HQHUJLD RGGDZDQD Z SURFHVLH KDPRZDQLD E\áD ZFDáRĞFL Z\NRU]\VW\ZDQD QD SRWU]HE\ UR]UXFKX LQQ\FK SRMD]GyZ MHVW ZáDĞFLZLH QLHPRĪOLZH >@ 1DOHĪ\ MHGQDN ]DXZDĪ\ü ĪH ]PLDQD UR]NáDGX MD]G\ GODSRV]F]HJyOQ\FK SU]HMD]GyZRRNRáRVHNXQGPRĪH]PLHQLüELODQVHQHUJHW\F]Q\REOLVNR %LRUąF SRZ\ĪV]H SRG XZDJĊ QDOHĪ\ VWZLHUG]Lü ĪH Z SU]\V]á\P DOJRU\WPLH RSW\PDOL]DFML UXFKX NROHMRZHJR QDOHĪ\ XZ]JOĊGQLü SDUDPHWU RNUHĞODMąF\ VWRSLHĔ Z\NRU]\VWDQLD HQHUJLL SRFKRG]ąFHM ]UHNXSHUDFML Z ZDULDQFLH MHM Z\PLDQ\ PLĊG]\ SRMD]GDPL5R]ZLą]DQLHWRPD]DVWRVRZDQLHJáyZQLHZUXFKXPLHMVNLPLSRGPLHMVNLPMDN UyZQLHĪ QD JáyZQ\FK VWDFMDFK ZĊ]áRZ\FK :\QLND WR ] GXĪHM F]ĊVWRWOLZRĞFL NXUVRZDQLD SRFLąJyZDFR]DW\PLG]LHPQRJRĞFLSRZWDU]DQ\FKF\NOLUR]UXFK±KDPRZDQLH:WDNLFK V\WXDFMDFKQDZHW]GDZDáRE\VLĊPDáD]PLDQDZUR]NáDG]LHMD]G\PRĪHSU]\QLHĞü]QDF]QH RV]F]ĊGQRĞFL Z SRVWDFL PQLHMV]HJR ]XĪ\FLD HQHUJLL HOHNWU\F]QHM QD FHOH WUDNF\MQH 3U]\NáDGNRU]\VWQHMV\WXDFMLGODZ\PLDQ\HQHUJLLPLĊG]\SRMD]GDPL]RVWDáSU]HGVWDZLRQ\ QDZ\NUHVLHUXFKX U\V

(37) .

(38) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. 5\V2EV]DU\PRĪOLZHMZ\PLDQ\HQHUJLLPLĊG]\SRMD]GDPL & ' . 3U]\NáDGRZD V\WXDFMDNRRUG\QDFML UR]NáDGRZHM PLĊG]\ KDPXMąF\PL LUXV]DMąF\PL SRMD]GDPLWDNDE\E\áPRĪOLZ\WUDQVIHUHQHUJLLPLĊG]\QLPLLVWQLHMHQDOLQLDFK6.0RUD] PHWUD U\V

(39) :Sá\ZDMąQDWRXZDUXQNRZDQLDWDNLHMDN OLF]QRĞüF\NOLKDPRZDQLDLUR]UXFKX]ZLą]DQD]GXĪ\PQDWĊĪHQLHPUXFKXQDOLQLL VWRVRZDQLH]D]Z\F]DMWHJRVDPHJRURG]DMXWDERUX F\NOLF]QRĞüUR]NáDGXMD]G\ QLHZLHONLH RGOHJáRĞFL PLĊG]\ SRMD]GDPL QD VLHFL D FR ]D W\P LG]LH QLVNLH VWUDW\ WUDQVIHUXHQHUJLLPLĊG]\SRMD]GDPL VWRVXQNRZRQLHVNRPSOLNRZDQ\XNáDGWRURZ\ QD SURVW\FK OLQLRZ\FK XNáDGDFK WRURZ\FK EUDN NRQLHF]QRĞFL VNRPXQLNRZDQLD SRMD]GyZSRUXV]DMąF\FKVLĊZSU]HFLZQ\FKNLHUXQNDFK. 5\V6FKHPDWNRRUG\QDFMLUR]NáDGRZHMF\NOLKDPRZDQLDLUR]UXFKXQDREV]DUDFKVWDF\MQ\FK OLQLLSRGPLHMVNLHM & ' .

