❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ ❚❡❝♥♦❧♦❣✐❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛
▼♦❞❡❧♦s ❛❧t❡r♥❛t✐✈♦s ❡♠ ✜❧❛s ▼✴●✴✶
❙✐❧✈✐❛ ▼❛r✐❛ Pr❛❞♦
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ ❚❡❝♥♦❧♦❣✐❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛
▼♦❞❡❧♦s ❛❧t❡r♥❛t✐✈♦s ❡♠ ✜❧❛s ▼✴●✴✶✳
❙✐❧✈✐❛ ▼❛r✐❛ Pr❛❞♦
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋r❛♥❝✐s❝♦ ▲♦✉③❛❞❛ ◆❡t♦
❚r❛❜❛❧❤♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊s✲ t❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ✲ ❉❊s✴❯❋❙❈❛r ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❊st❛tíst✐❝❛✳
Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária UFSCar Processamento Técnico
com os dados fornecidos pelo(a) autor(a)
P896ma Prado, Silvia Maria Modelos alternativos em filas M/G/1 / Silvia Maria Prado. -- São Carlos : UFSCar, 2016. 174 p.
Tese (Doutorado) -- Universidade Federal de São Carlos, 2015.
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❛♣r❡s❡♥t❛r ♠♦❞❡❧♦s ❞❡ ✜❧❛s ❛❧t❡r♥❛t✐✈♦s ❛♦ ▼✴●✴✶✱ ♥♦s q✉❛✐s ❛s ❝❤❡❣❛❞❛s s❡❣✉❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥✱ ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ✉s✉á✲ r✐♦s ♥♦ s✐st❡♠❛ ❡ ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ❝❛♥❛✐s ❞❡ ❛t❡♥❞✐♠❡♥t♦ sã♦ ❞❡s❝♦♥❤❡❝✐❞♦s✳ ◆❡st❡ ❝❛s♦✱ ♦❜s❡r✈❛♠♦s ❛♣❡♥❛s ♦ ❝❛♥❛❧ ❞❡ s❡r✈✐ç♦ q✉❡ ✐rá ♦❢❡r❡❝❡r ♦ ♠á①✐♠♦ ♦✉ ♦ ♠í♥✐♠♦ t❡♠♣♦ ❞❡ s❡r✈✐ç♦✳ P❛r❛ ✐st♦✱ ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ s❡r✈✐ç♦ sã♦ ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛ ❝♦♠♣♦s✐çã♦ ❞❛ ❞✐str✐✲ ❜✉✐çã♦ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥ tr✉♥❝❛❞❛ ♥♦ ♣♦♥t♦ ③❡r♦✱ ✉s❛❞❛ ♣❛r❛ ♠♦❞❡❧❛r ♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ❞❡ ❛t❡♥❞✐♠❡♥t♦✱ ❝♦♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧ ♣❛r❛ ♦ ♠á①✐♠♦ ❡ ♦ ♠í♥✐♠♦ t❡♠✲ ♣♦s ❞❡ s❡r✈✐ç♦✳ ❉❡st❛ ❢♦r♠❛✱ s✉r❣❡♠ ♥♦✈❛s ❞✐str✐❜✉✐çõ❡s ❞❡ s❡r✈✐ç♦ q✉❡ sã♦ ❞❡♥♦♠✐♥❛❞❛s ❞❡ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❣❡r❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼❆❳❈❖▼P●✱ ❡ ▼í♥✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❣❡r❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼■◆❈❖▼P●✱ ❡✱ ❛s✲ s✐♠✱ ♦❜t❡♠♦s ♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P●✴✶ ❡ ▼✴▼■◆❈❖▼P●✴✶✳ ❈♦♠♦ ❞✐str✐✲ ❜✉✐çõ❡s ❣❡r❛✐s ✉s❛♠♦s ❛s ❞✐str✐❜✉✐çõ❡s ❡①♣♦♥❡♥❝✐❛❧✱ ❲❡✐❜✉❧❧ ❡ ❇✐r♥❜❛✉♠ ❙❛✉♥❞❡rs✳ P❛r❛ ✐❧✉str❛r ♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ♣r♦♣♦st♦s ✉♠ ❛♠♣❧♦ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ é ❢❡✐t♦ ❡ ❞❛❞♦s r❡❛✐s t❛♠❜é♠ sã♦ ✉t✐❧✐③❛❞♦s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ▼♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴●✴✶❀ ❞✐str✐❜✉✐çã♦ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥❀ ❞✐str✐✲ ❜✉✐çã♦ ❞♦ ♠á①✐♠♦ ❡ ❞♦ ♠í♥✐♠♦ t❡♠♣♦s ❞❡ s❡r✈✐ç♦✳
