(erl)library.tee.gr/digital/techr/1970/techr_1970_11_533_707.pdf · 2016-07-13 · teuxo(j )tr.i...
TRANSCRIPT
707
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Eit aVYXQovov mh OlUTOV V71 Eqaarlvcw t1trpWIKOV OiXTVOV
vme(oijr 6 1euroX1UeOtOVrm ~ (lVrIOI~ IlOqJ HIJI yHPV(WTIi(tlW CtVgc~JII V1p1Jijr bltlpoundraUwocwt xu ni xavovl(1ir dooii iaxdshyr~ euroxJoyij lto r a ap n(OX(lOwetopLVTV otlQav bUTVYXavOshylvTJr OUtw afJIWVW( ppoundui)(uwc toii 6)((oV XOOTOV lirof3tshyJampOlWC tv (lVYX(((Jpound neo~ xAaaatxOv JI)(TVOV UIIW V1t EQfOr
Lila rij bpaf1oyijr lc066wv ToV reOfllllKOV nQoY9aflfmla~oi) tic Towihov rStXTtJO)l ctC1o)Opil1r ola rilt nllqovorl w Aitl elval aVIOTOV va cved)fi ~ 3eJ rlO t TJ olKOVOfltidiJr )WrOIJOflr tijlt XlV~apoundWr bzl TW10 yupvqroZtXWV JtOPWII xoi rije XQl10Ixqr ampllov xut 01(1 (1vyxe (aewl 1tQor rrv vrptGTapamplv rOICnJnv TOt 6lgtavov va 61ama1WOr ea r imdeXI JTcetOWQOl 1tEeCUreeW pCIshywacwf lOV OAtxov ftEytcrrov daTal AET Oveyiar TOV OtXTVOV
Eli tTJv uehnwatv Ta~h1Jv ElveH 7loUaxtr OVV(llr 1 7lf20aeyshyrla lt Ek TTJV (3ddaTYv aravopTJv 6 a71AWV pE1a3oAwv tit nv attQal oUX71EeCHwaEWt nir xnryrJEWr ftiaq TWV yElPVe u rshyxwv OE(JPWV (3oaElTWv fuefJivrwv EX T~ erpaeJioy rwv pdMshyclwv 10U reaJIJuxov neoyeapftQHOJloiJ cmoTdEaft(1lwv
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Aoyf[ A - Z de nEpintooOIv ICatQ til v 6nopoundav otv KattOtll 00shyvatov va OtEK1IepOlW9fl ampno to poundvOlaUEOOUlt YEqJUpootlI(O OEshycrJlaC Evltp at 1EPuatlICaL 600L A - B A - E unoAoyishy~OVtOI 010 tilv DamICilv jt6vov KlVllOW StEKnEPQlOOVEI f t~ OXO-rll 606e A - Z 6A6KAIlPov -rilv amp1tOJlEVOUoav IClvllolV jtpound to poundltItPEnOJltvalt JllKpae onooAEiae eIlt to O(KTUOV nl 1-2 (OOoL UIICpCilt nl9avOtlltOe OnooAeuroIampv ElvOl poundn(OIle KOI 01 oovshyStoooat to Z npoe to (m6Aolna KtV1pO Z - B Z - r Z-6 KAn )
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Ele totODtov OqJlcrtaUEVOV 05iKtoov unEppoi1e Jlpound 1t poKa8ooplshyojtEvllV OElpOV olaSoXIKoO poundUyxolJ TOOV OeuroOuampv de -r6 6110Tov it 01EIC1IpoundpaiooOle wPlOU~VllC KIVi]OeuroWlt de Erlang t~ t v6e KEVtpOU A 1IPOl wPlcrutva QAAa 1(euroVtpa B - Z poundUltPQVi(poundl otashy9EPOV 1C6cH Ot ej9EtOl t6 poundpwfllJla Mv 9oJtto Sova-rov Ol OAAIlt KatavOIJ f[e ti1 OOYKEVtpOO~poundVTle Ei~ A KIViloEwe pound1It t4)v mapshy1000ampV ye4QOptutKampV ~EOtpoundWV aj 111lt poundol6TTle 6000 va poundmshy
bull EycvvijGIl sf~ Xloll 16 19J 7 4JII~~QroOXOt H)fItPOAOyot - Mrj)OVtKOC ITOAUTlXveoU Mov4 xou (1961) 4tiUttwp -MX(lVIK6t n oJunxvr(ou Moshyvoxou (1966) 4tnMluutODxo~ OKOVO~O)o)O t middot MIlX(Jv ro6I -00 ortoii noshyuttxvelou (1966) TtxvucOt trrt CJUlBao~ t oO Ynoup-ycou IUVfOV~OOO ( fOO 1968 middotEKIOICt~ KoGrn lfltlt If EvovjllJlhou T)poundrrIKolvfIW(Ot 111lt IIO)Uf~XIII1C1It Ixo f OC navllluOfn loo llofjlti)V On6 toO 1969 EIIiIKEMl
de Texv~lCl(V lti)V Tn1J1 1 KO~VWVlwv 1C0i d~ 9lIHO Q1Koliol11lt0c npOYpolshylonOIiOO 1lt01 ElllxpnO ~ oKflt EpEOVn c
bullbull Eyevvil8n etc KiJGnpu t6 (9)5 4111QIlJorOflXOlt H)cupo)6yo - Mll XUshyVIKOo llo)ureXlielou Moyu xou ( 1962) MnX(JvI Ilt Ot tlt 4EIi 11110 Toii 196$ npOI(JT6licv~ 1IIe AEH ntploxlt Xop(v(lou (l970)
708 TeXYUCCl XPOVIICQ NotJ1JlpLor 1970
tEUXO(j )tri ftlcr l~ TOO 0111(00 oOtO~ fii 6poundtl~)v lit npoundpintoomiddot mv noTa Kurovo)Jil eu cirrETIAt l TIlV nfAtiatllv VOIV
EI~ tnV (J)vtXEIOV napououi~etal AUOIlt TOlgt JtpoaAit~IQtO~ 6 EqlClP)JOyit Jlf96Swv toO rpaJIIJI ICOO npoypaJ1IJUTtOPOU t nt auvOCtOl) )UCTOOU i)7tEP POiJ~ TO 61tottliltTjJUTU o UllCpivovulI npcX ta avticHOIXa 6u bulltoou iS IOOOXI--tt OlfKntptl IMatrot tne omppotc t~iryovtCu 1St OOJ11tEpQOJlOta OVv0J1EVa vo 6SlYOouv d r Ka)Ut tpav EKItt61)xOOIV tOO lnt6PXOVtO~ S IICtUOV Kui llEirooIV lCuta OUVE1tEIQV r Glv 6AtlCcUv Sonavltuv
2 YTToOYla~oc TOO bulluyiOTOU OLKOO K6aTOuc K(lTo Tliv 61060XIKftY 61tKmpahJlt1lv Tfie umppoft
T6 )ttyIOtOV 6AII(0 K6010~ Ko OI KT OOU ~ de (jXfIJlU I jlETQ
liLaS01 I ~ I) C OtEKrtEpalwaEw T~C onpoundp pollC OUVOTOI va unoAo yloSI EUkOAwlt ~qgt Ooov Elvat yv(Ocrrll1lnpoc OIEIC1tEpaiwcw
ICivloU Efe euroIC ClOl llV Ko teu9uvotv KOla lrlv wpov aiXllilaquo 11 lJ Ey iotll SIEKnEpaIWtllol [K(lVOtllC buat llC YE()UPOO tll(ii l Ceumiddot ~EUlI r~ Erlang (G RL) lCaL to ICOa we OtlKIIEpal(hOlo~ IHOoe jlov6oC KIVrOEW e (l1RL) Ola t~c avttalOXOO CpoundtX6W~
To 6Xucov KOOtOr Ko npOICUlT tEI OICl 1tOAAoftAOOI OOjlO1 t~ olF 1tepaloulJpoundVTlc 1C1Vraoox de Il lav lCQnu9uvmv (oltK1tCpalwmiddot t11Cr hcovotne t~C QYUOTO(XOU opoundolJnc) lJ6 TO TOpound) a VTlo(oixou Iovalitoloo K0010UC Kal npoo9toum TlUv YIVOIJtY(i)V ~k T ~e liIEIC1tEpatOUIJeuroVle d Tae tnolJpoundvae tOEIC U1tEppofje Ele ERL Kat TOO IJovoli loiou KOOWJ poundCuatnC OOlJle H li lurrEpClIo umiddot JIpoundvTl de tICQ01n v tGlv tnOJltvOlY li EO fb J OrrEPPOn unoAoyi~Emiddot Tal ((Vo)oYIKGX 009EVTOe On t oaoY a t ICO Torp8avouaa l auymiddot OIOAi~t I ~ paalK ICIVCHfOi 5O0v KOj h EiYOI ~~ UlTEppofle ~xouv tac oOt~m9avOmiddott1ltUi KuUllilyenewe Jilae tAEuStpuc YnOIJ IJtic poundIe tilv lii(TllnV Kol Wta ouVenElov OtEK1tEPQlOOt~ t(lJv J-I t otp tOlhllC
nlNA3 I
n ~B I r (Erlang)Z1tltl)ll
A-B 2 43 4 8 l I
]A - r 3 42 6 3I A-A 4 3 52 4 8
IA - E 9 7 5 3 4 10
A - Z 10 9 l 5 4 25I IZ
I(Erlang) 4 9 12 51 1 20 I 6
Eni toOmiddotnivaKoe ( avayp6cpoVt Cll ~ rropaoEIYIJa Opl9lJntlkui tlJlui TampV ovwpEP9tvt wv IlEypound9Gw
Ai Ot T)AtIl B - Z Qvucpkpovtat Eilt ta KEVtpO nponplo~loO ICtIL qgttpouv de t T)v ioatv t(ov Tilv aovo)IICl1V lTp6~ o I E~ntpa iroo l v eft TilV QVT(OtOllOV ICOTEu(luVOV kiVnoL v Za Zr Zz d~ EHL AI OpoundlptIt A - B _A - Z avtIcpepOVTOL etC tac litOlJtIlt KtIt qlCpouv poundIe t6 Or~ IOV liKPOV tWV trl v OLEKlttPOLWt U-n v 106middot tn tO teov ITa nmiddot n z bianlt poundit ERL TO unO t lIv Otl AO)V KtI i OElpampV 0xl~QH6)J flla ~p90yoovla ltPpoundPouv d e t6 tOcolIPI middot K6v twv TO 1C6oTOC cit IK1rCpCluhcTfU) K ee K Dr Kl1 ~ltu 1J0v(ioe KIVrlOIh)e Erlang ftP6C (6 ovtiOTOtlOV Ki vTpOV tf Oti)AllC 1ltacp ( lie Iito~ lle Tfi e ((vTlOl oiXou YPCIJI )Ji)C euroI e lo)JlajJatI Ku~ lJovri6ac OUt co Stov va OIEKttrPOIWOoOV Jieuro a tp TOO A p~ r 4 EftL ( 7r ~ 4) np~ E 12 B ftL (ZE J2) I(OTD tilv ropav JiGY(CJlne Klvi)OUiN (oiXJl1iC) tVlt1 f OrO Jill A- r liUVU TOI va SIEIC1ttPOI61O1 KOnl IJt YlatOv 3 BRI (nr = J) 1i Stolln A- E 10 ERL (n l3 -= 10) K_O T6 KOcrT~ OIEIC1tE(XlIOr OEffiI tv6 Erlang de E IJtOql Tf( OtOJlIle A - E ovipXcshytal npO( tOutOIlt t~ 3 ~ov65tl~ yplijJU t~ (Kbl gt1= 3) IJ FOJJ t Lic lieolJllC A - 6 sic 4 IJov600t (KIA - ) KOK
E-= tilC 6AIKflc KtviOE(jirl ll pOc B Za = 6 F HL pt ouv Sta tlie ytqlUPOOtIIC11 Ccu~ [~ A - 8 ns s EHL PUOL Kt) ICVIl01C 67tSP OllJ-ltOuPyGt 1(6crto~ Kosmiddot na = 25 = 10 VOIJIO~aTlKalV
110VUOWV -H Ulto)O l1to Kivn01 (l)1tepp01i ) Zo - n o - Anr J ERL M rrtrta l t i~ tflv 1 rcpuj)ltlltl Kli v t Eot lv A - r Kai
npoOTiOt ta l dC nv POC1ll(tlV KivlOlv npc)( r Zr - 4 l~ HL b r fj~ 6 A1 i c tOtHne KlVtl OE(i)t lilpound nepOIOCVtOl 3 E HL
nr J 06 (n r = 3) n tO -Z = n =- 4 +-I -= f 6Oo t fe1 IHmiddot1
nooocpcpol ltV1l l lVl0 tcoc OUVIOt OJ-l CVu ~t o middot Aor = 06 middot I =
06 BR r U7tpoundpPOf- tw i a Zr -o 06middot4 = 24 BRL 13001middot Kf~ I(IVitot~ OUtW Ctvl1PXEtal to K6OTo~ ei
a(Krr middot Zr + KBrmiddotAar) = 06(2middot4+ 3 middot 1) = 66jl0vQoae XPT)JOtoe
6la rrpocr9E()(W HOV t lTi ~upou 6t11lClvQII OAfl) to)v yeuroltflupwmiddot tt KG)v E middot fWv Kat tli o 660u t a]u 1C tKAoyi rrpOI(UretEI to jltytOtov OA II(6v KOotOe Ko
Ko = KBO middot n8 + o(KrrmiddotZr -r KarmiddotAor)+ 13 [K66 middot Z6+
+ ( I - a)(Kr Zr t KBABr)) + -f[K EE ZE + (I - ~)middot
[Kbull bull Z + (J -a)(KrEmiddotZr + KBE middot ABr)] I Kzz Zz +
+ ( l - y)[ KEZ ZO+ (I -P) [Koz middotZ + (I - a ) (K rzmiddotZr +
+ K07 ABr)]] tvea ABr ~ Z - nB (I)
fTr a e Zr + Asr
fT ~ ~ Z - (I - 0) (Zr + Anr)
n y ~ ZE + (I - p) [Z-i (I - a) (Zr r ABr ) ]
6 ~ avtlJ(aTUataoEOJc t Qv tlJlGlv toD 1tivolCoe I Eie TOV t 1J rrov (I) o~I3UVOJiEV
Ko ~ 25 + 06 ( 1middot3 + 4 2) + 072 (9middot2 + 163 +
+ 04 middot4) + 066 (J2 middot ] + 252middot 5 + 04 5middot 7 +
+ 011 9) + 20 middot4 + 40 5 + 08 1middot 5 +
+ 0 15middot9 + 004middot10 = 176 V01J101J jlOvOOElt
H liIEl( nr paioocrte tfe 6 n~ KIVOt~ ele to ~v AOytp Sincov IJE I( i) laooyIKiie Ota pa6aE(Ot Tfl l)1teppo ie otOlxi~poundl Enomiddot Jitv(i)t 176 VOJiIOlJaTlKclJ JiovQoac
1 -e+opl-1oyi TOU rp0I-1I-IKOO npoYP0I-1I-0Tlaj1ou [hi Tl shy~[4IIYIKOy 6iKTUOY im[ppofj
To aV(i) Qvorprgev ttp613ATlIJa tlculEocroc tfJ lt ae)tiot11C ammiddot VOIIe Tile tll~I llcovIKi) lt ICtV11arCJ)(j cI OiKtUOV tIC middot(EqlUcOOtnwv CE~poundcoV tui Moov tCT(oTnt hAo-d)c ouvatut v QVU19t1 e lt KAOmiddot allcov laquonp6I3An~LO JittQqlOpUeraquo) tOO rpa~LIJI otJ npOnoIlIJQnmiddot O~oO io wi)tO UljliOtOvtal In (lttonO I onootolfltll Ai (i 1 rn ) ~ 1i OOptOlJlvae noaOtntae J-Iovnli(i)V fl ) 7t X t t llayLo Kg 150middot ltla -JIt at onola l StO ll va IJEtQ()ep9oi)v Ele n li la lPopouc laquot 6middot nOt~ npOopIOjloCm Bj (j = I n) )Jt WPt OIJEvllV ~ T) Tl)01V 1-10 v60(lJV bJ ](Oto t OtoOtOV t p6nov ampaTC V(I ~AoXlatono nOi) t6 oIK6v KO O1O C IEtOqlOpa~ tOD JfPOOVt~
AI np6 ~ centta(popav ~ poundKuatou t Onou Ai noaOtTltEt 3i (npoomiddot cpopa) Ut lllUlfOUIJEVaa ele euro KaOtOv t6nov Bj 1t006l n TE ~ bJ (~ tOtt) ICut to e~OOO Kii avO JIEta~tpOJ-ltvnv ~IOV6~O h T D t6ttou UltOOtoiC AI ert t6v t onov rrpOoplaJ-loO BJ napialovmiddot tal un6 1l0P~i1v ttiVOKOe ( n ivol 2)
EiC t6 Tn AEltpo)vlKOv OiKROV t OU OXillJoToC I aVflatOIXouV a( lTpO( OICI( 7tamppoi(i)Clv IlEacp t6)v 1tqlUpOOtlK6)V ~tutEoov KUl ttie toxlitnc 6So jlOVUOI~ Fflanj 1tpO~ ni~ 7tOaOt11 tac ~e(Qcposhypue bj to Ktvtpa npoopl OIJO O S r6 np~ tOUt t 0 7tOUC rrpoomiddot PIOIJOi) Bj Jl i OUjKiKp lJi ivnv IClvIla lv I(ui oi StOJI UI A - B A - r ~ e t~ V 7ttPIWpt(Tjltvnv iKav6nlta li lE](1tE PUUUOE(IIt (ll E RL 1t Jltc tOi X 6noue 1J[(gtOtOAtie AI Jipound t o ftepLooptOJ-l CVOV li uval-II1C6v cit povaoac 1l6tacpopdC To K60tOC IJttOCamplOpOt KU UVt Ilt1tOIXEi repo to -OOtOe SId trlv pctupfpaalv hOt Erlang ~tOf~1 middottl~ d vtl O1o[zOll ~fuC(i)t (t61t0c QJfOO(OAC) t1C t o t vmiddot tPOV npooptolJoO (t6 rro 1tPOOP1CTjJuil) To KOOtOe TOO t O 9cO)shyPEita l otagepO lI IJt) hTlpeatilJlEVOV a rr6 OUIOIJeurocOOE1 C t il a1middot vlicreOl T6 Tt9tV np613AllJo oOVa tOI roe poundK to(Jrou vu t~Ptu(le oo~ np6PAn ~ttt rpal-llltKoi) npoypaJI~IatIOJlO) Koi (OIOlttpm Ugtt
