Td corrigé Title - ITU pdf

Title - ITU

... la distorsion de phase est très importante et doit également être corrigée. ..... IM?35, 4. KAHN, L. R. [juillet 1952] SSB transmission by envelope elimination and  ...




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\par }\pard \s18\qj\sb120\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036 \tab (B, EB, E, P)
\par }\pard \s18\qj\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036
\par 5.\tab }{\ul\lang1036 Charge sur le }{\ul {\field{\*\fldinst SYMBOL 110 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\ul -}{\ul\lang1036 ème équipement}{\lang1036
\par
\par 6.\tab }{\ul\lang1036 Facteur d\rquote amélioration}{\lang1036
\par }\pard \s18\qj\sb120\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036 \tab (B, EB, E, P)
\par }\pard \s18\qj\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036
\par 7.\tab }{\ul\lang1036 Probabilité de x équipements spécifiés engagés}{\lang1036
\par }\pard \s18\qj\sb120\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036 \tab (B, EB, E, P)
\par }\pard \s18\qj\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036
\par 8.\tab }{\ul\lang1036 Commentaires Généraux}{\lang1036
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036 \page 1.\tab }{\ul\lang1036 Suppositions possibles pour l\rquote intensité d\rquote appel}{\lang1036
\par
\par \tab Considérons un groupe à accessibilité totale avec }{\i\lang1036 N}{\lang1036 sources et }{\i\lang1036 n}{\lang1036 équipement dans un système avec perte.}{\ul\lang1036
\par }\pard \s18\nowidctlpar\widctlpar\adjustright {\lang1036
\par
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par où }{\i\lang1036 N}{\lang1036 et }{\i\lang1036 n}{\lang1036 peuvent être finis ou infinis. 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\par
\par \tab Le système peut avoir }{\i\lang1036 p}{\lang1036 occupations simultanées }{\i\lang1036 (p)}{\lang1036 , où
\par
\par \tab }{\i\lang1036 0 }{\i\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 p }{\i\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 min (n, N) = r}{\lang1036 \tab \tab \tab \tab \tab \tab \tab \tab (TFL 1.1)
\par
\par \tab Dans l\rquote expression
\par
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\tab }{\tab \tab \tab \tab \tab \tab }{\lang1036 (TFL 1.4)
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par signifie que tous les équipements sont occupés dans le groupe à accessibilité totale. La dernière supposition }{\i\lang1036 W(n) = 0}{\lang1036 est appliquée seulement quand }{\i\lang1036 N\~}{\i\lang1036 {\field{\*\fldinst SYMBOL 179 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 \~n}{\lang1036 .
\par
\par \tab Il devrait être supposé plutôt que les appels rejetés ne devraient faire de tentatives répétées avec une intensité d\rquote appels élevée, i.e., l\rquote intensité d\rquote appels ne devrait pas être changée par l\rquote existence de la congestion. L\rquote insertion de (TFL 1.3) et (TFL 1.4) dans (TGD\~2.8a) et (TGD 2.9) donne maintenant le distribution décrite dans la suite pour les groupes à accessibilité totale pour les systèmes avec perte..
