\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fprq2 Times New Roman;}{\f4\fswiss\fprq2 Arial;}{\f5\fnil Courier Neu;}{\f6\fmodern\fprq1 Courier New;}{\f7\fmodern Courier New;}{\f8\froman Times New Roman;}{\f9\froman\fprq2 Symbol;}{\f10\froman\fcharset1 Times New Roman;}{\f11\froman\fprq2\fcharset2 Symbol;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;\red0\green128\blue0;\red0\green255\blue0;} \deflang1031\pard\ri4\plain\f4\fs48\cf0\b Warteschlangen \par \plain\f4\fs24\cf0 Prof. Dr. D\'f6rte Haftendorn, Dez. 04 Version vom 12.12.04\plain\f6\fs44\cf1\b \par \plain\f4\fs32\cf0\b lam Personen kommen im Mittel in Zeiteinheit Z an, z.B. 3 pro 1/4-Stunde. \par my Personen werden im Mittel pro Zeiteinheit Z bedient, z.B. 4 pro 1/4-Stunde.\plain\f6\fs44\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}delete lam, my: \par {\pntext\f1\'b7\tab}lam:=3:my:=4: \par {\pntext\f1\'b7\tab}rho:=lam/my //rho hei\'dft auch Auslastung \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw707\pich1208\picwgoal400\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs32\cf0\b \'dcbergangsmatrix\plain\f6\fs44\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}A:=matrix([[1-lam,lam, 0,0], \par \pard\li600\ri1\fi-300\plain\f6\fs32\cf1\b [my,1-lam-my,lam,0], \par [0,my,1-lam-my,lam], \par [0, 0,my,1-lam-my]]) \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw4198\pich2152\picwgoal2379\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs24\cf0 Eigentlich m\'fcsste es stets lam*h, my*h hei\'dfen mit einem h, das dann sp\'e4ter immer kleiner gemacht werden \par kann. Bei dem Problem, die Grenzverteilung zu bestimmen, f\'e4llt h dann aber heraus. Darum \par wird auf das Mitziehen in den Termen verzichtet.\plain\f6\fs44\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs44\cf1\b {\pntext\f1\'b7\tab}A-A^0 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw4198\pich2152\picwgoal2379\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs28\cf0 Beginnt man das Gleichungssystem vA=v zu l\'f6sen, so \par l\'e4sst man v1 zun\'e4chst in allen Gleichungen stehen . \par Man merkt: v2= rho*v1 und v(n+1) =rho*v(n), also eine geometrische Folge mit Faktor rho. \par v1 bestimmt man nun durch die Bedingung, dass v1+v2+v3+.....=1 \par sein muss, denn v muss stochastische Vektor sein, eine Verteilung beschreiben. \par Wegen der Summe der geometrische Reihe f\'fchr das zu v1=1-rho. \par Die Summe - und damit der Grenzwerteilung- existiert nur f\'fcr \par \plain\f4\fs44\cf0 rho<1, also lam