709 NotIJPpIO~ 1970
n)NA 2
il (j = ) n) 1
A Bn n po(t(j)opo
(i=[m) -[shy
A I Kl ] Ku K i ll
A --~Kil IKu [-- -I I---- a
A 1 11 middot- shy- 1shy
I------ -- shyAm Km1 (Km2 iKmn alii
_ oj _ -= - 1---- shy
I b
y
1 t I btl i a j = 1 bjj
np6~ATWO ppoundtarpopa~ t6 6rtofov onou Apoundi ClotKJ)v npoundpinlWOlY npoP)n~ato rpU~~1KoD npoypO~I~CI no-~ou
0 rpa~~IKoC npomiddot(pall~aHOpOc nGfHAOIJPUYpound1 npopiiUl(nu Ppound)lIGrOnolllO[(uC CLJtolpoundAOUI1EVCI poundK YPUJJIJ lK WV oUO tqpUtOO Y XapOKtl)pI01IKOV TOV1W V Ult01poundAfT TO -euro YOVO OIl 01 0 Lny tnl Auoi v tOOV OEY XPIlO l~ OnOIODtal KOnl t o n[iotOv aVUAUtlKUi jJt9000l )6Yltl tli tKHiopoundwC twv OACI a plO~IIFIKOi tn(tvushyjI)TtttKoi tOlOUtOI KO KULa Ka v6vu 0 OYIO~Oe TtlV(O(WV Oumiddot 10C 6 Tto-n4i t~Y Koiu IEpav ~tGooov npoltHnIOEtLe tltOVOAI) lt1lKI1J Kal aKplpou tvoqOJJtvwc t~lUPpoundOEWC tOO lfat Yto ot6xou el ~ Jtepin1wOIv npopn~ato nAEIOtWV IJf WpAl)rwv Kai I1 tYUAOO 6pI8~00 tlplKHiw AUOpoundWV WI TtC poundie 1nV nEpimiddot n1 WOlv (i npOtI7IWVraquo ~pound ov I06tl)10 Olo t ijc OUVpoundTtO~ t(pap shy~loyite OUOHW(ll IKWV AO(101lKampV Kuv6vwv
6lo 1O~ 1poundV1KUe nCplntWoW npop) Il~a1(uV rp(I~l1lKo(l nposhyYPO~I1UtlO~ Oi) anOnAti 1~ IJ1tO tOU O Danllig poundnlVo l9poundioa Simplex tTlv OIl~0VtlK0)tEPUV ~ E 900ov tHO tllV CiOlKil v mpimiddot ntWOlV tOOV npOnAlll-I(hwv IJpoundtaqlopae OVeuronlUx 01100 v ) )IE90shySo~ 1ite (CPOPE lOOUtl Kiic iWV10 t)~ - 010 Ti]V pound~EVPIltTlV JlOVOV ~l U OPX1Ki1 e POOlKfie Aooeltolt - ) 11pound9000lt o Ja7poundpollilo EWe laquoStep pi ng-Stoneraquo ill1t9000lt rodi ((todiried Oltrihtl shylion ileLh od) Kai ) OUYYPll(Jl I1t9000lt Enl jiofw El( LOushytwv Go XPllotJJorrolhow~poundv f a 000 rrpwlUC IldJoooIJC SU) 1llv t~poundUPpoundOIV 1i] c KO tOVO~it c KlVIl OEr~ Tl 6noio O-aLOtOltOLpoundl toe oon6yae poundIe 10 clva(j)rp9tv napOOSl)~a
Eov 1tapOot TlO(u~poundv pe Xu t ae npo PE1UIpOpQV ayvcJ)Otoue
no oOt l rae KI vnmwC Ete E RL IJtOIP 1 ~e St OI1 I)e i npoe to Ev shyIp OY J )o~j3Ovo~ poundv 10 OKoou90v OU01llUU t~IOWO(WV [[ Kai tnV n plle PCAtlo1onoilolv OiKOVO)llK Tl V ouvapulolv lll
~X II xu+ x11 + Xu + Xl = 5 X 11 + Xu + Xu ~ Xu -- X u = )
Xu + (32 - Xu - X H T xu= 8 i II X U + X n + lt I x~4 + X II = )0 Xu + xu+ Xu + X 6j + X = 25
Xu + Xl + Xu -- X 4 1 + Xl i = 6 XI~ + Xu + xn + X~ ~ - xu - 4
k I i I Xu + xs ~ + X t3 Xu = 9 Xu -0- Xu + X 3 ~ + Xu + X t t = 12
16 + X~I + X3~ X ~ ~ xu = 20
2xII + 3x I2 + 4x s + 4xl~ + 8x H + )x2 i 2xu + h2l + 4x h + 6x + 4X3 1 t 3xu 2X 3 3 + 4XH + 5x H 1 (III ) 9x H + 7xu - I- 5x H + 3x44 r 4XH + IOx u T 9xu I- 5xu + 5xu + 4x H = Z
EK lWV poundc l06loswv 1 0~ OUOtTlIlCltOe n III + n - I = 9 (VOl
aw~apttHo l OAAhwv 600poundvto fit on 0 OPI9IJoc ttoV OyvWshyOtWV rei) otlnth lJ01Oe 6vpoundP(poundtOI tie 25 U(JliOt01Ul nAila~ AU Gpoundwv FK 01)fU)V arroppimovwl ai ncpIpoundXouoOt lipvrJtlKae ttllae t(i)V (i yvWGtwV )tlI1 PavoJItvou o utW 1 OU OUVOAOU tooy laquo~nITpEn ampv Ii iQLKtooV AlIOEWVraquo) EK lOUtWY nO )IV 8tov va I1POOOIOP lOO1) I) H(3poundAT[otll ADm raquo ) tAuXlO tOnOl ouoa t~V oimiddot KOVOlJlKlV ouvap n lOlV [If
~Ia IJ1) Orvlollo U 25middot9 16 (IYVtiXHbJV )opp6vpoundTal OUOtn~llL 9 t~IOWOEWV I1 c ~ OYVWOTOUC nOpEXOY JJ lov laquopaO IKT]V AOOlVraquo M[u npoml (~q) 1 1n11 POOlKrP) AlIOte Aap~oVpoundtQl Ot6 tOo aKO )otJ90u KUYOVO~ li laquoPO Ppound1 00UTlKljc ywvi aeraquo Iu~q)cigtvw npOe t OOtOY npoY00J1IJOti Co l t(t1 poundtC 10 a vw oPIOtEpOV peOUVIOV tOU nivQJ(o (l0ppound100 mr n ywvio) 10001 pov6 oEe 610~pound va K(tshy) (POi) KUta t o ouva rov J) KivlOle (~h tllOI e) lOU KpoundYtpOU BL_Hmiddot 6 8U L va 11ft impoundpoKEloGi] tv toutOIe nOIC lmqcllwshylUen 1(0vOtllC (npoo~npo) 1D C OeuroOIJIle A - B = 5 ER1 oja 5 ~(V(iOEe Ev OUVamptEI q KtVpoundltal tH KOe~tWe fie to tn6~IEoV 6pGOYWVl OV t ni r1t audic oti) I)e Koi npoypa~~ati~el IJ1TO wue OutoOe nEpI Op I0 I10Ue poundv 1Plj~O fit 6)oKArlPOV to unOAolshynov 10 6noioy OUlJnAlpwvpoundl til y laquo(~ilLTlOlYraquo LOU B Eq) OOOV l(afuIpOj) i lttl tl)ol~ OUtl POOi~poundl tie oPI ~ovti(Ue poundie to in6shyI1EVQV op90yciH IOV (tnt rl) e Out ne o u pue) KOt npoycoJJllulimiddot ltEI tOOUe ~ovooae (1101pound va KOAUqlOij il tntlOIe lOU r uvru innppoOpoundwc poundv toGtOI tne 01 poundK 1tpoundPOl Wtl Kie lKaV011l10e (npoOlpo pae) tiilt A - r ] 6noio ci TtOtEAd tUl o1t6 1Or n (o shyypa~~OlloOpound[O(Ic JlOv6boe Eie A - r 13 Ka A r r Kut uOtOv t OV tp6noy 1rpoXOJppoundi n e 6PI~ovtiwe- KOGttu Ewe lhou 1p6aOpoundl de to KoLW oPlOtEPOV opOoywv1ov t oO rrimiddot VO KO e (vOtlObutiKit Y(Qv(o) middot0 Upla~Oe toov oUJJnlpou~poundwv opOoywvlWY QVtlO1OlXOUVtWV Eie tOv oPIG~OV tooV POOl[(ooV ~IE1 a~Al)tWV TnC AUOEWe otov v6 poundlvul noVtOtE m + n - I ~LOI 5 -I-- 5 1 9 tylt) t o unCl Ao lno [6 ~n OU~IJrWwetVtO OpOOYWVW avtlOto lXOuv rie I(ie (iIJn paOIKoeraquo ~1)6rvlKc1~ JJCshylQ~Al)t6e
To o Io-Oy K6crLu t i) e trpIKtie OoolK I)e 1oune AUO(WC nposhyKUTtt t t 010 noAju n1oola(JIJOU t ampV npOYPuJJIJ(ITI08 cI0(tiv ~oshyYOOWV pi to ovti o-rOtXOV I-I0VUOWlov 1(OotO~ Eilt t 6 na poshybE l Y~O 6vtPCTOI t oOtO tie
Kill -= 176 l1ov6ooe xpl)~lntOe
EtIK P10H n) iIJocw 1(IU1le npoe 10 uno 2 ruppound9tv a1tOtE~ MOl1 a Or HivUF l OLl i) vea KUtOVOI1Tl poundi vOl iooouvo ~o OI[(OVOshypllcWi H~ npoKUntouOl KUHl ttl V OLOOOXU nv OI poundKTtpoundjuiuOIV Lie VIpoundPPo)
H CLpEG1ioo aiitl) laquo( POOIKn AUo tltraquo 0(-56AW o rc01poundAEt tTlv I3poundAtiotlV AllOIV roO Ttpon) TlJJotOe Mio t l(u jl1l0te tGw KEOV ltgtp90Ywv[wv 100 n[VOKOC KOl o tll V WeOOOv OlanEp al(i O t l ~ - -iLfpping- - - Lollc - i1 lOt 010 tile npooJTljlEWe de r ilv paolKilv )UOlV ~I ii ~Tl POcrtKi] ~EtoP1Tl1fle Kat onO)lOKpOVshyO EWC tK LOutllC )Ilfi~ POOlKlie t OIUU1llt orlKvurl 0n OOIOtO OVtrj va (hAtlw8u iIpoundPO ItEpW H i l(1IJJlo~lt n paYJJOton Olpound lLOt OIcJ ti) rrpOo9 Tl KIle poundi C CKOCrtOV KtVOV (I1Tl OUl1nAlpwJJEVOV) opGoyWvLOV JlllL 110 VOOO C we t~~j101 Oe tfi e pao IKe AUO poundWe lCoi 010 o tOp9wTu)e tooV OUl1n~TlPWlJtvwv o pGofwvi wv tn~ ~ooIKfie AumWe Kut6 1OIOCt Ov tPOrtOV won 01 OUVO a)K Ol rrpoundp IJryiotl lt Cltn OE WC Koi npooq)opiie We Kai 6 P10pou l ampV OuOtshyampv ~eurolaPAntGlv va tEaKo)oo9noouv lo xuouoUt n oC tOushy101e vnOAOYI~Eta l 10 KOOtO 10 6noTo y npOKunLtl pound10 ti UAshyAaya) c tOO ouvOU00l100 I(oi t o ono1poundis opa 1 iOEtOI poundIe 10 lno poundK t iJJlOIV bpOOYwvLOV Eltp ooov n pO KUlllJ opVI)1IKOV KOO1Oe dYOI ouVO t OV va OrAtlWOi) i a PXlKT] paOlKf1 AUOIe blo toll npoypoPIJOtIO~oi) IJ OVoowv Ete to eKtll11)9tv 69poywvLOv ~ Wl ehal OUVt[OV va ~poundIWO~ 10 6ALICOV K601Olt
Kani tliv tKt lPlOIV npoxwp Ei tie tK LOi) tK1lI1WI-I EVOU 6~90shyywv iou tn i tn C u tlh OEl PaC euro ogtc t6 pound1t OIJpoundYOV ou~rrAIlrUptshyVO V flOll op90YWVlOV to 6noiov f1tltPETtpoundl tilv JlfnieOOlv r~ EV I(U1poundIAl~~tvov 6p8 0(0lVl0V i ilt fn o~ltvl r mlpae Alll shyAO VOW C paoi~poundl ne rrO AIV OOI~o iwc KaOpoundtOOC KOK tK tOU poundvoe KaLpound l~jI poundOU op80ywviou EI~ to bOIJeurovOV t we chou tnovEAO) poundilt t o oPXIKOV opEloyWYIOV
OaguOpoundIYPu EKtijlrJOIi t Ou opeo)wv IO() A - Z B EiC 10 op80ytiVJov A - Z B 1tpoypal1)la1i ~ttol I1lU )IovOlt KtVnOCWe r) ono[o OI)I110Up)poundi tn nAeuroOV K60to lt [0 l1o v6owv XflllJJOtoeAshyKOAOllElWC npoxwppoundi tl lt 6pl COY tilrlc EWC to 6p90YWVlOV A - Z E 16 6rtotov poundnltptrrEI 111 V I1UOPOOl V de ~v Kate l)TlJJ~l tvov
710 Notl-PpIOC 1970
OPSOYWVIOV Ti)~ tnOJltv11t om pile A - E Kfli t)((HIOVII ta~ 1tpotpaJ1)1atIO~Ei n Ul elc 0[10 5 1-1 000(11 Kurd 1 010 qj 1-111 ( rrllp~ 1J IJ ItEP JloOI t fili Jt PoCJ(Pop6~ ri A - Z O OtlO f~O IK(lVO shy11OuVrCJl 5 l-o a6amp~ xprHla Hl( Ei TO OpOUYOWIO V A - E L~ npoati AItUl ~dCL IlovciC o ui va (JU)l1tllpwe~ Ii t ~t 1 01~ toO E (llttp 1t poKO ~ti 1(6a 1o~ 3 )lov6oS(raquo Karoltlv ~~u f i~Ll 1l 61)1shyo v tiw~ Eli t o Op90YO)llOll A _ E lICO (kOHlilVt1 tat tvwushySo iI (Ioypa~ql CITI OO fi CT(I~ JIOVDOU 1(U~61 I(QStt(J) Ii ~ to A - 6 il twi 1tpo OO ~Tf 1 Iliav povooa ItOAIV 6PI~OVli(CX d TO A - 6 r Ka ~huto tit to A - r r Kat t EA-Dt 6PI~OVTi~ti to A - r D s ui roG bn0 10u npIlYIJQto1totpoundItU1 n t1ll(Jtpo(l ~ eI to aPXIshyI( w o p90ywvIOv A - Z B To 0)_IK61 K6(n~ IhtpXa-tQI tit
KZB - K7E + Kr F - K EI~ + K~~ - K6r t-- Krl - KrB 10 - 5 -- 3 - 5 r 2 - 3 + 2 - 3 _ 1
1-1 TlI-lII OUTl -d 9E tQ1 tie to 0PSOYWVIOV A Z B Kat Qutov roV tpono v tK1IP()Vtal OAO ta Jn 0W lnAllPWJEVQ 6p90shyyii)vto KOt bIUU010OtOI Lav tlltpovi(oV1UI upvnweu tl]JQi Tilv JlrtUurEpuV upvrrcIICIl v tll-lTiv Qv1ll(uEhati TI ~ Ou) (cawv p oshyvdo ruv iioll Qnon)o()v t v )JIICPOlpoundPOV nocr6t11 tr~ Ti namICii Aua uv 6rcoiu ouvTlvtriOll f i t 6PI~OV TLUV Kf1tl68uVOI V Kltu titv I(U_II(IIV httl-ll)otv rou aVtlOt0 1XOU op90yulViou
niNA J (AuOI~ I)
I nI I Z (RRL)E1 fO I1IJ f~ H I A
A - B 5 + 2 + 4 + 4 + 11 5I A - f I 2 3+ 2 + 5 +8
A-A i O 6 -4 2 8- ~ 6
A - E 73 + 2 101 t 2 [ + 1 1 I
I 20 25A- Z + 1 - 2 5 Z
(BRL) 6 4 9 I 12 20 51 I I I El e t6 1tupao poundIY)Ju (1tlva 3) ~ JHpaVL~pound1(H il JIpoundyaAUtEpa opvl) shytlKri ttJlit - 2 de TO 6p8o-ywvlov A - Z I Aihll QvtlICo9ishyatara l 010 tfe 11J1fc 3 Ti 6rcola QrcoUM L lliv 1-l1lCrottpa y TlshyJlTlV Jl e ra~u tlOY tl]Joov 5 I(ui 3 t Oe ~aClIKfe AI(1EWe trie 6rroialt O llvuVtti tIe poundilt 6PLOV1iOV ttteueuvalV I(urri ttiv KUICAIKliv tlCtil-ll1alv 1oC opeoywviou A - Z I Ai (mO)OI1tOI lll-loi 1 1) t3uOHi~~ AUCIEUX npoClapI-l6~ovt Ul lwpa nAiov de til v tav T1)J~V tOO 6p90ymviou A - Z A SIU vo eculoAou6t1couv imiddot ClXUouGal at cruv91)IoOI KEpi )lE)i o-rl1 rcpocrql(l pii~ 11111 r napoundUlC Ka l CiP IOI-l Oi) T(OV a --C(Hxtiwv tqr AUOCWC In n - I a 9 DOno AalJ~6Vpoundtal ft AUcnlaquo 2 (nt ffle 4) fiiC 6rroiae to 6)d6v K60tOc QvfpX tal poundilaquo K~ = 170 I-lOv60ue EloICovoJwu]J~vwv 176 - 170 = 6 Jlovaooov havn rTje 1tPWTll ilXJEOOlt
n I N A=4 (AultJle 2)
n~ B
i I I I (ERL)ArAtal111 ZI
A - B 5 +4 + 4 I+ 9 5+ 2