\par
\par 2.\tab }{\ul\lang1036 Distributions de trafic}{\lang1036
\par
\par \tab Dépendant du choix des suppositions (TFL 1.3), différentes distributions de trafic peuvent maintenant être dérivées:
\par
\par }{\b\lang1036 DISTRIBUTION DE BERNOULLI }{\lang1036 (}{\i\lang1036 N }{\i\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 n}{\lang1036 )
\par
\par \tab Les suppositions (TGD 2.8) + (TFL 1.3B) + (TFL 1.4) insérées dans (TGD 2.8a) et (TGD 2.9) donnent
\par
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\par
\par }{\b\lang1036 DISTRIBUTION D\rquote ENGSET (}{\i\lang1036 N > n}{\b\lang1036 )}{\lang1036
\par
\par \tab Les suppositions (TGD 2.8) + (TFL 1.3EB) + (TFL 1.4) insérées dans (TGD 2.8a) et (TGD 2.9) donnent
\par
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\par }{\b\lang1036 DISTRIBUTION BINOMIALE NEGATIVE TRONQUEE (}{\i\lang1036 N = }{\i\lang1036 {\field{\*\fldinst SYMBOL 165 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 , n finie}{\b\lang1036 )}{\lang1036
\par
\par \tab Suppositions (TGD 2.8) + (TFL 1.3TNB) + (TFL 1.4) insérées dans (TGD 2.8a) + (TGD 2.9) donne
\par
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\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 \row }\pard\plain \s18\qj\nowidctlpar\widctlpar\adjustright \fs20\lang2057 {\lang1036
\par }\pard \s18\qj\keep\keepn\nowidctlpar\widctlpar\adjustright {\lang1036 \tab Il devrait être noté que:
\par
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 1.\tab}}\pard \s18\qj\fi-283\li1003\keep\keepn\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec\pnstart1\pnindent283\pnhang{\pntxta .}}\ls1\adjustright {\lang1036 La distribution d\rquote Engset (BE) est une distribution de Bernoulli tronquée (B)
\par }\pard \s18\qj\fi-283\li1003\keep\keepn\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 2.\tab}}\pard \s18\qj\fi-283\li1003\keep\keepn\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec\pnstart1\pnindent283\pnhang{\pntxta .}}\ls1\adjustright {\lang1036 La distribution d\rquote Erlang (E) est une distribution de poisson tronquée (P)
\par }\pard \s18\qj\keep\keepn\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036 de la même façon que les deux distributions binomiales négatives (TNB) et (NB).
\par
\par \tab Il devrait être également noté que:
\par
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 1.\tab}}\pard \s18\qj\fi-283\li1003\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls2\pnrnot0\pndec\pnstart1\pnindent283\pnhang{\pntxta .}}\ls2\adjustright {\lang1036 (B) et (EB) supposent que l\rquote intensité d\rquote appel décroît avec un nombre croissant d\rquote occupations.
\par }\pard \s18\qj\fi-283\li1003\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 2.\tab}}\pard \s18\qj\fi-283\li1003\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls2\pnrnot0\pndec\pnstart1\pnindent283\pnhang{\pntxta .}}\ls2\adjustright {\lang1036 (P) et (E) suppose une intensité d\rquote appel constante indépendante du nombre d\rquote occupations.
\par }\pard \s18\qj\fi-283\li1003\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 3.\tab}}\pard \s18\qj\fi-283\li1003\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls2\pnrnot0\pndec\pnstart1\pnindent283\pnhang{\pntxta .}}\ls2\adjustright {\lang1036 (NB) et (TNB) suppose que l\rquote intensité d\rquote appel croit avec un nombre croissant d\rquote occupations.
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab Les distributions les plus fréquemment utilisées dans la théorie du trafic sont (B) (EB) et (E). Les trois autres (P), (NB) et (TNB) sont moins utilisées dans la théorie, mais ont été incluses ici pour illustrer comment les différentes suppositions (TFL\~1.3) peuvent fournir différentes descriptions du processus du trafic stationnaire. (NB) et (TNB) sont quelquefois utilisées pour décrire les propriétés du trafic de débordement. Cependant, puisque (NB) et (TNB) sont moins communément utilisées, elles devraient être omises dans le texte suivant. Pour la dérivation des expressions de la congestion, trafic écoulé, etc., le lecteur est référé à une littérature supplémentaire dans le sujet.
\par
\par 3.\tab }{\ul\lang1036 Congestion}{\lang1036
\par
\par \tab Le temps, E, est généralement dérivée à partir des distributions de trafic }{\i\lang1036 [p]}{\lang1036 , pour }{\i\lang1036 p = n}{\lang1036 . Cf la définition dans (TGD\~3.1) et (TGD\~3.3).
\par
\par \tab La congestion d\rquote appel, B, est dérivée à partir des distributions de trafic comme défini dans (TGD 3.2) et (TGD 3.4).