❆❜str❛❝t
❚❤❡ ♠❛✐♥ ❛✐♠ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❞❡✈❡❧♦♣ ❛❧t❡r♥❛t✐✈❡ q✉❡✉✐♥❣ ♠♦❞❡❧s t♦ ▼✴ ●✴✶✱ ✐♥ ✇❤✐❝❤ ❛rr✐✈❛❧s ❢♦❧❧♦✇ ❛ P♦✐ss♦♥ ♣r♦❝❡ss✱ t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❝✉st♦♠❡rs ♦♥ t❤❡ s②st❡♠ ❛♥❞ t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ s❡r✈✐❝❡ ❝❤❛♥♥❡❧s ❛r❡ ✉♥❦♥♦✇♥✳ ❖✉r ✐♥t❡r❡st ✐s ❥✉st t♦ ♦❜s❡r✈❡ t❤❡ s❡r✲ ✈✐❝❡ ❝❤❛♥♥❡❧ t❤❛t ✇✐❧❧ ♦✛❡r t❤❡ ♠❛①✐♠✉♠ ♦r ♠✐♥✐♠✉♠ s❡r✈✐❝❡ t✐♠❡✳ ❲❤❡r❡❢♦r❡✱ t❤❡ s❡r✈✐❝❡ ❞✐str✐❜✉t✐♦♥s ❛r❡ ♦❜t❛✐♥❡❞ ❢r♦♠ t❤❡ ❝♦♠♣♦s✐t✐♦♥ ♦❢ t❤❡ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥ ❞✐str✐❜✉✲ t✐♦♥ tr✉♥❝❛t❡❞ ❛t ③❡r♦✱ ✉s❡❞ t♦ ♠♦❞❡❧ t❤❡ ♥✉♠❜❡r ♦❢ s❡r✈✐❝❡ ❝❤❛♥♥❡❧s✱ ✇✐t❤ t❤❡ ❣❡♥❡r❛❧ ❞✐s✲ tr✐❜✉t✐♦♥ t♦ t❤❡ ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ s❡r✈✐❝❡ t✐♠❡✳ ❚❤✉s✱ ✇❡ ♦❜t❛✐♥ ♥❡✇ ❞✐str✐❜✉t✐♦♥s ❢♦r s❡r✈✐❝❡ t✐♠❡✱ ✇❤✐❝❤ ❛r❡ ❝❛❧❧❡❞ ▼❛①✐♠✉♠✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❣❡♥❡r❛❧✱ ❞❡♥♦t❡❞ ❜② ▼❆❳❈❖▼P● ❞✐str✐❜✉t✐♦♥✱ ❛♥❞ ▼✐♥✐♠✉♠✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❣❡♥❡r❛❧✱ ❞❡♥♦t❡❞ ❜② ▼■◆❈❖▼P● ❞✐str✐❜✉t✐♦♥✱ ❝♦♥s❡q✉❡♥t❧②✱ ✇❡ ♦❜t❛✐♥ t❤❡ q✉❡✉❡ ♠♦❞❡❧s ▼✴▼❆❳❈❖▼P●✴✶ ❛♥❞ ▼✴▼■◆❈❖▼P●✴ ✶✱ r❡s♣❡❝t✐✈❡❧②✳ ❆s ❣❡♥❡r❛❧ ❞✐str✐❜✉t✐♦♥s✱ ✇❡ ✉s❡ t❤❡ ❞✐str✐❜✉t✐♦♥s ❡①♣♦♥❡♥t✐❛❧✱ ❲❡✐❜✉❧❧ ❛♥❞ ❇✐r♥❜❛✉♠ ❙❛✉♥❞❡rs✳ ❚♦ ✐❧❧✉str❛t❡ t❤❡ ♣r♦♣♦s❡❞ q✉❡✉❡ ♠♦❞❡❧s✱ ❛ s✐♠✉❧❛t✐♦♥ st✉❞② ✐s ❞♦♥❡ ❛♥❞ ❛❧s♦ r❡❛❧ ❞❛t❛ ❛r❡ ✉s❡❞✳
❑❡②✇♦r❞s✿ ▼✴●✴✶ q✉❡✉❡❀ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥ ❞✐str✐❜✉t✐♦♥❀ ❞✐str✐❜✉t✐♦♥ ❢♦r t❤❡ ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ s❡r✈✐❝❡ t✐♠❡✳
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶
✷ ■♥tr♦❞✉çã♦ ❛ t❡♦r✐❛ ❞❛s ✜❧❛s ✼
✷✳✶ ■♥tr♦❞✉çã♦ ❛♦ ❝♦♥❝❡✐t♦ ❞❡ ✜❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✶✳✶ Pr✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ✜❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷ Pr♦♣r✐❡❞❛❞❡ P❛st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸ ▼♦❞❡❧♦ ❞❡ ✜❧❛ M/G/1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸✳✶ Pr♦❜❛❜✐❧✐❞❛❞❡s ❞♦ r❡❣✐♠❡ ❡st❛❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹ ❈♦♠❡♥tár✐♦s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸ ▼♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P●✴✶ ❡ ▼✴▼■◆❈❖▼P●✴✶ ✷✷
✸✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ❙❡❧❡çã♦ ❞❡ ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✸ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹ ▼♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❊✴✶ ❡ ▼✴▼■◆❈❖▼P❊✴✶ ✹✽