A - f I 2 6 34- 1 I middot- 3
A - A + 0 2 6 -I ~ -1-4 I 8
A-B + 4 + 2 i 10 I t 21 10~ 2
A - 7 3 2+ 3 1- 3 20 I 25
Z (ERL) 4 12 20 516 I 9 I i
Mia tKtll-lllO IC t wv tOlnoov 1-1-1) al)~I1tATlpwetVtWV 6p90)wviwv TOU rrlvaKo 4 KUta la npoavatpt pgevtO OUlKVOEI 6tl oilv ElV(Ll
OUVOf i] lJin llEpUlteuroPW j3EATiwOlt Tf)e AUOEcu SIOll ouotv orgtshyeoywvlov Ant~avEI opVnuICTiV Ttl-lt1V nnDUt lpoUIJampV tv fOUshytol ~ (Il l pound)JltpuV1CtmiddottUI EiI T6 6peo(wVI0V A - a H n tljJIl 0 Ii ortoia ~Jo Ol~ETi pO (thtuil fI tlIwn 1lldl) cnltpbu1 tnV tnishyrtu~ t v t Tipo( luOf~ icroouvo]Joll OiKOV()I-lII~ rt 06 t1)V I3nshy01 t v Auenv 2 n p6rJUtt ilVtlI)OIOf-IV11~ lTiy lllJtiV 0 Oil tfj~ ttl-lil I I-lputqmt p c ra~ lampV ttl-lwV KUL f tf)c (JaOlKlle AtshycrEWe t(11I OUVCIV(WI-l t (ov d 6p(~o vtiuV Katt(Ouvalv 11 0 10
li]v 1CU1_l l(l)v - illnOlV tOl opeo)wvlou A - 1 B Kai ovashynpooapIJ 6~o~ t Jiy A(l(JIV 2 we I(at npon you]J cVWC poundupiol(oshyOICOp l V Titv Vtov I(CllUVOIJ V tOU nivOKoe 5 (Auollt 3) A Ull Itpo~Jvpoundl6AIK6V KOOtO K~ 170 POV(lSfOV middot Elot i~lnall Ili)v Ktv(bV opeoywv iu)V fliltl~ 6ioEI arrOICAtIOllKiigtlt epoundtIUO t l~IU ( A IiVIK9poundio(H IUOpoundI e 2 COL J QrcOnAOUV b W)JIvwc tao ~EAtishyalae KU tU VO~u tll KtvT10tW En looV imuPxouoGlv oea)J6lv
n I N A 5 (A0~ 3)
i (I RL)B f A Z ~ I n
tgt tCl l-ll1 E
5A - R [ 5 + Z 4 4 [ - 9 I
JO J I + 2 i + l 6 3A - f
8A - A I I 6 + 2[ +4
+4 + 3 +2 10 +2 10A - E
A-Z I -- J + 3 3 2 1 20 I 25
[ I (ERL) 6 4 9 51
1 12 1 20 I 4 ~LI p(ul(Jlfi TW anOTfA(OjJClTW
Efl) oaov nampUPIClKOI-lEVl) 010 tflt bpapIlOYfe toi) fpajJlJlKOD npo)puJ]JurICll-IoO ICa1av01-I1) ~l-llQaVi~t I-ltlCp61 fPOV K6o-r0l tvavll t OU UltPIOTQ~IEVOU K6C1ttH- tOtl Sll(tuOu elval OK6nII-lOV va t1ClUof1 KUto roio v worrov 8G TO OU VClTOV vei E1tLtfDXSt1 ft KUtaV0J-ltl lOrn t va ilTtlipu KuvOnOIltll(Il npoatr)IOIlt de al)tT)v ~AVEU o))u)11lt lfllt TCI VIKnr to) O1)CIlrilW-rO~ CClSishyltTt C11al 10Uto rro AA QKIlt ~ )vHt6V 01 6rU1K u i)ayl)lt tlr OEI t tUn Ol) tllIV OEapWy KCli ola[h(JaacUl4 dl~ unEPP0i)lt mO ot~ (J1JTj~ d~ lgtt(Jl-Il)v Ti]V 1t1pircthtOlV aimiv 90 t~CtQaWIJEV tni t i Pelo t l toO 6VIlltpEPetvtO~ rrapu5ei) lJutor
T6 UnOtiAEOI-ICl crrt toO niVul(o 4 DelievIIpound1 Ott KVl1ate foO KtvtpOU S Zn t~ 6 EHL OIfJnrPCtt OUHll I-l fOI) 1(lIV oe0l-loov A-B(5 FRL) KoiA-f(l EH L) ~ to f(4tI IL) t6)v 5cojJwv A - r (2 ER L) Ka i A - a (2 B H L) ft toU I (9 ERL) 11 tOW A- A (6 EHL) lto A- Z (J BRL) ~ toO E (12 EH L) s tilgtv A- E (10 ImiddotRL) Klli A- Z (2 ERL) ltviigt ~ t 00 Z (20 ERL) QnOKAElotll(iiX 010 tllt A - Z -H ICUtuVolln autl) ouvutUl Vo npoClqYI Cle~ Sui ~5aooXLKillt SUKrc ~ pallshyOew t ft o U1tE PPll~ l(utG 1f] v ClElpoV A - B A - r A - I A - Z Kai A - E A - Z middotYrOAOYICII-lamp tOU OAll(OO KGOtoolt Ut(l TO Ele 2 OElKVU fi lnpOYjlan 611 100TO IiEI OOtal El~ J72 vOshy1J100]JUlll(ae )J oVuB~ ne 1tp6lt tftV OPXIKIlV AUOIV ft AUOIe aut l) olUlPipCI Kata to Oll 11 U1tlppOn ffe opoundOI-lTle A - A 681)shy)poundITClI ICat cueerav Ete tnV 60011 tCIxotl1lt poundICOyfjpound A - Z napal(ul-lntol-ltv l1C tTjc ot ol-lne A - E
1-1 Kuravo]JY 100 rdvUKOe 5 nOPOUOliJ~EI 1-1(0 tiAAI1V ouvat6shy111Ta olaooXIICfC OIampK1tCpalciJCIEOllt -riiC I(Lvrionx I(Uta tftv crt lPOV
0) A - B A - A A - Z ~) A - r A - A A - Z ltoi y) A - E A - Z
T6 6AII(6v ICOO-roe tl)lt ua-cwlt TUUtl)C UVBC-Xftnl KUfO ttl de 2 EIC 171 5 vOIiICl]Jatl KtIC l-I-ovli5ult JlIKp6upov 1(010 11 tPCgt K6shyO1OUC li] C AUOE~ 3 EvtaOeu t1 UrclflP0 11 tne A tl 6ol))lishytal K(n EOeuroIeiav d niv OICfJUlV A - I no(wKrljl1tto]JEVI1e t il OtCllJn A - i 1 oe UItEPPOij t1lt A - 6 I(al EU6dav de 1nV A - Z (~)~ I(ai npol1you]JpoundVhl~
rEVIKU)lt 010 tU)V I-l ES60wv 100 rpa]J]JIKo() DpoYPuJl]Jano]Jo()
711 Notl-l~ploC 1910
Elval ouvat6v va 5lartlcto(81) tic cnJV8EtOV 5Ktuov OrtEPPOitlt Mv 11 rtPOOOlOPlC3Elcu lh QAAW V )le8oooov ii poundjlrteIPlte~C CEIshypo poundAiy(ou tU)v 5tc)l~v teal 5lEKrtfpUIWCEooc tFlc UrtEPPOtjC Elvol ~ EvSeOpoundIY)lEVn ItpoteuAoDoCl t6 poundAOXIIJWV KOcnolt EtC havdnv 1tpoundpirttOOOIV dVUL Suvatov va J-tfL(81) r6 OA11(0V 1(6shymo 51 oAAaytje r flc crfl pampe EAhxou cruIlCllltiwooC rtp6C t0 onoshylpound)ecl(l tflr 51lt1 tOO rpa)lIlII(OO npOypnI-lIlCltICJJOO rtPOcrOlOshypl~o)lelnlt 3poundldclne KUtalOpflc tflc I(lvncreooc
BlpLoypa+(a
I ChllTmann CW Adwlf R r 1 r1lQI ELmiddot Oj1erallons Reshyscarch Wlell-Muenl~bcn 19fi I
J(tr ll H OlHrll ions Rpellrlll ~ 1 llltgart 1966
I J(oldtl naln lt ( [lie EHllrli(dcrurg (it- FmlIrnmiddot(middothnClt( t~r i shylthtnlanoli in (11 ( WCltlS l ln ( I7 DI~rrtd l )o) Il 1 11 llnClI shyrJw ll 196ti
4 Kvgtt-i r AmllOllljlrocnlt Cal imo)o 1 [opo OvtojIO(IV HrO6 tllltlKlI() 0[1100 (Tt(VIIIU XPOIIo raquo Tll)X~ 110 1969
lox 1 r Elau(l)Y c(~ tOY rp(IlIIlK O npoypltlJPUftOl-Iov middotE)middot ) 1 FtUlPlU Eno t-lpnOW ti)v EpcvvW II] ) AOifll 19tfI
6 0gt11 r AI TftI Col fOC rpOlllJllIou npO(palIlU TIO IJ ol) poundI lYl poundru)o(t1 nil (rou(I(IgtI EE E f AOUI 1910
1 Saulll LT )llll lem l wal ~l elhod s ()f OHraUOns Resralch f cG raw-llill N(~ ltwk li~
Bestimmung der optimalen Verkehrsverteilung
In Ueberlauf - Fernsprechnetzen mit Hilfe
der linearen Programmierung
Von O Kokklnakll- G Karvdls
lCunfallung
lu einem Ueberlauf-FeruwohlneLz wird del Ve rkehr uber die Qu erbtindeJ hoher Ausnuzunlj und den LeLzweg gcrinshyger Verluslwahrscheinlichkeil nach eine r vorbetimmLen Reihenfolge abgewickelt womil e ine belrachlliche Verrinshygerung der gesamten max imalcn VermilLlungskosten ershyli eH wird im Ve rglei ch Zll jen en eines klassisch en Nelzes ohne Ueb~rlauls mciglj c hkeil des Vcrkehrs Durch Anwendu ng cler linearen Progtomm ierung auf ein
solches Nelz behandelt in d e l vorliegenden Arbeit ist es mogli ch di e wirl schartH ch optimale Aurteilung des Ver kehrs auf die Qu(wwr g-c und rlen R egelweg 2U bestimmen und durch V ergleirll mil d cr vorhondenen VelleiJung les tshyzus lellen ob finpound witn( Reduzierung rter maximoien Gesomtkos trn frrcichhol isl In diese m FaJl ist cs meistens mogli ch ~ich dt~r OJgt I imalcn crleilung durch ei nfache Aenshydcrllng-cn an rlcr Rrihfnrolge dcr Ueherlau[sab icklung nath den gr~(bni5sfn der lineltlren Programmicr llng ~ u n (l hern
bull (Cborll In Chlos (19 37) Dplom - Elektro ingcnleur der Te(llni$shychen lIocll~( lllllr ) l unlt1Hn (l 9B ) )1nitor - lngcnl l ur (19 66) und Dllllom~Wlrl sdians lnlZ (gtn irr ( 9(7) (t f ~t III (ln U och3ebuJe Sell 1961 wlilln~cJlarlllcht[ Mi1artwitf r 1m 1~ ()lIT( lln tlio llsn inl5tcrlurrL 111)(0 8eH 19liU ausrrnrrlrnUI(hcr Trorl~s l)r rur Prtll)larilrlchlfntechnik an der Tech nisrnen Fakullat der Unicnltl1l Pllras Er hal slclt in
Ka rllrlli1LIuP(hnlk und In Fla~cn nrr qrl$chanl lchen Plan ifi kaUon lind I TIlruIJlnH ngsr(lrselun~ I)(f lal~ i pound rl
IriJorrn In Kythlra (19 35) Olplom-Flektr ()illJen IElur d e l T erjmjs shy
hln lllt)ch ritHIr )tillI~hcn (El6 ) l1L I 96 hlll~ni ~llr ncr Cellrn ll lshyr hC1l Ilr itmIUlls-G cell scllarl (I) Bll) L it r def OrTI-K rtIifS hnrillih (19 70)
708 TeXYUCCl XPOVIICQ NotJ1JlpLor 1970
tEUXO(j )tri ftlcr l~ TOO 0111(00 oOtO~ fii 6poundtl~)v lit npoundpintoomiddot mv noTa Kurovo)Jil eu cirrETIAt l TIlV nfAtiatllv VOIV
EI~ tnV (J)vtXEIOV napououi~etal AUOIlt TOlgt JtpoaAit~IQtO~ 6 EqlClP)JOyit Jlf96Swv toO rpaJIIJI ICOO npoypaJ1IJUTtOPOU t nt auvOCtOl) )UCTOOU i)7tEP POiJ~ TO 61tottliltTjJUTU o UllCpivovulI npcX ta avticHOIXa 6u bulltoou iS IOOOXI--tt OlfKntptl IMatrot tne omppotc t~iryovtCu 1St OOJ11tEpQOJlOta OVv0J1EVa vo 6SlYOouv d r Ka)Ut tpav EKItt61)xOOIV tOO lnt6PXOVtO~ S IICtUOV Kui llEirooIV lCuta OUVE1tEIQV r Glv 6AtlCcUv Sonavltuv
2 YTToOYla~oc TOO bulluyiOTOU OLKOO K6aTOuc K(lTo Tliv 61060XIKftY 61tKmpahJlt1lv Tfie umppoft
T6 )ttyIOtOV 6AII(0 K6010~ Ko OI KT OOU ~ de (jXfIJlU I jlETQ
liLaS01 I ~ I) C OtEKrtEpalwaEw T~C onpoundp pollC OUVOTOI va unoAo yloSI EUkOAwlt ~qgt Ooov Elvat yv(Ocrrll1lnpoc OIEIC1tEpaiwcw
ICivloU Efe euroIC ClOl llV Ko teu9uvotv KOla lrlv wpov aiXllilaquo 11 lJ Ey iotll SIEKnEpaIWtllol [K(lVOtllC buat llC YE()UPOO tll(ii l Ceumiddot ~EUlI r~ Erlang (G RL) lCaL to ICOa we OtlKIIEpal(hOlo~ IHOoe jlov6oC KIVrOEW e (l1RL) Ola t~c avttalOXOO CpoundtX6W~
To 6Xucov KOOtOr Ko npOICUlT tEI OICl 1tOAAoftAOOI OOjlO1 t~ olF 1tepaloulJpoundVTlc 1C1Vraoox de Il lav lCQnu9uvmv (oltK1tCpalwmiddot t11Cr hcovotne t~C QYUOTO(XOU opoundolJnc) lJ6 TO TOpound) a VTlo(oixou Iovalitoloo K0010UC Kal npoo9toum TlUv YIVOIJtY(i)V ~k T ~e liIEIC1tEpatOUIJeuroVle d Tae tnolJpoundvae tOEIC U1tEppofje Ele ERL Kat TOO IJovoli loiou KOOWJ poundCuatnC OOlJle H li lurrEpClIo umiddot JIpoundvTl de tICQ01n v tGlv tnOJltvOlY li EO fb J OrrEPPOn unoAoyi~Emiddot Tal ((Vo)oYIKGX 009EVTOe On t oaoY a t ICO Torp8avouaa l auymiddot OIOAi~t I ~ paalK ICIVCHfOi 5O0v KOj h EiYOI ~~ UlTEppofle ~xouv tac oOt~m9avOmiddott1ltUi KuUllilyenewe Jilae tAEuStpuc YnOIJ IJtic poundIe tilv lii(TllnV Kol Wta ouVenElov OtEK1tEPQlOOt~ t(lJv J-I t otp tOlhllC
nlNA3 I
n ~B I r (Erlang)Z1tltl)ll
A-B 2 43 4 8 l I
]A - r 3 42 6 3I A-A 4 3 52 4 8
IA - E 9 7 5 3 4 10
A - Z 10 9 l 5 4 25I IZ
I(Erlang) 4 9 12 51 1 20 I 6
Eni toOmiddotnivaKoe ( avayp6cpoVt Cll ~ rropaoEIYIJa Opl9lJntlkui tlJlui TampV ovwpEP9tvt wv IlEypound9Gw
Ai Ot T)AtIl B - Z Qvucpkpovtat Eilt ta KEVtpO nponplo~loO ICtIL qgttpouv de t T)v ioatv t(ov Tilv aovo)IICl1V lTp6~ o I E~ntpa iroo l v eft TilV QVT(OtOllOV ICOTEu(luVOV kiVnoL v Za Zr Zz d~ EHL AI OpoundlptIt A - B _A - Z avtIcpepOVTOL etC tac litOlJtIlt KtIt qlCpouv poundIe t6 Or~ IOV liKPOV tWV trl v OLEKlttPOLWt U-n v 106middot tn tO teov ITa nmiddot n z bianlt poundit ERL TO unO t lIv Otl AO)V KtI i OElpampV 0xl~QH6)J flla ~p90yoovla ltPpoundPouv d e t6 tOcolIPI middot K6v twv TO 1C6oTOC cit IK1rCpCluhcTfU) K ee K Dr Kl1 ~ltu 1J0v(ioe KIVrlOIh)e Erlang ftP6C (6 ovtiOTOtlOV Ki vTpOV tf Oti)AllC 1ltacp ( lie Iito~ lle Tfi e ((vTlOl oiXou YPCIJI )Ji)C euroI e lo)JlajJatI Ku~ lJovri6ac OUt co Stov va OIEKttrPOIWOoOV Jieuro a tp TOO A p~ r 4 EftL ( 7r ~ 4) np~ E 12 B ftL (ZE J2) I(OTD tilv ropav JiGY(CJlne Klvi)OUiN (oiXJl1iC) tVlt1 f OrO Jill A- r liUVU TOI va SIEIC1ttPOI61O1 KOnl IJt YlatOv 3 BRI (nr = J) 1i Stolln A- E 10 ERL (n l3 -= 10) K_O T6 KOcrT~ OIEIC1tE(XlIOr OEffiI tv6 Erlang de E IJtOql Tf( OtOJlIle A - E ovipXcshytal npO( tOutOIlt t~ 3 ~ov65tl~ yplijJU t~ (Kbl gt1= 3) IJ FOJJ t Lic lieolJllC A - 6 sic 4 IJov600t (KIA - ) KOK