\par
\par }{\b\lang1036 BERNOULLI}{\lang1036
\par
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\cell }\pard \s18\qr\keep\keepn\nowidctlpar\widctlpar\intbl\adjustright {\lang1036
\par
\par
\par
\par (TFL 3.1E)\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 \row }\trowd \trgaph108\trleft3261\trkeep\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \clvertalt\clbrdrl\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb \cellx6663\pard\plain \s18\qc\sb120\keep\keepn\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 Première formule d\rquote Erlang\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 \row }\trowd \trgaph108\trleft3261\trkeep\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \clvertalt\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb \cellx6663\pard\plain \s18\qc\keep\keepn\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\i\lang1036 B = E = E}{\i\lang1036\sub n}{\i\lang1036 (A)}{\lang1036 \cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 \row }\pard\plain \s18\qc\nowidctlpar\widctlpar\adjustright \fs20\lang2057 {\lang1036
\par
\par (}{\i\lang1036 B = E}{\lang1036 puisque l\rquote intensité dépend du nombre d\rquote occupations)
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par }{\b\lang1036 POISSON}{\lang1036
\par
\par }\trowd \trgaph107\trleft4253\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \cltxlrtb \cellx5750\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb \cellx9639\pard \s18\qc\sb120\sa120\nowidctlpar\widctlpar\intbl\adjustright {\i\lang1036 E = B = 0}{\lang1036 \cell }\pard \s18\qr\sb120\sa120\nowidctlpar\widctlpar\intbl\adjustright {\lang1036 (TFL 3.1P)\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\lang1036 \row }\pard\plain \s18\qc\nowidctlpar\widctlpar\adjustright \fs20\lang2057 {\lang1036
\par (Puisque }{\i\lang1036 n = }{\i\lang1036 {\field{\*\fldinst SYMBOL 165 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 )
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par }{\i\ul\lang1036 Formule itérative}{\lang1036
\par
\par \tab Pour le calcul numérique des probabilités d\rquote état }{\i\lang1036 [p]}{\lang1036 , le temps de congestion }{\i\lang1036 E}{\lang1036 et la congestion d\rquote appel }{\i\lang1036 B}{\lang1036 , comme d\rquote autres caractéristiques des distributions de trafic, il est fréquemment convenable d\rquote utiliser la formule itérative.
\par
\par \tab Il suit déjà à partir de (TGD 1.1) que }{\i\lang1036 [p]}{\lang1036 peut être calculé à partir de }{\i\lang1036 [p-1]}{\lang1036 , viz
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036 pour }{\i\lang1036 0 < p }{\i\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 m}{\lang1036
\par
\par \tab La récurrence commence par }{\i\lang1036 t}{\i\lang1036\sub 0}{\i\lang1036 = 1}{\lang1036 et continue jusqu\rquote à la valeur élevée possible de }{\i\lang1036 p}{\lang1036 .
\par
\par \tab Les probabilités d\rquote état sont donc obtenues comme
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036 qui devrait satisfaire la condition
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab De la même façon, la formule itérative peut être obtenue à partir du calcul de congestion. Deux exemples devraient être donnés ici:
\par
\par \tab La }{\ul\lang1036 Congestion d\rquote appel}{\lang1036 pour la distribution d\rquote }{\ul\lang1036 Engset}{\lang1036
\par
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\tab \tab \tab \tab (TFL 3.4)
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par où }{\i\lang1036 B}{\i\lang1036\sub 0}{\i\lang1036 = 1}{\lang1036 et la récurrence est finie pour }{\i\lang1036 {\field{\*\fldinst SYMBOL 110 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 = m}{\lang1036 .
\par
\par \tab La }{\ul\lang1036 Formule d\rquote Erlang}{\lang1036 peut facilement être calculée à partir de l\rquote expression de récurrence
\par
\par }\pard \s18\li3600\nowidctlpar\widctlpar\adjustright {\pard\plain \s18\li3600\nowidctlpar\widctlpar\adjustright \fs20\lang1036 {\object\objemb\objw2220\objh580{\*\objclass Equation.3}{\*\objdata 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\tab \tab \tab \tab (TFL 3.5)
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
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\par
\par \tab La formule de récurrence peut être obtenue pour d\rquote autres expressions.