(40) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . 0RĪOLZHMHVW]DWHPZSURZDG]HQLDGRDOJRU\WPXZVSRPDJDMąFHJRXNáDGDQLHUR]NáDGyZ MD]G\ GRGDWNRZ\FK RJUDQLF]HĔ WDN DE\ F]DV UR]SRF]ĊFLD KDPRZDQLD SU]H] SRMD]G 3 U\V

(41) E\áPRĪOLZLHMDNQDMEDUG]LHM]EOLĪRQ\GRF]DVXUR]SRF]ĊFLDUR]UXFKXSU]H]SRMD]G 3 DQDORJLF]QLHGODSRMD]GyZ3L3

(42) 3RQDGWRZDUWRGRSXĞFLüV\WXDFMĊĪHQDREV]DU]H MHGQHM VWDFML QLH PXV]ą ]QDMGRZDü VLĊ MHGQRF]HĞQLH SRMD]G\ R SU]HFLZQ\FK NLHUXQDFK MD]G\ U\V

(43) 1DOHĪ\ ]DWHP XZ]JOĊGQLü V\WXDFMĊ ]SU]HDQDOL]RZDQLHP UXFKX QD FDá\P RGFLQNX ]DVLODQLD WDN DE\ RSW\PDOQH VNRRUG\QRZDQLH SURFHVyZ UR]UXFKX LKDPRZDQLD GRW\F]\áRQLHW\ONRZ\RGUĊEQLRQ\FKVWDFML:W\PSU]\SDGNXRSW\PDOQ\PUR]ZLą]DQLHP EĊG]LH]JUDQLHMHGQRF]HĞQLHWU]HFKSRMD]GyZ&]DVUR]SRF]ĊFLDUR]UXFKXSU]H]SRMD]G3 U\V

(44) SRZLQLHQE\üPRĪOLZLH]EOLĪRQ\GRF]DVXUR]SRF]ĊFLDKDPRZDQLD]DUyZQRSU]H] SRMD]G 3 MDN L 3 GąĪąF GR PDNV\PDOL]DFML Z\NRU]\VWDQLD HQHUJLL SRFKRG]ąFHM ]UHNXSHUDFML. 5\V6FKHPDWNRRUG\QDFMLUR]NáDGRZHMF\NOLKDPRZDQLDLUR]UXFKXQDFDá\PRGFLQNX]DVLOD QLDOLQLLSRGPLHMVNLHM & ' . .RU]\VWDQLH ] RSLVDQHM NRQFHSFML UR]NáDGRZHJR ]V\QFKURQL]RZDQLD KDPXMąF\FK LUXV]DMąF\FKSRMD]GyZMHVWRPDZLDQHZOLWHUDWXU]HJáyZQLHZNRQWHNĞFLHPHWUD>@ :H ZVND]DQ\FK SUDFDFK XGRZRGQLRQR PRĪOLZRĞü ]DRV]F]ĊG]HQLD SRQDG HQHUJLL FRGDMHZ\PLHUQHNRU]\ĞFL]DUyZQRHNRQRPLF]QHMDNLĞURGRZLVNRZH 'XĪR EDUG]LHM UR]EXGRZDQD V\WXDFMD EĊG]LH PLDáD PLHMVFH QD REV]DUDFK VWDFML ZĊ]áR Z\FK :\QLND WR ] EDUG]LHM UR]EXGRZDQHJR XNáDGX WRURZHJR UyĪQRURGQRĞFL REVáXJLZD QHJRWDERUX ZLĊNV]HM URWDFML UXFKX SRMD]GyZ DOH UyZQLHĪ ] NRQLHF]QRĞFL XZ]JOĊGQLHQLD LQWHJUDFMLUR]NáDGRZHMXPRĪOLZLDMąFHMSU]HVLDGNLSDVDĪHUyZ:W\PSU]\SDGNXRSW\PDOL ]DFMD NRV]WyZ ]XĪ\FLD HQHUJLL EĊG]LH ]DWHP PLDáD SRGU]ĊGQ\ DVSHNW ZVWRVXQNX GR LQWH JUDFMLSRV]F]HJyOQ\FKSRáąF]HĔ1DGU]ĊGQ\PNU\WHULXPRSW\PDOL]DFMLSR]RVWDQLHUyZQLHĪ F]DV SU]HMD]GX 3U]\ RJUDQLF]HQLDFK RPDZLDQHM VWUDWHJLL QDOHĪ\ UyZQLHĪ ZVSRPQLHü R DVSHNFLHWHFKQLF]Q\P SURMHNWRZDQLD LEXGRZ\ QDSRZLHWU]Q\FK OLQLL]DVLODMąF\FK JG]LH SU]ĊVáD L]RORZDQH OXE L]RODWRU\ VHNF\MQH ]QDMGXMą VLĊ QDMF]ĊĞFLHM QDRGFLQNDFK JG]LH SR FLąJLF\NOLF]QLHKDPXMą:SU]\SDGNXJG\ZVąVLHGQLFKVHNFMDFK]DVLODQLDEĊG]LHSDQRZD áRUyĪQHQDSLĊFLHSRMD]GSU]HMHĪGĪDMąF\SU]H]WDNLRGFLQHNL]RORZDQ\]SRERUHPOXERG GDZDQLHP HQHUJLL GR VLHFL PRĪH Z\WZRU]\ü áXN HOHNWU\F]Q\ SRPLĊG]\ RGELHUDNLHP DSU]HZRGHP]DVLODMąF\P3URZDG]LWRGRV]\EV]HMGHJUDGDFML]DUyZQRVLHFLWUDNF\MQHMMDN LRGELHUDNyZSUąGXSRMD]GyZWUDNF\MQ\FK>@.