E-= tilC 6AIKflc KtviOE(jirl ll pOc B Za = 6 F HL pt ouv Sta tlie ytqlUPOOtIIC11 Ccu~ [~ A - 8 ns s EHL PUOL Kt) ICVIl01C 67tSP OllJ-ltOuPyGt 1(6crto~ Kosmiddot na = 25 = 10 VOIJIO~aTlKalV
110VUOWV -H Ulto)O l1to Kivn01 (l)1tepp01i ) Zo - n o - Anr J ERL M rrtrta l t i~ tflv 1 rcpuj)ltlltl Kli v t Eot lv A - r Kai
npoOTiOt ta l dC nv POC1ll(tlV KivlOlv npc)( r Zr - 4 l~ HL b r fj~ 6 A1 i c tOtHne KlVtl OE(i)t lilpound nepOIOCVtOl 3 E HL
nr J 06 (n r = 3) n tO -Z = n =- 4 +-I -= f 6Oo t fe1 IHmiddot1
nooocpcpol ltV1l l lVl0 tcoc OUVIOt OJ-l CVu ~t o middot Aor = 06 middot I =
06 BR r U7tpoundpPOf- tw i a Zr -o 06middot4 = 24 BRL 13001middot Kf~ I(IVitot~ OUtW Ctvl1PXEtal to K6OTo~ ei
a(Krr middot Zr + KBrmiddotAar) = 06(2middot4+ 3 middot 1) = 66jl0vQoae XPT)JOtoe
6la rrpocr9E()(W HOV t lTi ~upou 6t11lClvQII OAfl) to)v yeuroltflupwmiddot tt KG)v E middot fWv Kat tli o 660u t a]u 1C tKAoyi rrpOI(UretEI to jltytOtov OA II(6v KOotOe Ko
Ko = KBO middot n8 + o(KrrmiddotZr -r KarmiddotAor)+ 13 [K66 middot Z6+
+ ( I - a)(Kr Zr t KBABr)) + -f[K EE ZE + (I - ~)middot
[Kbull bull Z + (J -a)(KrEmiddotZr + KBE middot ABr)] I Kzz Zz +
+ ( l - y)[ KEZ ZO+ (I -P) [Koz middotZ + (I - a ) (K rzmiddotZr +
+ K07 ABr)]] tvea ABr ~ Z - nB (I)
fTr a e Zr + Asr
fT ~ ~ Z - (I - 0) (Zr + Anr)
n y ~ ZE + (I - p) [Z-i (I - a) (Zr r ABr ) ]
6 ~ avtlJ(aTUataoEOJc t Qv tlJlGlv toD 1tivolCoe I Eie TOV t 1J rrov (I) o~I3UVOJiEV
Ko ~ 25 + 06 ( 1middot3 + 4 2) + 072 (9middot2 + 163 +
+ 04 middot4) + 066 (J2 middot ] + 252middot 5 + 04 5middot 7 +
+ 011 9) + 20 middot4 + 40 5 + 08 1middot 5 +
+ 0 15middot9 + 004middot10 = 176 V01J101J jlOvOOElt
H liIEl( nr paioocrte tfe 6 n~ KIVOt~ ele to ~v AOytp Sincov IJE I( i) laooyIKiie Ota pa6aE(Ot Tfl l)1teppo ie otOlxi~poundl Enomiddot Jitv(i)t 176 VOJiIOlJaTlKclJ JiovQoac
1 -e+opl-1oyi TOU rp0I-1I-IKOO npoYP0I-1I-0Tlaj1ou [hi Tl shy~[4IIYIKOy 6iKTUOY im[ppofj
To aV(i) Qvorprgev ttp613ATlIJa tlculEocroc tfJ lt ae)tiot11C ammiddot VOIIe Tile tll~I llcovIKi) lt ICtV11arCJ)(j cI OiKtUOV tIC middot(EqlUcOOtnwv CE~poundcoV tui Moov tCT(oTnt hAo-d)c ouvatut v QVU19t1 e lt KAOmiddot allcov laquonp6I3An~LO JittQqlOpUeraquo) tOO rpa~LIJI otJ npOnoIlIJQnmiddot O~oO io wi)tO UljliOtOvtal In (lttonO I onootolfltll Ai (i 1 rn ) ~ 1i OOptOlJlvae noaOtntae J-Iovnli(i)V fl ) 7t X t t llayLo Kg 150middot ltla -JIt at onola l StO ll va IJEtQ()ep9oi)v Ele n li la lPopouc laquot 6middot nOt~ npOopIOjloCm Bj (j = I n) )Jt WPt OIJEvllV ~ T) Tl)01V 1-10 v60(lJV bJ ](Oto t OtoOtOV t p6nov ampaTC V(I ~AoXlatono nOi) t6 oIK6v KO O1O C IEtOqlOpa~ tOD JfPOOVt~
AI np6 ~ centta(popav ~ poundKuatou t Onou Ai noaOtTltEt 3i (npoomiddot cpopa) Ut lllUlfOUIJEVaa ele euro KaOtOv t6nov Bj 1t006l n TE ~ bJ (~ tOtt) ICut to e~OOO Kii avO JIEta~tpOJ-ltvnv ~IOV6~O h T D t6ttou UltOOtoiC AI ert t6v t onov rrpOoplaJ-loO BJ napialovmiddot tal un6 1l0P~i1v ttiVOKOe ( n ivol 2)
EiC t6 Tn AEltpo)vlKOv OiKROV t OU OXillJoToC I aVflatOIXouV a( lTpO( OICI( 7tamppoi(i)Clv IlEacp t6)v 1tqlUpOOtlK6)V ~tutEoov KUl ttie toxlitnc 6So jlOVUOI~ Fflanj 1tpO~ ni~ 7tOaOt11 tac ~e(Qcposhypue bj to Ktvtpa npoopl OIJO O S r6 np~ tOUt t 0 7tOUC rrpoomiddot PIOIJOi) Bj Jl i OUjKiKp lJi ivnv IClvIla lv I(ui oi StOJI UI A - B A - r ~ e t~ V 7ttPIWpt(Tjltvnv iKav6nlta li lE](1tE PUUUOE(IIt (ll E RL 1t Jltc tOi X 6noue 1J[(gtOtOAtie AI Jipound t o ftepLooptOJ-l CVOV li uval-II1C6v cit povaoac 1l6tacpopdC To K60tOC IJttOCamplOpOt KU UVt Ilt1tOIXEi repo to -OOtOe SId trlv pctupfpaalv hOt Erlang ~tOf~1 middottl~ d vtl O1o[zOll ~fuC(i)t (t61t0c QJfOO(OAC) t1C t o t vmiddot tPOV npooptolJoO (t6 rro 1tPOOP1CTjJuil) To KOOtOe TOO t O 9cO)shyPEita l otagepO lI IJt) hTlpeatilJlEVOV a rr6 OUIOIJeurocOOE1 C t il a1middot vlicreOl T6 Tt9tV np613AllJo oOVa tOI roe poundK to(Jrou vu t~Ptu(le oo~ np6PAn ~ttt rpal-llltKoi) npoypaJI~IatIOJlO) Koi (OIOlttpm Ugtt
709 NotIJPpIO~ 1970
n)NA 2
il (j = ) n) 1
A Bn n po(t(j)opo
(i=[m) -[shy
A I Kl ] Ku K i ll
A --~Kil IKu [-- -I I---- a
A 1 11 middot- shy- 1shy
I------ -- shyAm Km1 (Km2 iKmn alii
_ oj _ -= - 1---- shy
I b
y
1 t I btl i a j = 1 bjj
np6~ATWO ppoundtarpopa~ t6 6rtofov onou Apoundi ClotKJ)v npoundpinlWOlY npoP)n~ato rpU~~1KoD npoypO~I~CI no-~ou
0 rpa~~IKoC npomiddot(pall~aHOpOc nGfHAOIJPUYpound1 npopiiUl(nu Ppound)lIGrOnolllO[(uC CLJtolpoundAOUI1EVCI poundK YPUJJIJ lK WV oUO tqpUtOO Y XapOKtl)pI01IKOV TOV1W V Ult01poundAfT TO -euro YOVO OIl 01 0 Lny tnl Auoi v tOOV OEY XPIlO l~ OnOIODtal KOnl t o n[iotOv aVUAUtlKUi jJt9000l )6Yltl tli tKHiopoundwC twv OACI a plO~IIFIKOi tn(tvushyjI)TtttKoi tOlOUtOI KO KULa Ka v6vu 0 OYIO~Oe TtlV(O(WV Oumiddot 10C 6 Tto-n4i t~Y Koiu IEpav ~tGooov npoltHnIOEtLe tltOVOAI) lt1lKI1J Kal aKplpou tvoqOJJtvwc t~lUPpoundOEWC tOO lfat Yto ot6xou el ~ Jtepin1wOIv npopn~ato nAEIOtWV IJf WpAl)rwv Kai I1 tYUAOO 6pI8~00 tlplKHiw AUOpoundWV WI TtC poundie 1nV nEpimiddot n1 WOlv (i npOtI7IWVraquo ~pound ov I06tl)10 Olo t ijc OUVpoundTtO~ t(pap shy~loyite OUOHW(ll IKWV AO(101lKampV Kuv6vwv
6lo 1O~ 1poundV1KUe nCplntWoW npop) Il~a1(uV rp(I~l1lKo(l nposhyYPO~I1UtlO~ Oi) anOnAti 1~ IJ1tO tOU O Danllig poundnlVo l9poundioa Simplex tTlv OIl~0VtlK0)tEPUV ~ E 900ov tHO tllV CiOlKil v mpimiddot ntWOlV tOOV npOnAlll-I(hwv IJpoundtaqlopae OVeuronlUx 01100 v ) )IE90shySo~ 1ite (CPOPE lOOUtl Kiic iWV10 t)~ - 010 Ti]V pound~EVPIltTlV JlOVOV ~l U OPX1Ki1 e POOlKfie Aooeltolt - ) 11pound9000lt o Ja7poundpollilo EWe laquoStep pi ng-Stoneraquo ill1t9000lt rodi ((todiried Oltrihtl shylion ileLh od) Kai ) OUYYPll(Jl I1t9000lt Enl jiofw El( LOushytwv Go XPllotJJorrolhow~poundv f a 000 rrpwlUC IldJoooIJC SU) 1llv t~poundUPpoundOIV 1i] c KO tOVO~it c KlVIl OEr~ Tl 6noio O-aLOtOltOLpoundl toe oon6yae poundIe 10 clva(j)rp9tv napOOSl)~a
Eov 1tapOot TlO(u~poundv pe Xu t ae npo PE1UIpOpQV ayvcJ)Otoue
no oOt l rae KI vnmwC Ete E RL IJtOIP 1 ~e St OI1 I)e i npoe to Ev shyIp OY J )o~j3Ovo~ poundv 10 OKoou90v OU01llUU t~IOWO(WV [[ Kai tnV n plle PCAtlo1onoilolv OiKOVO)llK Tl V ouvapulolv lll
~X II xu+ x11 + Xu + Xl = 5 X 11 + Xu + Xu ~ Xu -- X u = )
Xu + (32 - Xu - X H T xu= 8 i II X U + X n + lt I x~4 + X II = )0 Xu + xu+ Xu + X 6j + X = 25
Xu + Xl + Xu -- X 4 1 + Xl i = 6 XI~ + Xu + xn + X~ ~ - xu - 4
k I i I Xu + xs ~ + X t3 Xu = 9 Xu -0- Xu + X 3 ~ + Xu + X t t = 12
16 + X~I + X3~ X ~ ~ xu = 20
2xII + 3x I2 + 4x s + 4xl~ + 8x H + )x2 i 2xu + h2l + 4x h + 6x + 4X3 1 t 3xu 2X 3 3 + 4XH + 5x H 1 (III ) 9x H + 7xu - I- 5x H + 3x44 r 4XH + IOx u T 9xu I- 5xu + 5xu + 4x H = Z
EK lWV poundc l06loswv 1 0~ OUOtTlIlCltOe n III + n - I = 9 (VOl
aw~apttHo l OAAhwv 600poundvto fit on 0 OPI9IJoc ttoV OyvWshyOtWV rei) otlnth lJ01Oe 6vpoundP(poundtOI tie 25 U(JliOt01Ul nAila~ AU Gpoundwv FK 01)fU)V arroppimovwl ai ncpIpoundXouoOt lipvrJtlKae ttllae t(i)V (i yvWGtwV )tlI1 PavoJItvou o utW 1 OU OUVOAOU tooy laquo~nITpEn ampv Ii iQLKtooV AlIOEWVraquo) EK lOUtWY nO )IV 8tov va I1POOOIOP lOO1) I) H(3poundAT[otll ADm raquo ) tAuXlO tOnOl ouoa t~V oimiddot KOVOlJlKlV ouvap n lOlV [If
~Ia IJ1) Orvlollo U 25middot9 16 (IYVtiXHbJV )opp6vpoundTal OUOtn~llL 9 t~IOWOEWV I1 c ~ OYVWOTOUC nOpEXOY JJ lov laquopaO IKT]V AOOlVraquo M[u npoml (~q) 1 1n11 POOlKrP) AlIOte Aap~oVpoundtQl Ot6 tOo aKO )otJ90u KUYOVO~ li laquoPO Ppound1 00UTlKljc ywvi aeraquo Iu~q)cigtvw npOe t OOtOY npoY00J1IJOti Co l t(t1 poundtC 10 a vw oPIOtEpOV peOUVIOV tOU nivQJ(o (l0ppound100 mr n ywvio) 10001 pov6 oEe 610~pound va K(tshy) (POi) KUta t o ouva rov J) KivlOle (~h tllOI e) lOU KpoundYtpOU BL_Hmiddot 6 8U L va 11ft impoundpoKEloGi] tv toutOIe nOIC lmqcllwshylUen 1(0vOtllC (npoo~npo) 1D C OeuroOIJIle A - B = 5 ER1 oja 5 ~(V(iOEe Ev OUVamptEI q KtVpoundltal tH KOe~tWe fie to tn6~IEoV 6pGOYWVl OV t ni r1t audic oti) I)e Koi npoypa~~ati~el IJ1TO wue OutoOe nEpI Op I0 I10Ue poundv 1Plj~O fit 6)oKArlPOV to unOAolshynov 10 6noioy OUlJnAlpwvpoundl til y laquo(~ilLTlOlYraquo LOU B Eq) OOOV l(afuIpOj) i lttl tl)ol~ OUtl POOi~poundl tie oPI ~ovti(Ue poundie to in6shyI1EVQV op90yciH IOV (tnt rl) e Out ne o u pue) KOt npoycoJJllulimiddot ltEI tOOUe ~ovooae (1101pound va KOAUqlOij il tntlOIe lOU r uvru innppoOpoundwc poundv toGtOI tne 01 poundK 1tpoundPOl Wtl Kie lKaV011l10e (npoOlpo pae) tiilt A - r ] 6noio ci TtOtEAd tUl o1t6 1Or n (o shyypa~~OlloOpound[O(Ic JlOv6boe Eie A - r 13 Ka A r r Kut uOtOv t OV tp6noy 1rpoXOJppoundi n e 6PI~ovtiwe- KOGttu Ewe lhou 1p6aOpoundl de to KoLW oPlOtEPOV opOoywv1ov t oO rrimiddot VO KO e (vOtlObutiKit Y(Qv(o) middot0 Upla~Oe toov oUJJnlpou~poundwv opOoywvlWY QVtlO1OlXOUVtWV Eie tOv oPIG~OV tooV POOl[(ooV ~IE1 a~Al)tWV TnC AUOEWe otov v6 poundlvul noVtOtE m + n - I ~LOI 5 -I-- 5 1 9 tylt) t o unCl Ao lno [6 ~n OU~IJrWwetVtO OpOOYWVW avtlOto lXOuv rie I(ie (iIJn paOIKoeraquo ~1)6rvlKc1~ JJCshylQ~Al)t6e
To o Io-Oy K6crLu t i) e trpIKtie OoolK I)e 1oune AUO(WC nposhyKUTtt t t 010 noAju n1oola(JIJOU t ampV npOYPuJJIJ(ITI08 cI0(tiv ~oshyYOOWV pi to ovti o-rOtXOV I-I0VUOWlov 1(OotO~ Eilt t 6 na poshybE l Y~O 6vtPCTOI t oOtO tie
Kill -= 176 l1ov6ooe xpl)~lntOe
EtIK P10H n) iIJocw 1(IU1le npoe 10 uno 2 ruppound9tv a1tOtE~ MOl1 a Or HivUF l OLl i) vea KUtOVOI1Tl poundi vOl iooouvo ~o OI[(OVOshypllcWi H~ npoKUntouOl KUHl ttl V OLOOOXU nv OI poundKTtpoundjuiuOIV Lie VIpoundPPo)
H CLpEG1ioo aiitl) laquo( POOIKn AUo tltraquo 0(-56AW o rc01poundAEt tTlv I3poundAtiotlV AllOIV roO Ttpon) TlJJotOe Mio t l(u jl1l0te tGw KEOV ltgtp90Ywv[wv 100 n[VOKOC KOl o tll V WeOOOv OlanEp al(i O t l ~ - -iLfpping- - - Lollc - i1 lOt 010 tile npooJTljlEWe de r ilv paolKilv )UOlV ~I ii ~Tl POcrtKi] ~EtoP1Tl1fle Kat onO)lOKpOVshyO EWC tK LOutllC )Ilfi~ POOlKlie t OIUU1llt orlKvurl 0n OOIOtO OVtrj va (hAtlw8u iIpoundPO ItEpW H i l(1IJJlo~lt n paYJJOton Olpound lLOt OIcJ ti) rrpOo9 Tl KIle poundi C CKOCrtOV KtVOV (I1Tl OUl1nAlpwJJEVOV) opGoyWvLOV JlllL 110 VOOO C we t~~j101 Oe tfi e pao IKe AUO poundWe lCoi 010 o tOp9wTu)e tooV OUl1n~TlPWlJtvwv o pGofwvi wv tn~ ~ooIKfie AumWe Kut6 1OIOCt Ov tPOrtOV won 01 OUVO a)K Ol rrpoundp IJryiotl lt Cltn OE WC Koi npooq)opiie We Kai 6 P10pou l ampV OuOtshyampv ~eurolaPAntGlv va tEaKo)oo9noouv lo xuouoUt n oC tOushy101e vnOAOYI~Eta l 10 KOOtO 10 6noTo y npOKunLtl pound10 ti UAshyAaya) c tOO ouvOU00l100 I(oi t o ono1poundis opa 1 iOEtOI poundIe 10 lno poundK t iJJlOIV bpOOYwvLOV Eltp ooov n pO KUlllJ opVI)1IKOV KOO1Oe dYOI ouVO t OV va OrAtlWOi) i a PXlKT] paOlKf1 AUOIe blo toll npoypoPIJOtIO~oi) IJ OVoowv Ete to eKtll11)9tv 69poywvLOv ~ Wl ehal OUVt[OV va ~poundIWO~ 10 6ALICOV K601Olt