\par
\par 4.\tab }{\ul\lang1036 Trafic écoulé et offert}{\lang1036
\par
\par \tab Le trafic écoulé est défini par (TGD 3.5) et le trafic offert au groupe par (TGD 3.7)
\par
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\par
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\par \tab Pour la recherche aléatoire, chaque équipement est espéré avoir la même charge; cependant
\par
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab Pour la recherche séquentielle, les expressions deviennent plus compliquées. Seulement les expressions pour les distributions d\rquote Erlang et de Poisson semblent être simple
\par
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\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab L\rquote expression (TFL 5.2E) est bonne aussi pour les distributions de Poisson.
\par
\par
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\par
\par \tab Le facteur d\rquote amélioration qui décrit combien plus de trafic peut être écoulé quand un groupe croit de }{\i\lang1036 n}{\lang1036 à }{\i\lang1036 n\~+\~}{\i\lang1036 {\field{\*\fldinst SYMBOL 68 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 n}{\lang1036 équipements, il est défini par (TGD 3.10). Les expressions devraient être données ci-dessous pour une croissance de}{\i\lang1036 n}{\lang1036 à }{\i\lang1036 n\~+\~1}{\lang1036 équipements dans le groupe.
\par
\par }\pard \s18\qj\keep\keepn\nowidctlpar\widctlpar\adjustright {\b\lang1036 BERNOULLI}{\lang1036
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\tab \tab \tab \tab \tab (TFL 7.1E)
\par }\pard \s18\qr\nowidctlpar\widctlpar\adjustright {\lang1036 (Formule de Palm-Jacohaeus)
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab où }{\i\lang1036 E}{\i\lang1036\sub n}{\i\lang1036 (A)}{\lang1036 est la première formule d\rquote Erlang.
\par
\par }{\b\lang1036 POISSON}{\lang1036
\par
\par \tab Pas de signification puisque }{\i\lang1036 n = }{\i\lang1036 {\field{\*\fldinst SYMBOL 165 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036
\par
\par \tab Noter que les deux expressions }{\i\lang1036 H(x)}{\lang1036 pour EB et E ont l\rquote apparition de forme des probabilités conditionnelles. La même chose pour la distribution Binomiale négative tronquée.
\par
\par 8.\tab C}{\ul\lang1036 ommentaires généraux}{\lang1036
\par
\par \tab Les sections précédentes présenté brièvement la formule de distribution pour les distributions de trafic, congestion, trafic écoulé et offert et autres caractéristiques typiques pour les différentes distributions de trafic traitées ici. Quelques formules ont été simples et d\rquote autres moins simples. Il est toujours un avantage si une caractéristique de trafic peut être exprimée dans une formule simple. Il devient facile à comprendre ses significations et aussi faire des déductions algébriques supplémentaires surtout avec las calculs numériques.
\par
\par \tab L\rquote importance de la formule simple, cependant, la valeur changée avec le temps puisque la plus part des calculs dans les pays avancés sont aujourd\rquote hui faits par des ordinateurs électroniques. Cela signifie que la formule qui est simple pour l\rquote homme peut ne pas l\rquote êtres toujours pour le programme. Cependant, quelques formules contenant des signes de sommation ou de produit peuvent parfois être préférables pour la programmation.
\par
\par \tab Toutes les distributions données ci-dessus supposent que l\rquote intensité\~é d\rquote appel ne change pas par les appels rejetés. Cette supposition donne les expressions mathématiques simples. Il est, cependant, tout à fait possible d\rquote introduire une supposition que les sources de trafic, qui ont des appels rejetés, font des tentatives renouvelées avec une intensité d\rquote appel élevée. Une telle supposition devrait augmenter le réalisme de la description du processus de trafic, mais devrait également augmenter les complications mathématiques.
\par
\par \tab Cependant, une telle supposition devrait être introduite, elle doit être garder dans l\rquote esprit que la congestion, spécialement dans le groupe considéré, est seulement une raison mineure des tentatives répétées. Autres raisons sont généralement d\rquote une grande influence sur la quantité de tentative d\rquote appels répétées.
\par }\pard \s18\nowidctlpar\widctlpar\adjustright {\lang1036
\par \page }{\b\lang1036 Théorie de base du Télétrafic (T)}{\lang1036
\par }\pard \s18\qc\nowidctlpar\widctlpar\adjustright {\lang1036
\par
\par EXERCICES A
\par }\pard \s18\qc\nowidctlpar\widctlpar\tx1134\adjustright {\lang1036
\par }\pard \s18\qc\nowidctlpar\widctlpar\tx0\adjustright {\lang1036 Groupe à accessibilité totale, système avec perte d\rquote appel. Exercices de base.