✹✳✶ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❊✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✶✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✷ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❊✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✷✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
❙❯▼➪❘■❖ ❙❯▼➪❘■❖ ✹✳✸ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✸✳✶ ❙✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✸✳✷ ❈❛✐①❛ rá♣✐❞♦ ❞❡ s✉♣❡r♠❡r❝❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✹ ❈♦♠❡♥tár✐♦s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✺ ▼♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❲✴✶ ❡ ▼✴▼■◆❈❖▼P❲✴✶ ✽✺
✺✳✶ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❲✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✶✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✺✳✷ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❲✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✺✳✷✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✸ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✸✳✶ ❙✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✸✳✷ ❆❝❡ss♦s ❛ ✉♠ ❜❧♦❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✹ ❈♦♠❡♥tár✐♦s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷
✻ ▼♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❇❙✴✶ ❡ ▼✴▼■◆❈❖▼P❇❙✴✶ ✶✷✸
✻✳✶ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❇❙✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✻✳✶✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸ ✻✳✷ ▼♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❇❙✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ✻✳✷✳✶ ❊st✐♠❛çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ✻✳✸ ❘❡s✉❧t❛❞♦s ◆✉♠ér✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼ ✻✳✸✳✶ ❙✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼ ✻✳✸✳✷ ❉❛❞♦s ❞❡ ✢✉①♦ ❞❡ trá❢❡❣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✺ ✻✳✹ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵
✼ ❈♦♥❝❧✉sõ❡s ❡ ♣r♦♣♦st❛s ❢✉t✉r❛s ✶✻✷
❙❯▼➪❘■❖ ❙❯▼➪❘■❖
❆♣ê♥❞✐❝❡ ✶✻✾
✳✶ ❉✐str✐❜✉✐çã♦ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✾ ✳✷ ❚r✉♥❝❛♠❡♥t♦ ❞❛ sér✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ◆♦t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ✜❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✹✳✶ ❘❡s✉♠♦ ❞♦s ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✷ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❊✴✶ ❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✸ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❊✴✶ ❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✹ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