Kani tliv tKt lPlOIV npoxwp Ei tie tK LOi) tK1lI1WI-I EVOU 6~90shyywv iou tn i tn C u tlh OEl PaC euro ogtc t6 pound1t OIJpoundYOV ou~rrAIlrUptshyVO V flOll op90YWVlOV to 6noiov f1tltPETtpoundl tilv JlfnieOOlv r~ EV I(U1poundIAl~~tvov 6p8 0(0lVl0V i ilt fn o~ltvl r mlpae Alll shyAO VOW C paoi~poundl ne rrO AIV OOI~o iwc KaOpoundtOOC KOK tK tOU poundvoe KaLpound l~jI poundOU op80ywviou EI~ to bOIJeurovOV t we chou tnovEAO) poundilt t o oPXIKOV opEloyWYIOV
OaguOpoundIYPu EKtijlrJOIi t Ou opeo)wv IO() A - Z B EiC 10 op80ytiVJov A - Z B 1tpoypal1)la1i ~ttol I1lU )IovOlt KtVnOCWe r) ono[o OI)I110Up)poundi tn nAeuroOV K60to lt [0 l1o v6owv XflllJJOtoeAshyKOAOllElWC npoxwppoundi tl lt 6pl COY tilrlc EWC to 6p90YWVlOV A - Z E 16 6rtotov poundnltptrrEI 111 V I1UOPOOl V de ~v Kate l)TlJJ~l tvov
710 Notl-PpIOC 1970
OPSOYWVIOV Ti)~ tnOJltv11t om pile A - E Kfli t)((HIOVII ta~ 1tpotpaJ1)1atIO~Ei n Ul elc 0[10 5 1-1 000(11 Kurd 1 010 qj 1-111 ( rrllp~ 1J IJ ItEP JloOI t fili Jt PoCJ(Pop6~ ri A - Z O OtlO f~O IK(lVO shy11OuVrCJl 5 l-o a6amp~ xprHla Hl( Ei TO OpOUYOWIO V A - E L~ npoati AItUl ~dCL IlovciC o ui va (JU)l1tllpwe~ Ii t ~t 1 01~ toO E (llttp 1t poKO ~ti 1(6a 1o~ 3 )lov6oS(raquo Karoltlv ~~u f i~Ll 1l 61)1shyo v tiw~ Eli t o Op90YO)llOll A _ E lICO (kOHlilVt1 tat tvwushySo iI (Ioypa~ql CITI OO fi CT(I~ JIOVDOU 1(U~61 I(QStt(J) Ii ~ to A - 6 il twi 1tpo OO ~Tf 1 Iliav povooa ItOAIV 6PI~OVli(CX d TO A - 6 r Ka ~huto tit to A - r r Kat t EA-Dt 6PI~OVTi~ti to A - r D s ui roG bn0 10u npIlYIJQto1totpoundItU1 n t1ll(Jtpo(l ~ eI to aPXIshyI( w o p90ywvIOv A - Z B To 0)_IK61 K6(n~ IhtpXa-tQI tit
KZB - K7E + Kr F - K EI~ + K~~ - K6r t-- Krl - KrB 10 - 5 -- 3 - 5 r 2 - 3 + 2 - 3 _ 1
1-1 TlI-lII OUTl -d 9E tQ1 tie to 0PSOYWVIOV A Z B Kat Qutov roV tpono v tK1IP()Vtal OAO ta Jn 0W lnAllPWJEVQ 6p90shyyii)vto KOt bIUU010OtOI Lav tlltpovi(oV1UI upvnweu tl]JQi Tilv JlrtUurEpuV upvrrcIICIl v tll-lTiv Qv1ll(uEhati TI ~ Ou) (cawv p oshyvdo ruv iioll Qnon)o()v t v )JIICPOlpoundPOV nocr6t11 tr~ Ti namICii Aua uv 6rcoiu ouvTlvtriOll f i t 6PI~OV TLUV Kf1tl68uVOI V Kltu titv I(U_II(IIV httl-ll)otv rou aVtlOt0 1XOU op90yulViou
niNA J (AuOI~ I)
I nI I Z (RRL)E1 fO I1IJ f~ H I A
A - B 5 + 2 + 4 + 4 + 11 5I A - f I 2 3+ 2 + 5 +8
A-A i O 6 -4 2 8- ~ 6
A - E 73 + 2 101 t 2 [ + 1 1 I
I 20 25A- Z + 1 - 2 5 Z
(BRL) 6 4 9 I 12 20 51 I I I El e t6 1tupao poundIY)Ju (1tlva 3) ~ JHpaVL~pound1(H il JIpoundyaAUtEpa opvl) shytlKri ttJlit - 2 de TO 6p8o-ywvlov A - Z I Aihll QvtlICo9ishyatara l 010 tfe 11J1fc 3 Ti 6rcola QrcoUM L lliv 1-l1lCrottpa y TlshyJlTlV Jl e ra~u tlOY tl]Joov 5 I(ui 3 t Oe ~aClIKfe AI(1EWe trie 6rroialt O llvuVtti tIe poundilt 6PLOV1iOV ttteueuvalV I(urri ttiv KUICAIKliv tlCtil-ll1alv 1oC opeoywviou A - Z I Ai (mO)OI1tOI lll-loi 1 1) t3uOHi~~ AUCIEUX npoClapI-l6~ovt Ul lwpa nAiov de til v tav T1)J~V tOO 6p90ymviou A - Z A SIU vo eculoAou6t1couv imiddot ClXUouGal at cruv91)IoOI KEpi )lE)i o-rl1 rcpocrql(l pii~ 11111 r napoundUlC Ka l CiP IOI-l Oi) T(OV a --C(Hxtiwv tqr AUOCWC In n - I a 9 DOno AalJ~6Vpoundtal ft AUcnlaquo 2 (nt ffle 4) fiiC 6rroiae to 6)d6v K60tOc QvfpX tal poundilaquo K~ = 170 I-lOv60ue EloICovoJwu]J~vwv 176 - 170 = 6 Jlovaooov havn rTje 1tPWTll ilXJEOOlt
n I N A=4 (AultJle 2)
n~ B
i I I I (ERL)ArAtal111 ZI
A - B 5 +4 + 4 I+ 9 5+ 2
A - f I 2 6 34- 1 I middot- 3
A - A + 0 2 6 -I ~ -1-4 I 8
A-B + 4 + 2 i 10 I t 21 10~ 2
A - 7 3 2+ 3 1- 3 20 I 25
Z (ERL) 4 12 20 516 I 9 I i
Mia tKtll-lllO IC t wv tOlnoov 1-1-1) al)~I1tATlpwetVtWV 6p90)wviwv TOU rrlvaKo 4 KUta la npoavatpt pgevtO OUlKVOEI 6tl oilv ElV(Ll
OUVOf i] lJin llEpUlteuroPW j3EATiwOlt Tf)e AUOEcu SIOll ouotv orgtshyeoywvlov Ant~avEI opVnuICTiV Ttl-lt1V nnDUt lpoUIJampV tv fOUshytol ~ (Il l pound)JltpuV1CtmiddottUI EiI T6 6peo(wVI0V A - a H n tljJIl 0 Ii ortoia ~Jo Ol~ETi pO (thtuil fI tlIwn 1lldl) cnltpbu1 tnV tnishyrtu~ t v t Tipo( luOf~ icroouvo]Joll OiKOV()I-lII~ rt 06 t1)V I3nshy01 t v Auenv 2 n p6rJUtt ilVtlI)OIOf-IV11~ lTiy lllJtiV 0 Oil tfj~ ttl-lil I I-lputqmt p c ra~ lampV ttl-lwV KUL f tf)c (JaOlKlle AtshycrEWe t(11I OUVCIV(WI-l t (ov d 6p(~o vtiuV Katt(Ouvalv 11 0 10
li]v 1CU1_l l(l)v - illnOlV tOl opeo)wvlou A - 1 B Kai ovashynpooapIJ 6~o~ t Jiy A(l(JIV 2 we I(at npon you]J cVWC poundupiol(oshyOICOp l V Titv Vtov I(CllUVOIJ V tOU nivOKoe 5 (Auollt 3) A Ull Itpo~Jvpoundl6AIK6V KOOtO K~ 170 POV(lSfOV middot Elot i~lnall Ili)v Ktv(bV opeoywv iu)V fliltl~ 6ioEI arrOICAtIOllKiigtlt epoundtIUO t l~IU ( A IiVIK9poundio(H IUOpoundI e 2 COL J QrcOnAOUV b W)JIvwc tao ~EAtishyalae KU tU VO~u tll KtvT10tW En looV imuPxouoGlv oea)J6lv
n I N A 5 (A0~ 3)
i (I RL)B f A Z ~ I n
tgt tCl l-ll1 E
5A - R [ 5 + Z 4 4 [ - 9 I
JO J I + 2 i + l 6 3A - f
8A - A I I 6 + 2[ +4
+4 + 3 +2 10 +2 10A - E
A-Z I -- J + 3 3 2 1 20 I 25
[ I (ERL) 6 4 9 51
1 12 1 20 I 4 ~LI p(ul(Jlfi TW anOTfA(OjJClTW
Efl) oaov nampUPIClKOI-lEVl) 010 tflt bpapIlOYfe toi) fpajJlJlKOD npo)puJ]JurICll-IoO ICa1av01-I1) ~l-llQaVi~t I-ltlCp61 fPOV K6o-r0l tvavll t OU UltPIOTQ~IEVOU K6C1ttH- tOtl Sll(tuOu elval OK6nII-lOV va t1ClUof1 KUto roio v worrov 8G TO OU VClTOV vei E1tLtfDXSt1 ft KUtaV0J-ltl lOrn t va ilTtlipu KuvOnOIltll(Il npoatr)IOIlt de al)tT)v ~AVEU o))u)11lt lfllt TCI VIKnr to) O1)CIlrilW-rO~ CClSishyltTt C11al 10Uto rro AA QKIlt ~ )vHt6V 01 6rU1K u i)ayl)lt tlr OEI t tUn Ol) tllIV OEapWy KCli ola[h(JaacUl4 dl~ unEPP0i)lt mO ot~ (J1JTj~ d~ lgtt(Jl-Il)v Ti]V 1t1pircthtOlV aimiv 90 t~CtQaWIJEV tni t i Pelo t l toO 6VIlltpEPetvtO~ rrapu5ei) lJutor
T6 UnOtiAEOI-ICl crrt toO niVul(o 4 DelievIIpound1 Ott KVl1ate foO KtvtpOU S Zn t~ 6 EHL OIfJnrPCtt OUHll I-l fOI) 1(lIV oe0l-loov A-B(5 FRL) KoiA-f(l EH L) ~ to f(4tI IL) t6)v 5cojJwv A - r (2 ER L) Ka i A - a (2 B H L) ft toU I (9 ERL) 11 tOW A- A (6 EHL) lto A- Z (J BRL) ~ toO E (12 EH L) s tilgtv A- E (10 ImiddotRL) Klli A- Z (2 ERL) ltviigt ~ t 00 Z (20 ERL) QnOKAElotll(iiX 010 tllt A - Z -H ICUtuVolln autl) ouvutUl Vo npoClqYI Cle~ Sui ~5aooXLKillt SUKrc ~ pallshyOew t ft o U1tE PPll~ l(utG 1f] v ClElpoV A - B A - r A - I A - Z Kai A - E A - Z middotYrOAOYICII-lamp tOU OAll(OO KGOtoolt Ut(l TO Ele 2 OElKVU fi lnpOYjlan 611 100TO IiEI OOtal El~ J72 vOshy1J100]JUlll(ae )J oVuB~ ne 1tp6lt tftV OPXIKIlV AUOIV ft AUOIe aut l) olUlPipCI Kata to Oll 11 U1tlppOn ffe opoundOI-lTle A - A 681)shy)poundITClI ICat cueerav Ete tnV 60011 tCIxotl1lt poundICOyfjpound A - Z napal(ul-lntol-ltv l1C tTjc ot ol-lne A - E
1-1 Kuravo]JY 100 rdvUKOe 5 nOPOUOliJ~EI 1-1(0 tiAAI1V ouvat6shy111Ta olaooXIICfC OIampK1tCpalciJCIEOllt -riiC I(Lvrionx I(Uta tftv crt lPOV
0) A - B A - A A - Z ~) A - r A - A A - Z ltoi y) A - E A - Z
T6 6AII(6v ICOO-roe tl)lt ua-cwlt TUUtl)C UVBC-Xftnl KUfO ttl de 2 EIC 171 5 vOIiICl]Jatl KtIC l-I-ovli5ult JlIKp6upov 1(010 11 tPCgt K6shyO1OUC li] C AUOE~ 3 EvtaOeu t1 UrclflP0 11 tne A tl 6ol))lishytal K(n EOeuroIeiav d niv OICfJUlV A - I no(wKrljl1tto]JEVI1e t il OtCllJn A - i 1 oe UItEPPOij t1lt A - 6 I(al EU6dav de 1nV A - Z (~)~ I(ai npol1you]JpoundVhl~
rEVIKU)lt 010 tU)V I-l ES60wv 100 rpa]J]JIKo() DpoYPuJl]Jano]Jo()
711 Notl-l~ploC 1910
Elval ouvat6v va 5lartlcto(81) tic cnJV8EtOV 5Ktuov OrtEPPOitlt Mv 11 rtPOOOlOPlC3Elcu lh QAAW V )le8oooov ii poundjlrteIPlte~C CEIshypo poundAiy(ou tU)v 5tc)l~v teal 5lEKrtfpUIWCEooc tFlc UrtEPPOtjC Elvol ~ EvSeOpoundIY)lEVn ItpoteuAoDoCl t6 poundAOXIIJWV KOcnolt EtC havdnv 1tpoundpirttOOOIV dVUL Suvatov va J-tfL(81) r6 OA11(0V 1(6shymo 51 oAAaytje r flc crfl pampe EAhxou cruIlCllltiwooC rtp6C t0 onoshylpound)ecl(l tflr 51lt1 tOO rpa)lIlII(OO npOypnI-lIlCltICJJOO rtPOcrOlOshypl~o)lelnlt 3poundldclne KUtalOpflc tflc I(lvncreooc
BlpLoypa+(a
I ChllTmann CW Adwlf R r 1 r1lQI ELmiddot Oj1erallons Reshyscarch Wlell-Muenl~bcn 19fi I
J(tr ll H OlHrll ions Rpellrlll ~ 1 llltgart 1966
I J(oldtl naln lt ( [lie EHllrli(dcrurg (it- FmlIrnmiddot(middothnClt( t~r i shylthtnlanoli in (11 ( WCltlS l ln ( I7 DI~rrtd l )o) Il 1 11 llnClI shyrJw ll 196ti
4 Kvgtt-i r AmllOllljlrocnlt Cal imo)o 1 [opo OvtojIO(IV HrO6 tllltlKlI() 0[1100 (Tt(VIIIU XPOIIo raquo Tll)X~ 110 1969
lox 1 r Elau(l)Y c(~ tOY rp(IlIIlK O npoypltlJPUftOl-Iov middotE)middot ) 1 FtUlPlU Eno t-lpnOW ti)v EpcvvW II] ) AOifll 19tfI
6 0gt11 r AI TftI Col fOC rpOlllJllIou npO(palIlU TIO IJ ol) poundI lYl poundru)o(t1 nil (rou(I(IgtI EE E f AOUI 1910
1 Saulll LT )llll lem l wal ~l elhod s ()f OHraUOns Resralch f cG raw-llill N(~ ltwk li~
Bestimmung der optimalen Verkehrsverteilung
In Ueberlauf - Fernsprechnetzen mit Hilfe
der linearen Programmierung
Von O Kokklnakll- G Karvdls
lCunfallung
lu einem Ueberlauf-FeruwohlneLz wird del Ve rkehr uber die Qu erbtindeJ hoher Ausnuzunlj und den LeLzweg gcrinshyger Verluslwahrscheinlichkeil nach eine r vorbetimmLen Reihenfolge abgewickelt womil e ine belrachlliche Verrinshygerung der gesamten max imalcn VermilLlungskosten ershyli eH wird im Ve rglei ch Zll jen en eines klassisch en Nelzes ohne Ueb~rlauls mciglj c hkeil des Vcrkehrs Durch Anwendu ng cler linearen Progtomm ierung auf ein
solches Nelz behandelt in d e l vorliegenden Arbeit ist es mogli ch di e wirl schartH ch optimale Aurteilung des Ver kehrs auf die Qu(wwr g-c und rlen R egelweg 2U bestimmen und durch V ergleirll mil d cr vorhondenen VelleiJung les tshyzus lellen ob finpound witn( Reduzierung rter maximoien Gesomtkos trn frrcichhol isl In diese m FaJl ist cs meistens mogli ch ~ich dt~r OJgt I imalcn crleilung durch ei nfache Aenshydcrllng-cn an rlcr Rrihfnrolge dcr Ueherlau[sab icklung nath den gr~(bni5sfn der lineltlren Programmicr llng ~ u n (l hern