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036
\par
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 1\tab Quel est le }{\ul\lang1036 trafic offert}{\lang1036 exprimé en erlangs, si le }{\ul\lang1036 taux d\rquote appel}{\lang1036 et le }{\ul\lang1036 temps moyen de maintien}{\lang1036 sont, respectivement:
\par
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls3\adjustright {\lang1036 1,000 appels/heure\tab 90 sec.
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls3\adjustright {\lang1036 1,200 appels/heure\tab 2 min.
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 c)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls3\adjustright {\lang1036 4 appels/sec.\tab \tab 1.6 min.
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 d)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls3\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls3\adjustright {\lang1036 3 appels/min.\tab \tab 0.04 heure
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par TXA 2\tab Quel est le nombre d\rquote appels espéré par heure si le trafic offert est 35 erlangs et le temps de maintien moyen est 140 secondes?
\par
\par TXA 3\tab Quel est le temps moyen de maintien en secondes si le trafic offert = 33 erlangs et le taux d\rquote appels = 1,100 appels/heure?
\par
\par TXA 4\tab Dans un groupe constitué de 10 circuits, le nombre de circuits occupés a été lu d\rquote une manière continue durant une période de temps. Le développement en temps est montré dans la figure ci-dessous. Il est aussi donné, dans le diagramme, la proportion de la période totale quand exactement 0, 1, ... , 10 circuits sont engagés.
\par
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\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls4\adjustright {\lang1036 Calculer le trafic écoulé par le groupe durant la période et calculer le temps de congestion.
\par }\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls4\adjustright {\lang1036 Supposons que le groupe a été cherché à travers les points de temps donnés sur le diagramme. Quelle estimation pour le trafic écoulé et le temps de congestion devraient être obtenus?
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par TXA 5\tab Supposons qu\rquote un groupe }{onsiste }{\lang1036 de 10 circuits. Utilisant la table d\rquote Erlang, donner la congestion avec 4 chiffres après la virgule pour les valeurs suivantes de A = trafic offert:
\par
\par \tab \tab A = 1, 3, 5, 10, 15, 25, 50, 100, 200, 300 erlangs.
\par
\par TXA 6\tab Supposons qu\rquote un groupe offre un trafic de 10 erlangs. Utilisant la table d\rquote Erlang, donner la congestion avec 4 chiffres après la virgule pour les nombres suivants, }{\i\lang1036 n}{\lang1036 , de circuits:
\par
\par }\pard \s18\qj\fi-1134\li2574\nowidctlpar\widctlpar\adjustright {\lang1036 n = 1, 2, 3, 5, 7, 10, 13, 20, 23, 30.
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par TXA 7\tab Quel est le trafic le plus élevé en erlangs qui peut être offert à un groupe de 20 circuits si la congestion permise est au plus 0.005?
\par
\par TXA 8\tab Combien de circuits devraient être dans un groupe offrant un trafic de 48 erlangs si la congestion permise est au plus 0.002?
\par
\par TXA 9\tab Un groupe de 18 circuits offre un trafic avec le taux d\rquote appel de 480 appels/heure et le temps moyen de maintien est de 105 secondes.
\par
\par \tab Quel est le trafic offert, le temps de congestion, la congestion d\rquote appel, le trafic écoulé, la moyenne du trafic écoulé par circuit et le nombre espéré des appels rejetés par heure?
\par
\par TXA 10\tab Comment croit un trafic qui est écoulé par différents circuits dans un groupe de 5 circuits sous des conditions de recherche séquentielle et aléatoire, si le groupe offre le trafic de 2 erlangs?
\par
\par TXA 11\tab Montrer que la moyenne du trafic écoulé par circuit dans un groupe avec la recherche séquentielle est égal au trafic écoulé par circuit dans un groupe avec recherche aléatoire, si les groupes sont également larges et offrent le même trafic.