(45) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. :1,26., 2SW\PDOL]DFMDRUJDQL]DFMLUXFKXQDNROHLPDQDFHOXZ\EyUQDNDĪG\PV]F]HEOXRUJDQL]D F\MQ\PQDMOHSV]HJR]PRĪOLZ\FKZDULDQWyZSU]\F]\P]DSXQNWFHQWUDOQ\FDáHJRSURFHVX RUJDQL]DFMLUXFKXPRĪQDSU]\MąüHWDSNRQVWUXNFMLUR]NáDGyZMD]G\SRFLąJyZĝOHG]ąFSUR FHVSRGHMPRZDQLDGHF\]MLQDOHĪ\]DXZDĪ\üĪHSU]\Z\ERU]HRSW\PDOQ\FKGHF\]MLGHF\ GHQWSRVáXJXMHVLĊQDRJyáSU]\QDMPQLHMNLONRPDNU\WHULDPLMHGQRF]HĞQLH3U]\RSW\PDOL ]DFMLRUJDQL]DFMLUXFKXNROHMRZHJRPRJąWRE\üPLQLPDOL]DFMDF]DVXSRMHG\QF]HJRSU]H MD]GXPLQLPDOL]DFMDF]DVyZSU]HMD]GyZZV]\VWNLFKSRMD]GyZSRUXV]DMąF\FKVLĊSRDQDOL ]RZDQ\P RGFLQNX ] XZ]JOĊGQLHQLHP ZDJ SRV]F]HJyOQ\FK SRáąF]HĔ PLQLPDOL]DFMD F]D VyZRF]HNLZDQLDQDSU]HVLDGNĊZSRáąF]HQLDFKZ\PDJDMąF\FKVNRPXQLNRZDQLDPLQLPD OL]DFMDRSyĨQLHĔLLFKSURSDJDFMLDWDNĪHPLQLPDOL]DFMDNRV]WyZZW\PW\FK]ZLą]DQ\FK ]HQHUJLąWUDNF\MQą 6DPSURFHVGąĪHQLDGRRJUDQLF]DQLD]XĪ\FLDHQHUJLLUyZQR]QDF]QHJR]RJUDQLF]HQLHP SRQRV]RQ\FKQDQLąNRV]WyZEĊG]LH]DVDGQ\MHG\QLHSU]\UR]OLF]DQLXOLF]QLNRZ\P]XĪ\ WHMHQHUJLL(QHUJRRV]F]ĊGQRĞüZRUJDQL]DFMLUXFKXNROHMRZHJRPRĪQDRVLąJQąüQLHW\ONR SRSU]H]VWRVRZDQLHMD]G\PRĪOLZLHHIHNW\ZQHMSRGZ]JOĊGHPHQHUJHW\F]Q\PDOHUyZQLHĪ SRSU]H]VWRVRZDQLHQRZRF]HVQ\FKWHFKQLNZ\PLDQ\HQHUJLLPLĊG]\SRMD]GDPLZSURFHVLH KDPRZDQLDUHNXSHUDF\MQHJR1LH]Z\NOHZDĪQHMHVWXZ]JOĊGQLHQLHPRĪOLZRĞFLW\FKSURFH VyZ MXĪ SU]\ NRQVWUXNFML UR]NáDGyZ MD]G\ D QLH MHG\QLH QD SR]LRPLH G]LDáDĔ ZHZQĊWU] Q\FKZSU]HGVLĊELRUVWZDFKWUDQVSRUWXNROHMRZHJR %LEOLRJUDILD . $OEUHFKW72HWWLFK6A new integrated approach to dynamic schedule synchronization and energy saving train control.&RPSXWHUVLQUDLOZD\V9,,,6RXWKDPSWRQ $PEUR]LDN7-DFKLPRZVNL 53\]D' 6]F]HSDĔVNL( Analysis of the traffic stream distribution in terms of identification of areas with the highest exhaust pollutioQ3ROLVK$FDGHP\RI6FLHQFHV$UFKLYHV RI7UDQVSRUW:DUV]DZDV $XHUEDFK 3 .XNOD : + 4 %5 w % !