bull (Cborll In Chlos (19 37) Dplom - Elektro ingcnleur der Te(llni$shychen lIocll~( lllllr ) l unlt1Hn (l 9B ) )1nitor - lngcnl l ur (19 66) und Dllllom~Wlrl sdians lnlZ (gtn irr ( 9(7) (t f ~t III (ln U och3ebuJe Sell 1961 wlilln~cJlarlllcht[ Mi1artwitf r 1m 1~ ()lIT( lln tlio llsn inl5tcrlurrL 111)(0 8eH 19liU ausrrnrrlrnUI(hcr Trorl~s l)r rur Prtll)larilrlchlfntechnik an der Tech nisrnen Fakullat der Unicnltl1l Pllras Er hal slclt in
Ka rllrlli1LIuP(hnlk und In Fla~cn nrr qrl$chanl lchen Plan ifi kaUon lind I TIlruIJlnH ngsr(lrselun~ I)(f lal~ i pound rl
IriJorrn In Kythlra (19 35) Olplom-Flektr ()illJen IElur d e l T erjmjs shy
hln lllt)ch ritHIr )tillI~hcn (El6 ) l1L I 96 hlll~ni ~llr ncr Cellrn ll lshyr hC1l Ilr itmIUlls-G cell scllarl (I) Bll) L it r def OrTI-K rtIifS hnrillih (19 70)
709 NotIJPpIO~ 1970
n)NA 2
il (j = ) n) 1
A Bn n po(t(j)opo
(i=[m) -[shy
A I Kl ] Ku K i ll
A --~Kil IKu [-- -I I---- a
A 1 11 middot- shy- 1shy
I------ -- shyAm Km1 (Km2 iKmn alii
_ oj _ -= - 1---- shy
I b
y
1 t I btl i a j = 1 bjj
np6~ATWO ppoundtarpopa~ t6 6rtofov onou Apoundi ClotKJ)v npoundpinlWOlY npoP)n~ato rpU~~1KoD npoypO~I~CI no-~ou
0 rpa~~IKoC npomiddot(pall~aHOpOc nGfHAOIJPUYpound1 npopiiUl(nu Ppound)lIGrOnolllO[(uC CLJtolpoundAOUI1EVCI poundK YPUJJIJ lK WV oUO tqpUtOO Y XapOKtl)pI01IKOV TOV1W V Ult01poundAfT TO -euro YOVO OIl 01 0 Lny tnl Auoi v tOOV OEY XPIlO l~ OnOIODtal KOnl t o n[iotOv aVUAUtlKUi jJt9000l )6Yltl tli tKHiopoundwC twv OACI a plO~IIFIKOi tn(tvushyjI)TtttKoi tOlOUtOI KO KULa Ka v6vu 0 OYIO~Oe TtlV(O(WV Oumiddot 10C 6 Tto-n4i t~Y Koiu IEpav ~tGooov npoltHnIOEtLe tltOVOAI) lt1lKI1J Kal aKplpou tvoqOJJtvwc t~lUPpoundOEWC tOO lfat Yto ot6xou el ~ Jtepin1wOIv npopn~ato nAEIOtWV IJf WpAl)rwv Kai I1 tYUAOO 6pI8~00 tlplKHiw AUOpoundWV WI TtC poundie 1nV nEpimiddot n1 WOlv (i npOtI7IWVraquo ~pound ov I06tl)10 Olo t ijc OUVpoundTtO~ t(pap shy~loyite OUOHW(ll IKWV AO(101lKampV Kuv6vwv
6lo 1O~ 1poundV1KUe nCplntWoW npop) Il~a1(uV rp(I~l1lKo(l nposhyYPO~I1UtlO~ Oi) anOnAti 1~ IJ1tO tOU O Danllig poundnlVo l9poundioa Simplex tTlv OIl~0VtlK0)tEPUV ~ E 900ov tHO tllV CiOlKil v mpimiddot ntWOlV tOOV npOnAlll-I(hwv IJpoundtaqlopae OVeuronlUx 01100 v ) )IE90shySo~ 1ite (CPOPE lOOUtl Kiic iWV10 t)~ - 010 Ti]V pound~EVPIltTlV JlOVOV ~l U OPX1Ki1 e POOlKfie Aooeltolt - ) 11pound9000lt o Ja7poundpollilo EWe laquoStep pi ng-Stoneraquo ill1t9000lt rodi ((todiried Oltrihtl shylion ileLh od) Kai ) OUYYPll(Jl I1t9000lt Enl jiofw El( LOushytwv Go XPllotJJorrolhow~poundv f a 000 rrpwlUC IldJoooIJC SU) 1llv t~poundUPpoundOIV 1i] c KO tOVO~it c KlVIl OEr~ Tl 6noio O-aLOtOltOLpoundl toe oon6yae poundIe 10 clva(j)rp9tv napOOSl)~a
Eov 1tapOot TlO(u~poundv pe Xu t ae npo PE1UIpOpQV ayvcJ)Otoue
no oOt l rae KI vnmwC Ete E RL IJtOIP 1 ~e St OI1 I)e i npoe to Ev shyIp OY J )o~j3Ovo~ poundv 10 OKoou90v OU01llUU t~IOWO(WV [[ Kai tnV n plle PCAtlo1onoilolv OiKOVO)llK Tl V ouvapulolv lll
~X II xu+ x11 + Xu + Xl = 5 X 11 + Xu + Xu ~ Xu -- X u = )
Xu + (32 - Xu - X H T xu= 8 i II X U + X n + lt I x~4 + X II = )0 Xu + xu+ Xu + X 6j + X = 25
Xu + Xl + Xu -- X 4 1 + Xl i = 6 XI~ + Xu + xn + X~ ~ - xu - 4
k I i I Xu + xs ~ + X t3 Xu = 9 Xu -0- Xu + X 3 ~ + Xu + X t t = 12
16 + X~I + X3~ X ~ ~ xu = 20
2xII + 3x I2 + 4x s + 4xl~ + 8x H + )x2 i 2xu + h2l + 4x h + 6x + 4X3 1 t 3xu 2X 3 3 + 4XH + 5x H 1 (III ) 9x H + 7xu - I- 5x H + 3x44 r 4XH + IOx u T 9xu I- 5xu + 5xu + 4x H = Z
EK lWV poundc l06loswv 1 0~ OUOtTlIlCltOe n III + n - I = 9 (VOl
aw~apttHo l OAAhwv 600poundvto fit on 0 OPI9IJoc ttoV OyvWshyOtWV rei) otlnth lJ01Oe 6vpoundP(poundtOI tie 25 U(JliOt01Ul nAila~ AU Gpoundwv FK 01)fU)V arroppimovwl ai ncpIpoundXouoOt lipvrJtlKae ttllae t(i)V (i yvWGtwV )tlI1 PavoJItvou o utW 1 OU OUVOAOU tooy laquo~nITpEn ampv Ii iQLKtooV AlIOEWVraquo) EK lOUtWY nO )IV 8tov va I1POOOIOP lOO1) I) H(3poundAT[otll ADm raquo ) tAuXlO tOnOl ouoa t~V oimiddot KOVOlJlKlV ouvap n lOlV [If
~Ia IJ1) Orvlollo U 25middot9 16 (IYVtiXHbJV )opp6vpoundTal OUOtn~llL 9 t~IOWOEWV I1 c ~ OYVWOTOUC nOpEXOY JJ lov laquopaO IKT]V AOOlVraquo M[u npoml (~q) 1 1n11 POOlKrP) AlIOte Aap~oVpoundtQl Ot6 tOo aKO )otJ90u KUYOVO~ li laquoPO Ppound1 00UTlKljc ywvi aeraquo Iu~q)cigtvw npOe t OOtOY npoY00J1IJOti Co l t(t1 poundtC 10 a vw oPIOtEpOV peOUVIOV tOU nivQJ(o (l0ppound100 mr n ywvio) 10001 pov6 oEe 610~pound va K(tshy) (POi) KUta t o ouva rov J) KivlOle (~h tllOI e) lOU KpoundYtpOU BL_Hmiddot 6 8U L va 11ft impoundpoKEloGi] tv toutOIe nOIC lmqcllwshylUen 1(0vOtllC (npoo~npo) 1D C OeuroOIJIle A - B = 5 ER1 oja 5 ~(V(iOEe Ev OUVamptEI q KtVpoundltal tH KOe~tWe fie to tn6~IEoV 6pGOYWVl OV t ni r1t audic oti) I)e Koi npoypa~~ati~el IJ1TO wue OutoOe nEpI Op I0 I10Ue poundv 1Plj~O fit 6)oKArlPOV to unOAolshynov 10 6noioy OUlJnAlpwvpoundl til y laquo(~ilLTlOlYraquo LOU B Eq) OOOV l(afuIpOj) i lttl tl)ol~ OUtl POOi~poundl tie oPI ~ovti(Ue poundie to in6shyI1EVQV op90yciH IOV (tnt rl) e Out ne o u pue) KOt npoycoJJllulimiddot ltEI tOOUe ~ovooae (1101pound va KOAUqlOij il tntlOIe lOU r uvru innppoOpoundwc poundv toGtOI tne 01 poundK 1tpoundPOl Wtl Kie lKaV011l10e (npoOlpo pae) tiilt A - r ] 6noio ci TtOtEAd tUl o1t6 1Or n (o shyypa~~OlloOpound[O(Ic JlOv6boe Eie A - r 13 Ka A r r Kut uOtOv t OV tp6noy 1rpoXOJppoundi n e 6PI~ovtiwe- KOGttu Ewe lhou 1p6aOpoundl de to KoLW oPlOtEPOV opOoywv1ov t oO rrimiddot VO KO e (vOtlObutiKit Y(Qv(o) middot0 Upla~Oe toov oUJJnlpou~poundwv opOoywvlWY QVtlO1OlXOUVtWV Eie tOv oPIG~OV tooV POOl[(ooV ~IE1 a~Al)tWV TnC AUOEWe otov v6 poundlvul noVtOtE m + n - I ~LOI 5 -I-- 5 1 9 tylt) t o unCl Ao lno [6 ~n OU~IJrWwetVtO OpOOYWVW avtlOto lXOuv rie I(ie (iIJn paOIKoeraquo ~1)6rvlKc1~ JJCshylQ~Al)t6e
To o Io-Oy K6crLu t i) e trpIKtie OoolK I)e 1oune AUO(WC nposhyKUTtt t t 010 noAju n1oola(JIJOU t ampV npOYPuJJIJ(ITI08 cI0(tiv ~oshyYOOWV pi to ovti o-rOtXOV I-I0VUOWlov 1(OotO~ Eilt t 6 na poshybE l Y~O 6vtPCTOI t oOtO tie
Kill -= 176 l1ov6ooe xpl)~lntOe
EtIK P10H n) iIJocw 1(IU1le npoe 10 uno 2 ruppound9tv a1tOtE~ MOl1 a Or HivUF l OLl i) vea KUtOVOI1Tl poundi vOl iooouvo ~o OI[(OVOshypllcWi H~ npoKUntouOl KUHl ttl V OLOOOXU nv OI poundKTtpoundjuiuOIV Lie VIpoundPPo)
H CLpEG1ioo aiitl) laquo( POOIKn AUo tltraquo 0(-56AW o rc01poundAEt tTlv I3poundAtiotlV AllOIV roO Ttpon) TlJJotOe Mio t l(u jl1l0te tGw KEOV ltgtp90Ywv[wv 100 n[VOKOC KOl o tll V WeOOOv OlanEp al(i O t l ~ - -iLfpping- - - Lollc - i1 lOt 010 tile npooJTljlEWe de r ilv paolKilv )UOlV ~I ii ~Tl POcrtKi] ~EtoP1Tl1fle Kat onO)lOKpOVshyO EWC tK LOutllC )Ilfi~ POOlKlie t OIUU1llt orlKvurl 0n OOIOtO OVtrj va (hAtlw8u iIpoundPO ItEpW H i l(1IJJlo~lt n paYJJOton Olpound lLOt OIcJ ti) rrpOo9 Tl KIle poundi C CKOCrtOV KtVOV (I1Tl OUl1nAlpwJJEVOV) opGoyWvLOV JlllL 110 VOOO C we t~~j101 Oe tfi e pao IKe AUO poundWe lCoi 010 o tOp9wTu)e tooV OUl1n~TlPWlJtvwv o pGofwvi wv tn~ ~ooIKfie AumWe Kut6 1OIOCt Ov tPOrtOV won 01 OUVO a)K Ol rrpoundp IJryiotl lt Cltn OE WC Koi npooq)opiie We Kai 6 P10pou l ampV OuOtshyampv ~eurolaPAntGlv va tEaKo)oo9noouv lo xuouoUt n oC tOushy101e vnOAOYI~Eta l 10 KOOtO 10 6noTo y npOKunLtl pound10 ti UAshyAaya) c tOO ouvOU00l100 I(oi t o ono1poundis opa 1 iOEtOI poundIe 10 lno poundK t iJJlOIV bpOOYwvLOV Eltp ooov n pO KUlllJ opVI)1IKOV KOO1Oe dYOI ouVO t OV va OrAtlWOi) i a PXlKT] paOlKf1 AUOIe blo toll npoypoPIJOtIO~oi) IJ OVoowv Ete to eKtll11)9tv 69poywvLOv ~ Wl ehal OUVt[OV va ~poundIWO~ 10 6ALICOV K601Olt
Kani tliv tKt lPlOIV npoxwp Ei tie tK LOi) tK1lI1WI-I EVOU 6~90shyywv iou tn i tn C u tlh OEl PaC euro ogtc t6 pound1t OIJpoundYOV ou~rrAIlrUptshyVO V flOll op90YWVlOV to 6noiov f1tltPETtpoundl tilv JlfnieOOlv r~ EV I(U1poundIAl~~tvov 6p8 0(0lVl0V i ilt fn o~ltvl r mlpae Alll shyAO VOW C paoi~poundl ne rrO AIV OOI~o iwc KaOpoundtOOC KOK tK tOU poundvoe KaLpound l~jI poundOU op80ywviou EI~ to bOIJeurovOV t we chou tnovEAO) poundilt t o oPXIKOV opEloyWYIOV
OaguOpoundIYPu EKtijlrJOIi t Ou opeo)wv IO() A - Z B EiC 10 op80ytiVJov A - Z B 1tpoypal1)la1i ~ttol I1lU )IovOlt KtVnOCWe r) ono[o OI)I110Up)poundi tn nAeuroOV K60to lt [0 l1o v6owv XflllJJOtoeAshyKOAOllElWC npoxwppoundi tl lt 6pl COY tilrlc EWC to 6p90YWVlOV A - Z E 16 6rtotov poundnltptrrEI 111 V I1UOPOOl V de ~v Kate l)TlJJ~l tvov
710 Notl-PpIOC 1970
OPSOYWVIOV Ti)~ tnOJltv11t om pile A - E Kfli t)((HIOVII ta~ 1tpotpaJ1)1atIO~Ei n Ul elc 0[10 5 1-1 000(11 Kurd 1 010 qj 1-111 ( rrllp~ 1J IJ ItEP JloOI t fili Jt PoCJ(Pop6~ ri A - Z O OtlO f~O IK(lVO shy11OuVrCJl 5 l-o a6amp~ xprHla Hl( Ei TO OpOUYOWIO V A - E L~ npoati AItUl ~dCL IlovciC o ui va (JU)l1tllpwe~ Ii t ~t 1 01~ toO E (llttp 1t poKO ~ti 1(6a 1o~ 3 )lov6oS(raquo Karoltlv ~~u f i~Ll 1l 61)1shyo v tiw~ Eli t o Op90YO)llOll A _ E lICO (kOHlilVt1 tat tvwushySo iI (Ioypa~ql CITI OO fi CT(I~ JIOVDOU 1(U~61 I(QStt(J) Ii ~ to A - 6 il twi 1tpo OO ~Tf 1 Iliav povooa ItOAIV 6PI~OVli(CX d TO A - 6 r Ka ~huto tit to A - r r Kat t EA-Dt 6PI~OVTi~ti to A - r D s ui roG bn0 10u npIlYIJQto1totpoundItU1 n t1ll(Jtpo(l ~ eI to aPXIshyI( w o p90ywvIOv A - Z B To 0)_IK61 K6(n~ IhtpXa-tQI tit
KZB - K7E + Kr F - K EI~ + K~~ - K6r t-- Krl - KrB 10 - 5 -- 3 - 5 r 2 - 3 + 2 - 3 _ 1
1-1 TlI-lII OUTl -d 9E tQ1 tie to 0PSOYWVIOV A Z B Kat Qutov roV tpono v tK1IP()Vtal OAO ta Jn 0W lnAllPWJEVQ 6p90shyyii)vto KOt bIUU010OtOI Lav tlltpovi(oV1UI upvnweu tl]JQi Tilv JlrtUurEpuV upvrrcIICIl v tll-lTiv Qv1ll(uEhati TI ~ Ou) (cawv p oshyvdo ruv iioll Qnon)o()v t v )JIICPOlpoundPOV nocr6t11 tr~ Ti namICii Aua uv 6rcoiu ouvTlvtriOll f i t 6PI~OV TLUV Kf1tl68uVOI V Kltu titv I(U_II(IIV httl-ll)otv rou aVtlOt0 1XOU op90yulViou
niNA J (AuOI~ I)
I nI I Z (RRL)E1 fO I1IJ f~ H I A
A - B 5 + 2 + 4 + 4 + 11 5I A - f I 2 3+ 2 + 5 +8
A-A i O 6 -4 2 8- ~ 6
A - E 73 + 2 101 t 2 [ + 1 1 I
I 20 25A- Z + 1 - 2 5 Z
(BRL) 6 4 9 I 12 20 51 I I I El e t6 1tupao poundIY)Ju (1tlva 3) ~ JHpaVL~pound1(H il JIpoundyaAUtEpa opvl) shytlKri ttJlit - 2 de TO 6p8o-ywvlov A - Z I Aihll QvtlICo9ishyatara l 010 tfe 11J1fc 3 Ti 6rcola QrcoUM L lliv 1-l1lCrottpa y TlshyJlTlV Jl e ra~u tlOY tl]Joov 5 I(ui 3 t Oe ~aClIKfe AI(1EWe trie 6rroialt O llvuVtti tIe poundilt 6PLOV1iOV ttteueuvalV I(urri ttiv KUICAIKliv tlCtil-ll1alv 1oC opeoywviou A - Z I Ai (mO)OI1tOI lll-loi 1 1) t3uOHi~~ AUCIEUX npoClapI-l6~ovt Ul lwpa nAiov de til v tav T1)J~V tOO 6p90ymviou A - Z A SIU vo eculoAou6t1couv imiddot ClXUouGal at cruv91)IoOI KEpi )lE)i o-rl1 rcpocrql(l pii~ 11111 r napoundUlC Ka l CiP IOI-l Oi) T(OV a --C(Hxtiwv tqr AUOCWC In n - I a 9 DOno AalJ~6Vpoundtal ft AUcnlaquo 2 (nt ffle 4) fiiC 6rroiae to 6)d6v K60tOc QvfpX tal poundilaquo K~ = 170 I-lOv60ue EloICovoJwu]J~vwv 176 - 170 = 6 Jlovaooov havn rTje 1tPWTll ilXJEOOlt