\par
\par TXA 12\tab Déterminer le trafic qui peut être offert à un groupe de 10 et 100 circuits si la valeur de congestion devrait être 0.005.
\par
\par \tab Supposons que ces trafics augmentent de 10 % et 20 %, respectivement. Calculer les valeurs de congestion résultante.
\par
\par \tab Aussi, donner le trafic écoulé et la moyenne du trafic écoulé par circuit pour tous les cas.
\par
\par TXA 13\tab Considérons un système d\rquote Erlang avec perte avec n circuits, l\rquote intensité d\rquote appels }{\lang1036 {\field{\*\fldinst SYMBOL 108 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 , et le temps de conversation exponentiellement distribuée par la moyenne }{\lang1036 {\field{\*\fldinst SYMBOL 116 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 .
\par
\par \tab Soit }{\i\lang1036 j}{\lang1036 un entier 0 }{\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 j }{\lang1036 {\field{\*\fldinst SYMBOL 163 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 n.
\par
\par \tab a) Dériver la fonction de distribution de l\rquote intervalle de temps à partir d\rquote un epoch quand l\rquote état }{\i\lang1036 (j)}{\lang1036 commence jusqu\rquote à ce que cet état fini.
\par
\par \tab b) Quelle est la moyenne de cet intervalle de temps?
\par
\par \tab c) Calculer la probabilité qu\rquote un état fini par une transition à (}{\i\lang1036 j-1}{\lang1036 ) et (}{\i\lang1036 j+1}{\lang1036 ) respectivement.
\par
\par TXA 14\tab Un pulsiomètre d\rquote abonné donne une impulsion au début d\rquote appel et puis une impulsion supplémentaire toutes les trois minutes durant la conversation. Supposons que le temps de conversation est une variable exponetiellement distribuée avec une moyenne de trois minutes. Calculer la proportion d\rquote appels qu\rquote il devait avoir:
\par
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls5\adjustright {\lang1036 exactement 2 impulsions
\par }\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls5\adjustright {\lang1036 moins que 2 impulsions
\par }\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 c)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls5\adjustright {\lang1036 plus que 2 impulsions
\par }\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 d)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls5\adjustright {\lang1036 au moins 2 impulsions
\par }\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 e)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls5\adjustright {\lang1036 au plus 2 impulsions
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\keep\keepn\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 15\tab Avec la même principe de taxation que l\rquote Exercice TXA 14, supposons que les intervalles d\rquote impulsion sont égaux à m et le temps moyen de conversation est égal à }{\i\lang1036 {\field{\*\fldinst SYMBOL 116 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 .}{\lang1036 Démontrer que le nombre moyen d\rquote impulsion par appel est:
\par }{\fs16\lang1036
\par }\pard \s18\li3600\keep\keepn\nowidctlpar\widctlpar\adjustright {\pard\plain \s18\li3600\keep\keepn\nowidctlpar\widctlpar\adjustright \fs20\lang2057 {\object\objemb\objw639\objh1020{\*\objclass Equation.3}{\*\objdata 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\par }\pard \s18\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 16\tab Sue un faisceau de circuits entre les centres A et B, la durée moyenne des conversations de A }{\lang1036 {\field{\*\fldinst SYMBOL 174 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 B est 4 minutes et de ceux de B }{\lang1036 {\field{\*\fldinst SYMBOL 174 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 A est 3 minutes. Supposons une distribution exponentielle pour les deux cas. La quantité d\rquote appels de A }{\lang1036 {\field{\*\fldinst SYMBOL 174 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 B représente 55 % des appels. Calculer la probabilité qu\rquote un appel arbitraire devrait avoir un temps de conversation }{\lang1036 {\field{\*\fldinst SYMBOL 62 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\lang1036 6 minutes.
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\fs16\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 17\tab Au temps 0, il y a 5 conversations en progression sur un groupe de circuits. Supposons que les temps de conversation sont distribués exponentiellement avec une moyenne de 3 minutes. Calculer la probabilité pour qu\rquote après 1 minute exactement, 2 de ces communications restent en progrès.