(46)

(47) 7 =HV]\W\ 1DXNRZH 3ROLWHFKQLNL 3R]QDĔVNLHM2UJDQL]DFMDL=DU]ąG]DQLH3R]QDĔV %RFKDUQLNRY<9*RRGPDQ&-+LOOPDQVHQ65REHUWV&7RELDV$0Optimal driving strategy for traction energy saving. (OHFWULF 3RZHU $SSOLFDWLRQV %LUPLQJKDP V %U]R]RZVNL$#%7.XULHU.ROHMRZ\:DUV]DZDV (QJHOKDUGW - Problemy metodyczne kalkulacji stawek %

(48) 8

(49)

(50) 7 7HFKQLND7UDQVSRUWX6]\QRZHJRàyGĨV (XURSHDQ(QYLURQPHQW$JHQF\Adaptation of transport to climate change in Europe.(($ /X[HPERXUJ *DODV=1\NRZVNL,ĩyáNLHZVNL=Programowanie wielokryterialne.3:(:DUV]DZD *HUDHWV ) .URRQ / 6FKRHEHO $ :DJQHU ' HW DO Algorithmic Methods for Railway Optimization 6SULQJHU%HUOLQV *LHG\PLQ 2 celów a sterowanie optymalne. 3U]HJOąG 6WDW\VW\F]Q\WRPQU]:DUV]DZD *RáĊELRZVNL 3 -DF\QD 0 Wybrane problemy planowania ruchu kolejowego 3UDFH 1DXNRZH 3: 7UDQVSRUW:DUV]DZDV.