n I N A=4 (AultJle 2)
n~ B
i I I I (ERL)ArAtal111 ZI
A - B 5 +4 + 4 I+ 9 5+ 2
A - f I 2 6 34- 1 I middot- 3
A - A + 0 2 6 -I ~ -1-4 I 8
A-B + 4 + 2 i 10 I t 21 10~ 2
A - 7 3 2+ 3 1- 3 20 I 25
Z (ERL) 4 12 20 516 I 9 I i
Mia tKtll-lllO IC t wv tOlnoov 1-1-1) al)~I1tATlpwetVtWV 6p90)wviwv TOU rrlvaKo 4 KUta la npoavatpt pgevtO OUlKVOEI 6tl oilv ElV(Ll
OUVOf i] lJin llEpUlteuroPW j3EATiwOlt Tf)e AUOEcu SIOll ouotv orgtshyeoywvlov Ant~avEI opVnuICTiV Ttl-lt1V nnDUt lpoUIJampV tv fOUshytol ~ (Il l pound)JltpuV1CtmiddottUI EiI T6 6peo(wVI0V A - a H n tljJIl 0 Ii ortoia ~Jo Ol~ETi pO (thtuil fI tlIwn 1lldl) cnltpbu1 tnV tnishyrtu~ t v t Tipo( luOf~ icroouvo]Joll OiKOV()I-lII~ rt 06 t1)V I3nshy01 t v Auenv 2 n p6rJUtt ilVtlI)OIOf-IV11~ lTiy lllJtiV 0 Oil tfj~ ttl-lil I I-lputqmt p c ra~ lampV ttl-lwV KUL f tf)c (JaOlKlle AtshycrEWe t(11I OUVCIV(WI-l t (ov d 6p(~o vtiuV Katt(Ouvalv 11 0 10
li]v 1CU1_l l(l)v - illnOlV tOl opeo)wvlou A - 1 B Kai ovashynpooapIJ 6~o~ t Jiy A(l(JIV 2 we I(at npon you]J cVWC poundupiol(oshyOICOp l V Titv Vtov I(CllUVOIJ V tOU nivOKoe 5 (Auollt 3) A Ull Itpo~Jvpoundl6AIK6V KOOtO K~ 170 POV(lSfOV middot Elot i~lnall Ili)v Ktv(bV opeoywv iu)V fliltl~ 6ioEI arrOICAtIOllKiigtlt epoundtIUO t l~IU ( A IiVIK9poundio(H IUOpoundI e 2 COL J QrcOnAOUV b W)JIvwc tao ~EAtishyalae KU tU VO~u tll KtvT10tW En looV imuPxouoGlv oea)J6lv
n I N A 5 (A0~ 3)
i (I RL)B f A Z ~ I n
tgt tCl l-ll1 E
5A - R [ 5 + Z 4 4 [ - 9 I
JO J I + 2 i + l 6 3A - f
8A - A I I 6 + 2[ +4
+4 + 3 +2 10 +2 10A - E
A-Z I -- J + 3 3 2 1 20 I 25
[ I (ERL) 6 4 9 51
1 12 1 20 I 4 ~LI p(ul(Jlfi TW anOTfA(OjJClTW
Efl) oaov nampUPIClKOI-lEVl) 010 tflt bpapIlOYfe toi) fpajJlJlKOD npo)puJ]JurICll-IoO ICa1av01-I1) ~l-llQaVi~t I-ltlCp61 fPOV K6o-r0l tvavll t OU UltPIOTQ~IEVOU K6C1ttH- tOtl Sll(tuOu elval OK6nII-lOV va t1ClUof1 KUto roio v worrov 8G TO OU VClTOV vei E1tLtfDXSt1 ft KUtaV0J-ltl lOrn t va ilTtlipu KuvOnOIltll(Il npoatr)IOIlt de al)tT)v ~AVEU o))u)11lt lfllt TCI VIKnr to) O1)CIlrilW-rO~ CClSishyltTt C11al 10Uto rro AA QKIlt ~ )vHt6V 01 6rU1K u i)ayl)lt tlr OEI t tUn Ol) tllIV OEapWy KCli ola[h(JaacUl4 dl~ unEPP0i)lt mO ot~ (J1JTj~ d~ lgtt(Jl-Il)v Ti]V 1t1pircthtOlV aimiv 90 t~CtQaWIJEV tni t i Pelo t l toO 6VIlltpEPetvtO~ rrapu5ei) lJutor
T6 UnOtiAEOI-ICl crrt toO niVul(o 4 DelievIIpound1 Ott KVl1ate foO KtvtpOU S Zn t~ 6 EHL OIfJnrPCtt OUHll I-l fOI) 1(lIV oe0l-loov A-B(5 FRL) KoiA-f(l EH L) ~ to f(4tI IL) t6)v 5cojJwv A - r (2 ER L) Ka i A - a (2 B H L) ft toU I (9 ERL) 11 tOW A- A (6 EHL) lto A- Z (J BRL) ~ toO E (12 EH L) s tilgtv A- E (10 ImiddotRL) Klli A- Z (2 ERL) ltviigt ~ t 00 Z (20 ERL) QnOKAElotll(iiX 010 tllt A - Z -H ICUtuVolln autl) ouvutUl Vo npoClqYI Cle~ Sui ~5aooXLKillt SUKrc ~ pallshyOew t ft o U1tE PPll~ l(utG 1f] v ClElpoV A - B A - r A - I A - Z Kai A - E A - Z middotYrOAOYICII-lamp tOU OAll(OO KGOtoolt Ut(l TO Ele 2 OElKVU fi lnpOYjlan 611 100TO IiEI OOtal El~ J72 vOshy1J100]JUlll(ae )J oVuB~ ne 1tp6lt tftV OPXIKIlV AUOIV ft AUOIe aut l) olUlPipCI Kata to Oll 11 U1tlppOn ffe opoundOI-lTle A - A 681)shy)poundITClI ICat cueerav Ete tnV 60011 tCIxotl1lt poundICOyfjpound A - Z napal(ul-lntol-ltv l1C tTjc ot ol-lne A - E
1-1 Kuravo]JY 100 rdvUKOe 5 nOPOUOliJ~EI 1-1(0 tiAAI1V ouvat6shy111Ta olaooXIICfC OIampK1tCpalciJCIEOllt -riiC I(Lvrionx I(Uta tftv crt lPOV
0) A - B A - A A - Z ~) A - r A - A A - Z ltoi y) A - E A - Z
T6 6AII(6v ICOO-roe tl)lt ua-cwlt TUUtl)C UVBC-Xftnl KUfO ttl de 2 EIC 171 5 vOIiICl]Jatl KtIC l-I-ovli5ult JlIKp6upov 1(010 11 tPCgt K6shyO1OUC li] C AUOE~ 3 EvtaOeu t1 UrclflP0 11 tne A tl 6ol))lishytal K(n EOeuroIeiav d niv OICfJUlV A - I no(wKrljl1tto]JEVI1e t il OtCllJn A - i 1 oe UItEPPOij t1lt A - 6 I(al EU6dav de 1nV A - Z (~)~ I(ai npol1you]JpoundVhl~
rEVIKU)lt 010 tU)V I-l ES60wv 100 rpa]J]JIKo() DpoYPuJl]Jano]Jo()
711 Notl-l~ploC 1910
Elval ouvat6v va 5lartlcto(81) tic cnJV8EtOV 5Ktuov OrtEPPOitlt Mv 11 rtPOOOlOPlC3Elcu lh QAAW V )le8oooov ii poundjlrteIPlte~C CEIshypo poundAiy(ou tU)v 5tc)l~v teal 5lEKrtfpUIWCEooc tFlc UrtEPPOtjC Elvol ~ EvSeOpoundIY)lEVn ItpoteuAoDoCl t6 poundAOXIIJWV KOcnolt EtC havdnv 1tpoundpirttOOOIV dVUL Suvatov va J-tfL(81) r6 OA11(0V 1(6shymo 51 oAAaytje r flc crfl pampe EAhxou cruIlCllltiwooC rtp6C t0 onoshylpound)ecl(l tflr 51lt1 tOO rpa)lIlII(OO npOypnI-lIlCltICJJOO rtPOcrOlOshypl~o)lelnlt 3poundldclne KUtalOpflc tflc I(lvncreooc
BlpLoypa+(a
I ChllTmann CW Adwlf R r 1 r1lQI ELmiddot Oj1erallons Reshyscarch Wlell-Muenl~bcn 19fi I
J(tr ll H OlHrll ions Rpellrlll ~ 1 llltgart 1966
I J(oldtl naln lt ( [lie EHllrli(dcrurg (it- FmlIrnmiddot(middothnClt( t~r i shylthtnlanoli in (11 ( WCltlS l ln ( I7 DI~rrtd l )o) Il 1 11 llnClI shyrJw ll 196ti
4 Kvgtt-i r AmllOllljlrocnlt Cal imo)o 1 [opo OvtojIO(IV HrO6 tllltlKlI() 0[1100 (Tt(VIIIU XPOIIo raquo Tll)X~ 110 1969
lox 1 r Elau(l)Y c(~ tOY rp(IlIIlK O npoypltlJPUftOl-Iov middotE)middot ) 1 FtUlPlU Eno t-lpnOW ti)v EpcvvW II] ) AOifll 19tfI
6 0gt11 r AI TftI Col fOC rpOlllJllIou npO(palIlU TIO IJ ol) poundI lYl poundru)o(t1 nil (rou(I(IgtI EE E f AOUI 1910
1 Saulll LT )llll lem l wal ~l elhod s ()f OHraUOns Resralch f cG raw-llill N(~ ltwk li~
Bestimmung der optimalen Verkehrsverteilung
In Ueberlauf - Fernsprechnetzen mit Hilfe
der linearen Programmierung
Von O Kokklnakll- G Karvdls
lCunfallung
lu einem Ueberlauf-FeruwohlneLz wird del Ve rkehr uber die Qu erbtindeJ hoher Ausnuzunlj und den LeLzweg gcrinshyger Verluslwahrscheinlichkeil nach eine r vorbetimmLen Reihenfolge abgewickelt womil e ine belrachlliche Verrinshygerung der gesamten max imalcn VermilLlungskosten ershyli eH wird im Ve rglei ch Zll jen en eines klassisch en Nelzes ohne Ueb~rlauls mciglj c hkeil des Vcrkehrs Durch Anwendu ng cler linearen Progtomm ierung auf ein
solches Nelz behandelt in d e l vorliegenden Arbeit ist es mogli ch di e wirl schartH ch optimale Aurteilung des Ver kehrs auf die Qu(wwr g-c und rlen R egelweg 2U bestimmen und durch V ergleirll mil d cr vorhondenen VelleiJung les tshyzus lellen ob finpound witn( Reduzierung rter maximoien Gesomtkos trn frrcichhol isl In diese m FaJl ist cs meistens mogli ch ~ich dt~r OJgt I imalcn crleilung durch ei nfache Aenshydcrllng-cn an rlcr Rrihfnrolge dcr Ueherlau[sab icklung nath den gr~(bni5sfn der lineltlren Programmicr llng ~ u n (l hern
bull (Cborll In Chlos (19 37) Dplom - Elektro ingcnleur der Te(llni$shychen lIocll~( lllllr ) l unlt1Hn (l 9B ) )1nitor - lngcnl l ur (19 66) und Dllllom~Wlrl sdians lnlZ (gtn irr ( 9(7) (t f ~t III (ln U och3ebuJe Sell 1961 wlilln~cJlarlllcht[ Mi1artwitf r 1m 1~ ()lIT( lln tlio llsn inl5tcrlurrL 111)(0 8eH 19liU ausrrnrrlrnUI(hcr Trorl~s l)r rur Prtll)larilrlchlfntechnik an der Tech nisrnen Fakullat der Unicnltl1l Pllras Er hal slclt in
Ka rllrlli1LIuP(hnlk und In Fla~cn nrr qrl$chanl lchen Plan ifi kaUon lind I TIlruIJlnH ngsr(lrselun~ I)(f lal~ i pound rl
IriJorrn In Kythlra (19 35) Olplom-Flektr ()illJen IElur d e l T erjmjs shy
hln lllt)ch ritHIr )tillI~hcn (El6 ) l1L I 96 hlll~ni ~llr ncr Cellrn ll lshyr hC1l Ilr itmIUlls-G cell scllarl (I) Bll) L it r def OrTI-K rtIifS hnrillih (19 70)
710 Notl-PpIOC 1970
OPSOYWVIOV Ti)~ tnOJltv11t om pile A - E Kfli t)((HIOVII ta~ 1tpotpaJ1)1atIO~Ei n Ul elc 0[10 5 1-1 000(11 Kurd 1 010 qj 1-111 ( rrllp~ 1J IJ ItEP JloOI t fili Jt PoCJ(Pop6~ ri A - Z O OtlO f~O IK(lVO shy11OuVrCJl 5 l-o a6amp~ xprHla Hl( Ei TO OpOUYOWIO V A - E L~ npoati AItUl ~dCL IlovciC o ui va (JU)l1tllpwe~ Ii t ~t 1 01~ toO E (llttp 1t poKO ~ti 1(6a 1o~ 3 )lov6oS(raquo Karoltlv ~~u f i~Ll 1l 61)1shyo v tiw~ Eli t o Op90YO)llOll A _ E lICO (kOHlilVt1 tat tvwushySo iI (Ioypa~ql CITI OO fi CT(I~ JIOVDOU 1(U~61 I(QStt(J) Ii ~ to A - 6 il twi 1tpo OO ~Tf 1 Iliav povooa ItOAIV 6PI~OVli(CX d TO A - 6 r Ka ~huto tit to A - r r Kat t EA-Dt 6PI~OVTi~ti to A - r D s ui roG bn0 10u npIlYIJQto1totpoundItU1 n t1ll(Jtpo(l ~ eI to aPXIshyI( w o p90ywvIOv A - Z B To 0)_IK61 K6(n~ IhtpXa-tQI tit
KZB - K7E + Kr F - K EI~ + K~~ - K6r t-- Krl - KrB 10 - 5 -- 3 - 5 r 2 - 3 + 2 - 3 _ 1
1-1 TlI-lII OUTl -d 9E tQ1 tie to 0PSOYWVIOV A Z B Kat Qutov roV tpono v tK1IP()Vtal OAO ta Jn 0W lnAllPWJEVQ 6p90shyyii)vto KOt bIUU010OtOI Lav tlltpovi(oV1UI upvnweu tl]JQi Tilv JlrtUurEpuV upvrrcIICIl v tll-lTiv Qv1ll(uEhati TI ~ Ou) (cawv p oshyvdo ruv iioll Qnon)o()v t v )JIICPOlpoundPOV nocr6t11 tr~ Ti namICii Aua uv 6rcoiu ouvTlvtriOll f i t 6PI~OV TLUV Kf1tl68uVOI V Kltu titv I(U_II(IIV httl-ll)otv rou aVtlOt0 1XOU op90yulViou
niNA J (AuOI~ I)
I nI I Z (RRL)E1 fO I1IJ f~ H I A
A - B 5 + 2 + 4 + 4 + 11 5I A - f I 2 3+ 2 + 5 +8
A-A i O 6 -4 2 8- ~ 6
A - E 73 + 2 101 t 2 [ + 1 1 I
I 20 25A- Z + 1 - 2 5 Z
(BRL) 6 4 9 I 12 20 51 I I I El e t6 1tupao poundIY)Ju (1tlva 3) ~ JHpaVL~pound1(H il JIpoundyaAUtEpa opvl) shytlKri ttJlit - 2 de TO 6p8o-ywvlov A - Z I Aihll QvtlICo9ishyatara l 010 tfe 11J1fc 3 Ti 6rcola QrcoUM L lliv 1-l1lCrottpa y TlshyJlTlV Jl e ra~u tlOY tl]Joov 5 I(ui 3 t Oe ~aClIKfe AI(1EWe trie 6rroialt O llvuVtti tIe poundilt 6PLOV1iOV ttteueuvalV I(urri ttiv KUICAIKliv tlCtil-ll1alv 1oC opeoywviou A - Z I Ai (mO)OI1tOI lll-loi 1 1) t3uOHi~~ AUCIEUX npoClapI-l6~ovt Ul lwpa nAiov de til v tav T1)J~V tOO 6p90ymviou A - Z A SIU vo eculoAou6t1couv imiddot ClXUouGal at cruv91)IoOI KEpi )lE)i o-rl1 rcpocrql(l pii~ 11111 r napoundUlC Ka l CiP IOI-l Oi) T(OV a --C(Hxtiwv tqr AUOCWC In n - I a 9 DOno AalJ~6Vpoundtal ft AUcnlaquo 2 (nt ffle 4) fiiC 6rroiae to 6)d6v K60tOc QvfpX tal poundilaquo K~ = 170 I-lOv60ue EloICovoJwu]J~vwv 176 - 170 = 6 Jlovaooov havn rTje 1tPWTll ilXJEOOlt
n I N A=4 (AultJle 2)
n~ B
i I I I (ERL)ArAtal111 ZI
A - B 5 +4 + 4 I+ 9 5+ 2
A - f I 2 6 34- 1 I middot- 3
A - A + 0 2 6 -I ~ -1-4 I 8
A-B + 4 + 2 i 10 I t 21 10~ 2
A - 7 3 2+ 3 1- 3 20 I 25
Z (ERL) 4 12 20 516 I 9 I i