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 18\tab Considérons un système d\rquote Erlang avec perte avec 10 circuits et un trafic offert }{\i\lang1036 A}{\lang1036 . Les circuits sont recherchés en ordre. Comment agrandi la proportion de temps
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls6\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls6\adjustright {\lang1036 est le circuit No. 9 occupé?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls6\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls6\adjustright {\lang1036 exactement 9 circuits sont occupés simultanément?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 c)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls6\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls6\adjustright {\lang1036 les 9 premiers circuits sont occupés simultanément?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 d)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls6\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls6\adjustright {\lang1036 les 9 premiers circuits sont occupés simultanément et le circuit No. 10 est libre?
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 19\tab Un groupe à accessibilité totale est constitué de 6 circuits et lui offert un trafic de 6 sources. Le trafic offert par source est supposé égal à 0.5 erlangs.
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par \tab Quel est le trafic offert, la congestion d\rquote appels et la congestion de temps?
\par
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 20\tab Un groupe à accessibilité totale est constitué de 6 circuits et lui est offert un trafic à partir d\rquote un grand nombre de sources. Le trafic offert total est supposé égal à 3 erlangs. Quelle est la congestion d\rquote appels et la congestion de temps?
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par TXA 21\tab Faire une comparaison entre les Exercices TXA 19 and TXA 20.
\par
\par }\trowd \trgaph107\trleft-107 \clvertalt\cltxlrtb \cellx2161\clvertalt\cltxlrtb \cellx3146\clvertalt\cltxlrtb \cellx3713\clvertalt\cltxlrtb \cellx4698\clvertalt\cltxlrtb \cellx5265\clvertalt\cltxlrtb \cellx6252\clvertalt\cltxlrtb \cellx6819\clvertalt\cltxlrtb \cellx7804\pard \s18\nowidctlpar\widctlpar\intbl\adjustright {TXA 22\cell Circuit 1\cell \cell }\pard \s18\qc\nowidctlpar\widctlpar\intbl\adjustright {\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{ }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{ }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\trowd \trgaph107\trleft-107 \clvertalt\cltxlrtb \cellx2161\clvertalt\cltxlrtb \cellx3146\clvertalt\cltxlrtb \cellx3713\clvertalt\cltxlrtb \cellx4698\clvertalt\cltxlrtb \cellx5265\clvertalt\cltxlrtb \cellx6252\clvertalt\cltxlrtb \cellx6819\clvertalt\cltxlrtb \cellx7804\pard\plain \s18\sb120\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\cell Circuit 2\cell \cell }\pard \s18\qc\sb120\nowidctlpar\widctlpar\intbl\adjustright {\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{ }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{ }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\pard\plain \s18\sb120\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\cell Circuit 3\cell \cell }\pard \s18\qc\sb120\nowidctlpar\widctlpar\intbl\adjustright {\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{ }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{\cell \cell }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{ }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\pard\plain \s18\sb120\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\cell Circuit 4\cell \cell }\pard \s18\qc\sb120\nowidctlpar\widctlpar\intbl\adjustright {\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{ }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{\cell \cell }{\fs18 {\field{\*\fldinst SYMBOL 161 \\f "Wingdings" \\s 9}{\fldrslt\f14\fs18}}}{ }{{\field{\*\fldinst SYMBOL 108 \\f "Wingdings" \\s 10}{\fldrslt\f14\fs20}}}{\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\pard\plain \s18\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\cell \cell \cell }\pard \s18\qc\nowidctlpar\widctlpar\intbl\adjustright {{\field{\*\fldinst SYMBOL 123 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{\cell \cell }{{\field{\*\fldinst SYMBOL 49 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{{\field{\*\fldinst SYMBOL 50 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{{\field{\*\fldinst SYMBOL 51 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{\cell \cell }{{\field{\*\fldinst SYMBOL 49 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{{\field{\*\fldinst SYMBOL 50 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{{\field{\*\fldinst SYMBOL 51 \\f "MT Extra" \\s 10}{\fldrslt\f129\fs20}}}{\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\trowd \trgaph107\trleft-107 \clvertalt\cltxlrtb \cellx2161\clvertalt\cltxlrtb \cellx3146\clvertalt\cltxlrtb \cellx3713\clvertalt\cltxlrtb \cellx4698\clvertalt\cltxlrtb \cellx5265\clvertalt\cltxlrtb \cellx6252\clvertalt\cltxlrtb \cellx6819\clvertalt\cltxlrtb \cellx7804\pard\plain \s18\sb120\nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\cell \cell \cell }\pard \s18\qc\sb120\nowidctlpar\widctlpar\intbl\adjustright {0\line circuit\line engagé\cell \cell 1 \line circuit\line engagé\cell \cell 2 \line circuits\line engagés\cell }\pard\plain \nowidctlpar\widctlpar\intbl\adjustright \fs20\lang2057 {\row }\pard\plain \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright \fs20\lang2057 {\fs16\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 Dans la figure ci-dessus, quelques états différents d\rquote occupation sont montré pour un groupe constitué de 4 circuits:
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\fs16\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls7\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls7\adjustright {\lang1036 Dessiner systématiquement tous les différents états d\rquote occupation pour ce groupe de circuits.