(51) :\EUDQH]DJDGQLHQLDRSW\PDOL]DFMLUXFKXNROHMRZHJRZFHOXPLQLPDOL]DFMLNRV]WyZ]XĪ\FLD. . *RQ]DOH]*LO$3DODFLQ5%DWW\33RZHOO-3Energy-efficient urban rail systems: strategies for an optimal management of regenerative braking energy.7UDQVSRUW5HVHDUFK$UHQD3DULV *XWHQEDXP-Modelowanie matematyczne systemów.3:1:DUV]DZDàyGĨ -DF\QD 0 Some aspects of multicriteria evaluation of traffic flow distribution in a multimodal transport corridor.3ROLVK$FDGHP\RI6FLHQFHV$UFKLYHVRI7UDQVSRUW:DUV]DZDV -DF\QD 0 Modelowanie i ocena systemów transportowych. 2ILF\QD :\GDZQLF]D 3: :DUV]DZD -DF\QD00HUNLV]-Proecological approach to modelling traffic organization in national transport system3ROLVK$FDGHP\RI6FLHQFHV$UFKLYHVRI7UDQVSRUW:DUV]DZDV -DF\QD0:DVLDN0/HZF]XN..áRGDZVNL0Simulation model of transport system of Poland as a tool for developing sustainable transport 3ROLVK $FDGHP\ RI 6FLHQFHV $UFKLYHV RI7UDQVSRUW :DUV]DZDV -DF\QD*RáGD,ĩDN-*RáĊELRZVNL3Models of traffic flow distribution for various scenarios of the development of proecological transport system 3ROLVK $FDGHP\ RI 6FLHQFHV $UFKLYHV RI7UDQVSRUW :DUV]DZDV -ĊGU\VD7Projekt Eco Driving - 985 7.RQIHUHQFMD7HOHNRPXQLNDFMD L,QIRUPDW\NDQD.ROHL:LVáD .DFSU]DN--0\VáHN3RGRVNL-Zasady trakcji elektrycznej:.Là:DUV]DZD .ROHMH0D]RZLHFNLH.06S]RRManagement Report.:DUV]DZD /XNDV]HZLF] 3 PhD Energy consumption and running time for trains 5R\DO ,QVWLWXWH RI7HFKQRORJ\6WRFNKROP 0HUNLV]--DF\QD00HUNLV]*XUDQRZVND$3LHOHFKD-The Parameters of Passenger Cars Engine in Terms of Real Drive Emission Test.3ROLVK $FDGHP\ RI 6FLHQFHV $UFKLYHV RI7UDQVSRUW :DUV]DZDV 1HXPDQQ - 0RUJHQVWHUQ 2 Theory of games and economic behaviour. 3ULQFHWRQ 8QLYHUVLW\ 3UHVV 3ULQFHWRQ 3D]GUR 3 Koncepcja ruchowej optymalizacji 8 wania odzyskowego. 7HFKQLND 7UDQVSRUWX6]\QRZHJRàyGĨV 3LHWU]DN.3LHWU]DN2Ekonomiczne i organizacyjne aspekty transportu kolejowego.:\GDZQLFWZR 8F]HOQLDQH:\ĪV]HM6]NRá\*RVSRGDUNLZ%\GJRV]F]\%\GJRV]F] 3.3 3ROVNLH /LQLH .ROHMRZH 6$ ; z infrastru

(52) ! # < # $7?7 !

(53) ! od 14 grudnia 2014 r.GRVWĊS2QOLQHZZZSONVDSO

(54) 3.3(QHJUJHW\ND6$Taryfa dla energii elektrycznej 2015.:DUV]DZD 3RGRVNL-Zasady trakcji elektrycznej.:.Là:DUV]DZD 3U]HUHPEHO 6 J

(55) !

(56) podmiejskiego i kryteria jego oceny.7UDNFMD L :DJRQ\ :DUV]DZDGRVWĊS2QOLQHZZZ]HXVNUEFRPSO

(57) 5DLOZD\%XVVLQHV)RUXPElektroenergetyka kolejowa.:DUV]DZD 6KXDL 6 7DR 7 ;LDQJ / =L\RX * A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy.,QWHOOLJHQW7UDQVSRUWDWLRQ6\VWHPVV =DJR]GRQ 3 SKM Warszawa - trakcyjnej oraz perspektywa

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

(59) . 0DULDQQD-DF\QD0LFKDá8UEDQLDN. HQHUJ\LQWHQVLYHULGHZHUHSUHVHQWHG$OVRWKHLGHDRIDQRSWLPDOVWUDWHJ\IRUGULYLQJLQRUGHUWRVDYHHQHUJ\ ZDVGLVFXVVHG ,Q DGGLWLRQ IRU WKH SURFHVVHV RI RSWLPL]LQJ WKH RUJDQL]DWLRQ RI WUDIILF RQ WKH UDLO QHWZRUN HQHUJ\ WUDQVIHU HIILFLHQF\ FULWHULRQ GHULYHG IURP UHFRYHU\ EHWZHHQ YHKLFOHV ZDV SURSRVHG $WWHQWLRQ LV SDLG WR WKH DIIHFW IDFWRUV IRU FRRSHUDWLRQ EHWZHHQ WUDLQV WKH GLVWDQFH EHWZHHQ YHKLFOHV EUDNLQJ WLPHV RYHUODS DQG VWDUWXS HWF

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

(61)