Mia tKtll-lllO IC t wv tOlnoov 1-1-1) al)~I1tATlpwetVtWV 6p90)wviwv TOU rrlvaKo 4 KUta la npoavatpt pgevtO OUlKVOEI 6tl oilv ElV(Ll
OUVOf i] lJin llEpUlteuroPW j3EATiwOlt Tf)e AUOEcu SIOll ouotv orgtshyeoywvlov Ant~avEI opVnuICTiV Ttl-lt1V nnDUt lpoUIJampV tv fOUshytol ~ (Il l pound)JltpuV1CtmiddottUI EiI T6 6peo(wVI0V A - a H n tljJIl 0 Ii ortoia ~Jo Ol~ETi pO (thtuil fI tlIwn 1lldl) cnltpbu1 tnV tnishyrtu~ t v t Tipo( luOf~ icroouvo]Joll OiKOV()I-lII~ rt 06 t1)V I3nshy01 t v Auenv 2 n p6rJUtt ilVtlI)OIOf-IV11~ lTiy lllJtiV 0 Oil tfj~ ttl-lil I I-lputqmt p c ra~ lampV ttl-lwV KUL f tf)c (JaOlKlle AtshycrEWe t(11I OUVCIV(WI-l t (ov d 6p(~o vtiuV Katt(Ouvalv 11 0 10
li]v 1CU1_l l(l)v - illnOlV tOl opeo)wvlou A - 1 B Kai ovashynpooapIJ 6~o~ t Jiy A(l(JIV 2 we I(at npon you]J cVWC poundupiol(oshyOICOp l V Titv Vtov I(CllUVOIJ V tOU nivOKoe 5 (Auollt 3) A Ull Itpo~Jvpoundl6AIK6V KOOtO K~ 170 POV(lSfOV middot Elot i~lnall Ili)v Ktv(bV opeoywv iu)V fliltl~ 6ioEI arrOICAtIOllKiigtlt epoundtIUO t l~IU ( A IiVIK9poundio(H IUOpoundI e 2 COL J QrcOnAOUV b W)JIvwc tao ~EAtishyalae KU tU VO~u tll KtvT10tW En looV imuPxouoGlv oea)J6lv
n I N A 5 (A0~ 3)
i (I RL)B f A Z ~ I n
tgt tCl l-ll1 E
5A - R [ 5 + Z 4 4 [ - 9 I
JO J I + 2 i + l 6 3A - f
8A - A I I 6 + 2[ +4
+4 + 3 +2 10 +2 10A - E
A-Z I -- J + 3 3 2 1 20 I 25
[ I (ERL) 6 4 9 51
1 12 1 20 I 4 ~LI p(ul(Jlfi TW anOTfA(OjJClTW
Efl) oaov nampUPIClKOI-lEVl) 010 tflt bpapIlOYfe toi) fpajJlJlKOD npo)puJ]JurICll-IoO ICa1av01-I1) ~l-llQaVi~t I-ltlCp61 fPOV K6o-r0l tvavll t OU UltPIOTQ~IEVOU K6C1ttH- tOtl Sll(tuOu elval OK6nII-lOV va t1ClUof1 KUto roio v worrov 8G TO OU VClTOV vei E1tLtfDXSt1 ft KUtaV0J-ltl lOrn t va ilTtlipu KuvOnOIltll(Il npoatr)IOIlt de al)tT)v ~AVEU o))u)11lt lfllt TCI VIKnr to) O1)CIlrilW-rO~ CClSishyltTt C11al 10Uto rro AA QKIlt ~ )vHt6V 01 6rU1K u i)ayl)lt tlr OEI t tUn Ol) tllIV OEapWy KCli ola[h(JaacUl4 dl~ unEPP0i)lt mO ot~ (J1JTj~ d~ lgtt(Jl-Il)v Ti]V 1t1pircthtOlV aimiv 90 t~CtQaWIJEV tni t i Pelo t l toO 6VIlltpEPetvtO~ rrapu5ei) lJutor
T6 UnOtiAEOI-ICl crrt toO niVul(o 4 DelievIIpound1 Ott KVl1ate foO KtvtpOU S Zn t~ 6 EHL OIfJnrPCtt OUHll I-l fOI) 1(lIV oe0l-loov A-B(5 FRL) KoiA-f(l EH L) ~ to f(4tI IL) t6)v 5cojJwv A - r (2 ER L) Ka i A - a (2 B H L) ft toU I (9 ERL) 11 tOW A- A (6 EHL) lto A- Z (J BRL) ~ toO E (12 EH L) s tilgtv A- E (10 ImiddotRL) Klli A- Z (2 ERL) ltviigt ~ t 00 Z (20 ERL) QnOKAElotll(iiX 010 tllt A - Z -H ICUtuVolln autl) ouvutUl Vo npoClqYI Cle~ Sui ~5aooXLKillt SUKrc ~ pallshyOew t ft o U1tE PPll~ l(utG 1f] v ClElpoV A - B A - r A - I A - Z Kai A - E A - Z middotYrOAOYICII-lamp tOU OAll(OO KGOtoolt Ut(l TO Ele 2 OElKVU fi lnpOYjlan 611 100TO IiEI OOtal El~ J72 vOshy1J100]JUlll(ae )J oVuB~ ne 1tp6lt tftV OPXIKIlV AUOIV ft AUOIe aut l) olUlPipCI Kata to Oll 11 U1tlppOn ffe opoundOI-lTle A - A 681)shy)poundITClI ICat cueerav Ete tnV 60011 tCIxotl1lt poundICOyfjpound A - Z napal(ul-lntol-ltv l1C tTjc ot ol-lne A - E
1-1 Kuravo]JY 100 rdvUKOe 5 nOPOUOliJ~EI 1-1(0 tiAAI1V ouvat6shy111Ta olaooXIICfC OIampK1tCpalciJCIEOllt -riiC I(Lvrionx I(Uta tftv crt lPOV
0) A - B A - A A - Z ~) A - r A - A A - Z ltoi y) A - E A - Z
T6 6AII(6v ICOO-roe tl)lt ua-cwlt TUUtl)C UVBC-Xftnl KUfO ttl de 2 EIC 171 5 vOIiICl]Jatl KtIC l-I-ovli5ult JlIKp6upov 1(010 11 tPCgt K6shyO1OUC li] C AUOE~ 3 EvtaOeu t1 UrclflP0 11 tne A tl 6ol))lishytal K(n EOeuroIeiav d niv OICfJUlV A - I no(wKrljl1tto]JEVI1e t il OtCllJn A - i 1 oe UItEPPOij t1lt A - 6 I(al EU6dav de 1nV A - Z (~)~ I(ai npol1you]JpoundVhl~
rEVIKU)lt 010 tU)V I-l ES60wv 100 rpa]J]JIKo() DpoYPuJl]Jano]Jo()
711 Notl-l~ploC 1910
Elval ouvat6v va 5lartlcto(81) tic cnJV8EtOV 5Ktuov OrtEPPOitlt Mv 11 rtPOOOlOPlC3Elcu lh QAAW V )le8oooov ii poundjlrteIPlte~C CEIshypo poundAiy(ou tU)v 5tc)l~v teal 5lEKrtfpUIWCEooc tFlc UrtEPPOtjC Elvol ~ EvSeOpoundIY)lEVn ItpoteuAoDoCl t6 poundAOXIIJWV KOcnolt EtC havdnv 1tpoundpirttOOOIV dVUL Suvatov va J-tfL(81) r6 OA11(0V 1(6shymo 51 oAAaytje r flc crfl pampe EAhxou cruIlCllltiwooC rtp6C t0 onoshylpound)ecl(l tflr 51lt1 tOO rpa)lIlII(OO npOypnI-lIlCltICJJOO rtPOcrOlOshypl~o)lelnlt 3poundldclne KUtalOpflc tflc I(lvncreooc
BlpLoypa+(a
I ChllTmann CW Adwlf R r 1 r1lQI ELmiddot Oj1erallons Reshyscarch Wlell-Muenl~bcn 19fi I
J(tr ll H OlHrll ions Rpellrlll ~ 1 llltgart 1966
I J(oldtl naln lt ( [lie EHllrli(dcrurg (it- FmlIrnmiddot(middothnClt( t~r i shylthtnlanoli in (11 ( WCltlS l ln ( I7 DI~rrtd l )o) Il 1 11 llnClI shyrJw ll 196ti
4 Kvgtt-i r AmllOllljlrocnlt Cal imo)o 1 [opo OvtojIO(IV HrO6 tllltlKlI() 0[1100 (Tt(VIIIU XPOIIo raquo Tll)X~ 110 1969
lox 1 r Elau(l)Y c(~ tOY rp(IlIIlK O npoypltlJPUftOl-Iov middotE)middot ) 1 FtUlPlU Eno t-lpnOW ti)v EpcvvW II] ) AOifll 19tfI
6 0gt11 r AI TftI Col fOC rpOlllJllIou npO(palIlU TIO IJ ol) poundI lYl poundru)o(t1 nil (rou(I(IgtI EE E f AOUI 1910
1 Saulll LT )llll lem l wal ~l elhod s ()f OHraUOns Resralch f cG raw-llill N(~ ltwk li~
Bestimmung der optimalen Verkehrsverteilung
In Ueberlauf - Fernsprechnetzen mit Hilfe
der linearen Programmierung
Von O Kokklnakll- G Karvdls
lCunfallung
lu einem Ueberlauf-FeruwohlneLz wird del Ve rkehr uber die Qu erbtindeJ hoher Ausnuzunlj und den LeLzweg gcrinshyger Verluslwahrscheinlichkeil nach eine r vorbetimmLen Reihenfolge abgewickelt womil e ine belrachlliche Verrinshygerung der gesamten max imalcn VermilLlungskosten ershyli eH wird im Ve rglei ch Zll jen en eines klassisch en Nelzes ohne Ueb~rlauls mciglj c hkeil des Vcrkehrs Durch Anwendu ng cler linearen Progtomm ierung auf ein
solches Nelz behandelt in d e l vorliegenden Arbeit ist es mogli ch di e wirl schartH ch optimale Aurteilung des Ver kehrs auf die Qu(wwr g-c und rlen R egelweg 2U bestimmen und durch V ergleirll mil d cr vorhondenen VelleiJung les tshyzus lellen ob finpound witn( Reduzierung rter maximoien Gesomtkos trn frrcichhol isl In diese m FaJl ist cs meistens mogli ch ~ich dt~r OJgt I imalcn crleilung durch ei nfache Aenshydcrllng-cn an rlcr Rrihfnrolge dcr Ueherlau[sab icklung nath den gr~(bni5sfn der lineltlren Programmicr llng ~ u n (l hern
bull (Cborll In Chlos (19 37) Dplom - Elektro ingcnleur der Te(llni$shychen lIocll~( lllllr ) l unlt1Hn (l 9B ) )1nitor - lngcnl l ur (19 66) und Dllllom~Wlrl sdians lnlZ (gtn irr ( 9(7) (t f ~t III (ln U och3ebuJe Sell 1961 wlilln~cJlarlllcht[ Mi1artwitf r 1m 1~ ()lIT( lln tlio llsn inl5tcrlurrL 111)(0 8eH 19liU ausrrnrrlrnUI(hcr Trorl~s l)r rur Prtll)larilrlchlfntechnik an der Tech nisrnen Fakullat der Unicnltl1l Pllras Er hal slclt in
Ka rllrlli1LIuP(hnlk und In Fla~cn nrr qrl$chanl lchen Plan ifi kaUon lind I TIlruIJlnH ngsr(lrselun~ I)(f lal~ i pound rl
IriJorrn In Kythlra (19 35) Olplom-Flektr ()illJen IElur d e l T erjmjs shy
hln lllt)ch ritHIr )tillI~hcn (El6 ) l1L I 96 hlll~ni ~llr ncr Cellrn ll lshyr hC1l Ilr itmIUlls-G cell scllarl (I) Bll) L it r def OrTI-K rtIifS hnrillih (19 70)
711 Notl-l~ploC 1910
Elval ouvat6v va 5lartlcto(81) tic cnJV8EtOV 5Ktuov OrtEPPOitlt Mv 11 rtPOOOlOPlC3Elcu lh QAAW V )le8oooov ii poundjlrteIPlte~C CEIshypo poundAiy(ou tU)v 5tc)l~v teal 5lEKrtfpUIWCEooc tFlc UrtEPPOtjC Elvol ~ EvSeOpoundIY)lEVn ItpoteuAoDoCl t6 poundAOXIIJWV KOcnolt EtC havdnv 1tpoundpirttOOOIV dVUL Suvatov va J-tfL(81) r6 OA11(0V 1(6shymo 51 oAAaytje r flc crfl pampe EAhxou cruIlCllltiwooC rtp6C t0 onoshylpound)ecl(l tflr 51lt1 tOO rpa)lIlII(OO npOypnI-lIlCltICJJOO rtPOcrOlOshypl~o)lelnlt 3poundldclne KUtalOpflc tflc I(lvncreooc
BlpLoypa+(a
I ChllTmann CW Adwlf R r 1 r1lQI ELmiddot Oj1erallons Reshyscarch Wlell-Muenl~bcn 19fi I
J(tr ll H OlHrll ions Rpellrlll ~ 1 llltgart 1966
I J(oldtl naln lt ( [lie EHllrli(dcrurg (it- FmlIrnmiddot(middothnClt( t~r i shylthtnlanoli in (11 ( WCltlS l ln ( I7 DI~rrtd l )o) Il 1 11 llnClI shyrJw ll 196ti
4 Kvgtt-i r AmllOllljlrocnlt Cal imo)o 1 [opo OvtojIO(IV HrO6 tllltlKlI() 0[1100 (Tt(VIIIU XPOIIo raquo Tll)X~ 110 1969
lox 1 r Elau(l)Y c(~ tOY rp(IlIIlK O npoypltlJPUftOl-Iov middotE)middot ) 1 FtUlPlU Eno t-lpnOW ti)v EpcvvW II] ) AOifll 19tfI
6 0gt11 r AI TftI Col fOC rpOlllJllIou npO(palIlU TIO IJ ol) poundI lYl poundru)o(t1 nil (rou(I(IgtI EE E f AOUI 1910
1 Saulll LT )llll lem l wal ~l elhod s ()f OHraUOns Resralch f cG raw-llill N(~ ltwk li~
Bestimmung der optimalen Verkehrsverteilung
In Ueberlauf - Fernsprechnetzen mit Hilfe
der linearen Programmierung
Von O Kokklnakll- G Karvdls
lCunfallung
lu einem Ueberlauf-FeruwohlneLz wird del Ve rkehr uber die Qu erbtindeJ hoher Ausnuzunlj und den LeLzweg gcrinshyger Verluslwahrscheinlichkeil nach eine r vorbetimmLen Reihenfolge abgewickelt womil e ine belrachlliche Verrinshygerung der gesamten max imalcn VermilLlungskosten ershyli eH wird im Ve rglei ch Zll jen en eines klassisch en Nelzes ohne Ueb~rlauls mciglj c hkeil des Vcrkehrs Durch Anwendu ng cler linearen Progtomm ierung auf ein
solches Nelz behandelt in d e l vorliegenden Arbeit ist es mogli ch di e wirl schartH ch optimale Aurteilung des Ver kehrs auf die Qu(wwr g-c und rlen R egelweg 2U bestimmen und durch V ergleirll mil d cr vorhondenen VelleiJung les tshyzus lellen ob finpound witn( Reduzierung rter maximoien Gesomtkos trn frrcichhol isl In diese m FaJl ist cs meistens mogli ch ~ich dt~r OJgt I imalcn crleilung durch ei nfache Aenshydcrllng-cn an rlcr Rrihfnrolge dcr Ueherlau[sab icklung nath den gr~(bni5sfn der lineltlren Programmicr llng ~ u n (l hern
bull (Cborll In Chlos (19 37) Dplom - Elektro ingcnleur der Te(llni$shychen lIocll~( lllllr ) l unlt1Hn (l 9B ) )1nitor - lngcnl l ur (19 66) und Dllllom~Wlrl sdians lnlZ (gtn irr ( 9(7) (t f ~t III (ln U och3ebuJe Sell 1961 wlilln~cJlarlllcht[ Mi1artwitf r 1m 1~ ()lIT( lln tlio llsn inl5tcrlurrL 111)(0 8eH 19liU ausrrnrrlrnUI(hcr Trorl~s l)r rur Prtll)larilrlchlfntechnik an der Tech nisrnen Fakullat der Unicnltl1l Pllras Er hal slclt in
Ka rllrlli1LIuP(hnlk und In Fla~cn nrr qrl$chanl lchen Plan ifi kaUon lind I TIlruIJlnH ngsr(lrselun~ I)(f lal~ i pound rl
IriJorrn In Kythlra (19 35) Olplom-Flektr ()illJen IElur d e l T erjmjs shy
hln lllt)ch ritHIr )tillI~hcn (El6 ) l1L I 96 hlll~ni ~llr ncr Cellrn ll lshyr hC1l Ilr itmIUlls-G cell scllarl (I) Bll) L it r def OrTI-K rtIifS hnrillih (19 70)