\par }\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\fs16\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\qj\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls7\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls7\adjustright {\lang1036 Combien d\rquote état différent d\rquote occupation avec exactement 0, 1, 2, 3, 4 circuits engagés sont obtenus?
\par }\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\fs16\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 c)\tab}}\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls7\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls7\adjustright {\lang1036 Quel est le nombre total d\rquote états différents d\rquote occupation?
\par }\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\fs16\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 d)\tab}}\pard \s18\fi-283\li1440\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls7\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls7\adjustright {\lang1036 Dans combien de ces cas les circuits No. 1 et No. 3 sont engagés?
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par TXA 23\tab Supposons un groupe constitué de n circuits dénombrés 1, 2, 3, ..., n.
\par
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 a)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls8\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls8\adjustright {\lang1036 Combien y a t-il d\rquote états différents si on ne s\rquote intéresse qu\rquote au nombre de circuits engagés?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 b)\tab}}\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls8\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls8\adjustright {\lang1036 Combien y a t-il d\rquote états différents si on s\rquote intéresse à savoir lesquels des circuits sont engagés?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 c)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls8\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls8\adjustright {\lang1036 Combien y a t-il d\rquote états différents du type considéré en b) avec exactement 0, 1, 2, ..., n circuits engagés?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 d)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls8\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls8\adjustright {\lang1036 Combien y a t-il d\rquote états différents du type considéré en b) avec x spécifiques circuits engagés et, simultanément, exactement p circuits engagés?
\par }\pard \s18\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl12\ls0\pnrnot0\pndec }\ilvl12\adjustright {\lang1036
\par {\pntext\pard\plain\s18 \fs20\lang1036 \hich\af0\dbch\af0\loch\f0 e)\tab}}\pard \s18\qj\fi-283\li1723\nowidctlpar\widctlpar{\*\pn \pnlvlbody\ilvl0\ls8\pnrnot0\pnlcltr\pnstart1\pnindent283\pnhang{\pntxta )}}\ls8\adjustright {\lang1036 Dénotons par [p] la probabilité qu\rquote exactement quelconque p de circuits sont engagés. Utiliser le résultat de c) et d) pour montrer comment H(x) devrait être calculé quand
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\nowidctlpar\widctlpar\adjustright {\lang1036 \tab \tab \tab }{\i\lang1036 H(x) = P }{\i\lang1036 {\field{\*\fldinst SYMBOL 123 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036 x circuits spécifiques engagés}{\i\lang1036 {\field{\*\fldinst SYMBOL 125 \\f "Symbol" \\s 10}{\fldrslt\f3\fs20}}}{\i\lang1036
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 24\tab Même supposition comme dans l\rquote exercice TXA 19. Calculer H(3), la probabilité pour que trois circuits spécifiques soient engagés (p.e. circuits Nos. 1, 2, 3 ou circuits Nos. 2, 4, 6).
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }\pard \s18\qj\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036 TXA 25\tab Même supposition comme dans l\rquote exercice TXA 20. Calculer H(3), la probabilité pour que trois circuits spécifiques soient engagés.
\par }\pard \s18\fi-1134\li1134\nowidctlpar\widctlpar\adjustright {\lang1036
\par }}
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