▼✴▼❆❳❈❖▼P❊✴✶ ♣❛r❛λ1✱ ρ1 = 0,8✱ µ1 = 1,0 ❡φ1 = 0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✺ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
▼✴▼❆❳❈❖▼P❊✴✶ ♣❛r❛λ1 = 0,9✱ ρ1 = 0,9✱ µ1 = 0,9 ❡φ1 = 0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✻ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡
✜❧❛ ▼✴▼■◆❈❖▼P❊✴✶ ♣❛r❛λ2 = 0,8✱ ρ2 = 0,8✱ µ2 = 1,0 ❡φ2 = 0✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✼ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡
✜❧❛ ▼✴▼■◆❈❖▼P❊✴✶ ♣❛r❛λ2 = 0,9✱ ρ2 = 0,9✱ µ2 = 1,0 ❡φ2 = 0✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✽ P♦r❝❡♥t❛❣❡♠ ❞❡ ❝♦♥❝♦r❞â♥❝✐❛ ❞♦s t❡st❡s ▲♦❣✲r❛♥❦ ❡ ◗✉✐q✉❛❞r❛❞♦ ♣❛r❛ ♦
♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳●❊✴✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✾ P♦r❝❡♥t❛❣❡♠ ❞❡ ❝♦♥❝♦r❞â♥❝✐❛ ❞♦s t❡st❡s ▲♦❣✲r❛♥❦ ❡ ◗✉✐q✉❛❞r❛❞♦ ♣❛r❛ ♦
♠♦❞❡❧♦ ❞❡ ✜❛❧ ▼✴▼■◆●❊✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✶✵ ❆s ❡st✐♠❛t✐✈❛s ❞❡Eb(Ymax)❡Eb(Ymin)♠♦❞❡❧♦s ▼✴▼❆❳●❊✴✶ ❡ ▼✴▼■◆●❊✴✶✳ ✼✾ ✹✳✶✶ ❚❛①❛s ❞❡ ♦❝✉♣❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳●❊✴✶ ❡ ▼✴▼■◆●❊✴✶✳ ✳ ✳ ✳ ✽✵
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✹✳✶✷ ▼❡❞✐❞❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳●❊✴✶✱ ▼✴▼■◆●❊✴✶ ❡ ▼✴▼✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✶✸ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✶✹ ❘❡s✉♠♦ ❞♦s ❞❛❞♦s ❞♦ ❝❛✐①❛ rá♣✐❞♦ ❡♠ ♠✐♥✉t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✶✺ ❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✉s❛♥❞♦ ♦ ♠♦❞❡❧♦ ▼✴▼❆❳❈❖▼P❊✴✶✳ ✽✷ ✹✳✶✻ ❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✉s❛♥❞♦ ♦ ♠♦❞❡❧♦ ▼✴▼■◆❈❖▼P❊✴✶✳ ✽✷ ✹✳✶✼ ▼❡❞✐❞❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳P❊✴✶✱ ▼✴▼■◆P❊✴✶
❡ ▼✴▼✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✶✽ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✺✳✶ ❘❡s✉♠♦s ❞♦s ❞❛❞♦s s✐♠✉❧❛❞♦s ♣❛r❛ ρ= 0,8 ❡ρ = 0,9✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✺✳✷ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴ ▼❆❳❈❖▼P❲✴✶ ❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✸ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❲✴✶ ❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✹ P♦r❝❡♥t❛❣❡♠ ❞❡ ❝♦♥❝♦r❞â♥❝✐❛ ❞♦s t❡st❡s ▲♦❣ r❛♥❦ ❡ ◗✉✐q✉❛❞r❛❞♦ ♣❛r❛ ♦
♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴❲✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✳✺ ❊st✐♠❛t✐✈❛s ❞❡Eb(Y1)♣❛r❛ ♠♦❞❡❧♦ ▼✴❲✴✶ ❞❛s s✐♠✉❧❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✳✻ ❆s t❛①❛s ❞❡ ♦❝✉♣❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴❲✴✶ ♣❛r❛ ❛s ❞✉❛s s✐♠✉❧❛çõ❡s✳ ✳ ✶✶✶ ✺✳✼ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❲✴✶ ♣❛r❛ λ1 = 0,8✱ ρ1 = 0,8✱µ1 = 1,0✱ k1 = 0,9 ❡
φ1 = 100 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✽ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ♠♦❞❡❧♦
❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❲✴✶ ♣❛r❛ ρ= 0,9✱ λ= 0,9✱ k= 0,9❡ φ= 0✳ ✳ ✳ ✳ ✳ ✶✶✹
✺✳✾ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❲✴✶ ♣❛r❛ λ2 = 0,8✱ρ2 = 0,8✱ µ2 = 1,0✱ k2 = 0,9 ❡
φ1 = 100✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✺✳✶✵ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❲✴✶ ♣❛r❛ λ2 = 0,9✱ ρ2 = 0,9✱ µ2 = 1,0✱ k2 = 0,9 ❡
φ2 = 100✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✺✳✶✶ ▼❡❞✐❞❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴❲✴✶ ❡ ▼✴▼✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✶✷ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✶✸ ❘❡s✉♠♦ ❞♦s t❡♠♣♦s ❡♥tr❡ ♦s ❛❝❡ss♦s ❡♠ s❡❣✉♥❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✺✳✶✹ ❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✺✳✶✺ ❆ ❡st✐♠❛t✐✈❛s ❞❡Eb(Ymax)❡Eb(Ymin)❞♦s ♠♦❞❡❧♦s ▼❆❳P❲ ❡ ▼■◆P❲ ❞❛❞♦
❡♠ s❡❣✉♥❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✺✳✶✻ ❚❛①❛s ❞❡ ♦❝✉♣❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳P❲✴✶ ❡ ▼✴▼■◆P❲✴✶✳ ✳ ✳ ✶✷✶ ✺✳✶✼ ▼❡❞✐❞❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳P❲✴✶✱ ▼✴▼■◆P❲✴✶
❡ ▼✴▼✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✺✳✶✽ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷
✻✳✶ ❘❡s✉♠♦s ❞♦s ❞❛❞♦s s✐♠✉❧❛❞♦s ❝♦♠ ρ= 0,8 ❡ ρ= 0,9✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼
✻✳✷ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❇❙✴✶ ❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽ ✻✳✸ ❊st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❇❙✴✶
❡ s❡✉s ❞❡s✈✐♦s✲♣❛❞rã♦ ✭❞♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽ ✻✳✹ ❊st✐♠❛t✐✈❛s ❞❡Eb(Y1)❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴❇❙✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾ ✻✳✺ P♦r❝❡♥t❛❣❡♠ ❞❡ ❝♦♥❝♦r❞â♥❝✐❛ ❞♦s t❡st❡s ▲♦❣✲r❛♥❦ ❡ ◗✉✐q✉❛❞r❛❞♦ ♣❛r❛ ♦
♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴❇❙✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾ ✻✳✻ ❚❛①❛s ❞❡ ♦❝✉♣❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴❇❙✴✶ ♣❛r❛ ❛s ❞✉❛s s✐♠✉❧❛çõ❡s✳ ✳ ✳ ✶✹✾ ✻✳✼ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P❇❙✴✶
♣❛r❛ λ= 0,8✱ ρ= 0,8✱α = 0,98✱ β = 7,0✱ φ= 90✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶
✻✳✽ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴ ▼❆❳✲ ❈❖▼P❇❙✴✶ ♣❛r❛λ = 0,9✱ρ = 0,9✱α = 0,98✱ β = 7,0 ❡ φ= 90✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✻✳✾ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❇❙✴✶ ♣❛r❛ λ= 0,8✱ ρ= 0,8✱α = 0,98✱ β = 7,0✱ φ= 0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸
✻✳✶✵ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ♠é❞✐❛s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼■◆❈❖▼P❇❙✴✶ ♣❛r❛λ2 = 0,9✱ ρ2 = 0,9✱ α2 = 0,98✱β2 = 7,0✱ φ2 = 90✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✹ ✻✳✶✶ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✺ ✻✳✶✷ ❘❡s✉♠♦ ❞♦s ❞❛❞♦s ❡♠ s❡❣✉♥❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✻ ✻✳✶✸ ❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦s ♠♦❞❡❧♦s ▼✴▼❆❳❈❖▼P❇❙✴✶
❡ ▼✴▼■◆❈❖▼P❇❙✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼ ✻✳✶✹ ❆s ❡st✐♠❛t✐✈❛s ❞❡ Eb(Ymax) ❡ Eb(Ymin)❡♠ s❡❣✉♥❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✾ ✻✳✶✺ ❚❛①❛s ❞❡ ♦❝✉♣❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳●❇❙✴✶ ❡ ▼✴▼■◆●❇❙✴✶✳ ✳ ✶✺✾ ✻✳✶✻ ▼❡❞✐❞❛s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳●❇❙✴✶✱ ▼✴▼■◆●❇❙✴✶
❡ ▼✴▼✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵ ✻✳✶✼ ❱❛❧♦r❡s ❞♦s ❝r✐tér✐♦s ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✸✳✶ ❊sq✉❡♠❛ ❞♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✹✳✶ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼❆❳●❊ ❡ ❛ ❢✉♥✲ çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ1 = 0,8✳ ✳ ✳ ✳ ✼✼ ✹✳✷ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼❆❳●❊ ❡ ❛ ❢✉♥✲
çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ1 = 0,9✳ ✳ ✳ ✳ ✼✼ ✹✳✸ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼■◆●❊ ❡ ❛ ❢✉♥çã♦
❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ2 = 0,8✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✹ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼■◆●❊ ❡ ❛ ❢✉♥çã♦
❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ2 = 0,9✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✺ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼❆❳P❊ ❡ ❛ ❢✉♥çã♦
❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✹✳✻ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞❡ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼■◆P❊ ❡ ❛ ❢✉♥çã♦
❞❡ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✺✳✶ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ ❡ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ= 0,8✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
✺✳✷ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ ❡ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ= 0,9✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✸ ❇❧♦❣ ❚❡♥❞ê♥❝✐❛s Pr♦✜ss✐♦♥❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽ ✺✳✹ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼❆❳P❲ ❡ ❛
❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
①✐
✺✳✺ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼■◆P❲ ❡ ❛ ❢✉♥✲ çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✻✳✶ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❇❙ ❡ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ = 0,8✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵ ✻✳✷ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❇❙ ❡ ❛ ❢✉♥çã♦ ❞♦
t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❡ trá❢❡❣♦ρ = 0,9✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵
✻✳✸ ❘❡❣✐ã♦ ❈❡♥tr❛❧ ❞❛ ❝✐❞❛❞❡ ❞❡ Pr❡s✐❞❡♥t❡ Pr✉❞❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✻ ✻✳✹ ❊sq✉❡♠❛ ❞♦ ✢✉①♦ ❞❡ trá❢❡❣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼ ✻✳✺ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼❆❳●❇❙ ❡ ❛
❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽ ✻✳✻ ❈♦♠♣❛r❛♥❞♦ ❛ ❢✉♥çã♦ ❞♦ t❡♠♣♦ r❡st❛♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ▼■◆●❇❙ ❡ ❛
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❯♠ ❞♦s ♠❛✐♦r❡s ♣r♦❜❧❡♠❛s ❡♠ s✐st❡♠❛s ❞❡ ✜❧❛ é ♠♦❞❡❧❛r ❞❡ ❢♦r♠❛ r❡❛❧íst✐❝❛ ❛ ♣❡r❢♦r♠❛♥❝❡ ❞❡ ❝❡♥tr❛✐s ❞❡ s❡r✈✐ç♦✱ ❛ss✐♠ ❝♦♠♦ ❡①♣❧✐❝❛r ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❞✐s♣❛r✐❞❛❞❡s ❡♥tr❡ ♦s ❛t❡♥❞✐♠❡♥t♦s ❞♦s ❞✐❢❡r❡♥t❡s s❡r✈✐❞♦r❡s ❞❛s ❝❡♥tr❛✐s✱ ✉♠❛ ✈❡③ q✉❡ ❛❧❣✉♥s ♣♦ss✉❡♠ ❧♦♥❣❛s ✜❧❛s ❡ ♦✉tr♦s s❡ ❡♥❝♦♥tr❛♠ ♦❝✐♦s♦s✳ ❆ ♥♦ss❛ q✉❡stã♦ é ❝♦♠♦ ❝♦♥str✉✐r ♥♦✈♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛✱ q✉❡ ✐♥❝♦r♣♦r❡♠ ♠❡❝❛♥✐s♠♦s ❞❡ ❛❥✉st❡ ❝♦♥tr❛ ❧♦♥❣❛s ✜❧❛s✳
❆s ❞✐s♣❛r✐❞❛❞❡s q✉❡ s✉r❣❡♠ ♥❛s ❝❡♥tr❛✐s r❛r❛♠❡♥t❡ sã♦ ✐♥❝♦r♣♦r❛❞❛s ♥♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛✳ ❖ ♥♦ss♦ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♣r♦♣ós✐t♦ ❡①♣❧✐❝á✲❧❛s✱ ❞❡s❡♥✲ ✈♦❧✈❡♥❞♦ ♥♦✈♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛✱ q✉❡ ♣♦ss✉❛♠ ♠❡❝❛♥✐s♠♦s ❞❡ ❛❥✉st❡ ♣❛r❛ r❡❡q✉✐❧✐❜r❛r ♦ s✐st❡♠❛ q✉❛♥❞♦ ♦❝♦rr❡ ✉♠ ❛✉♠❡♥t♦ ❞♦ ✢✉①♦ ❞❡ ✉s✉ár✐♦s ♥♦ s✐st❡♠❛✳ ❚❛✐s ♠♦❞❡❧♦s s❡rã♦ ❢♦❝❛❞♦s ♥♦s s❡r✈✐❞♦r❡s q✉❡ ♦❢❡r❡❝❡♠ ♦ ♠á①✐♠♦ ♦✉ ♦ ♠í♥✐♠♦ t❡♠♣♦s ❞❡ s❡r✈✐ç♦ ❡♥tr❡ t♦❞♦s ♦s s❡r✈✐❞♦r❡s ❡♠ ♣❛r❛❧❡❧♦✱ s❡♥❞♦ q✉❡ ♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡st❡s s❡r✈✐❞♦r❡s é ❞❡s❝♦♥❤❡❝✐❞♦✳
❈♦♠♦ ❡①❡♠♣❧♦✱ ❡♠ ✉♠ s✉♣❡r♠❡r❝❛❞♦✱ ❛❧❣✉♥s ✉s✉ár✐♦s ♥❡❝❡ss✐t❛♠ ❞❡ ✉♠ ♠❛✐♦r ♦✉ ♠❡♥♦r t❡♠♣♦ ❞❡ s❡r✈✐ç♦✳ ◗✉❛♥❞♦ ♦ ✉s✉ár✐♦ ♣♦ss✉✐ ♠✉✐t♦s ✐t❡♥s ❡♠ s❡✉ ❝❛rr✐♥❤♦ ❞❡ ❝♦♠♣r❛✱ ♦ s✉♣❡r♠❡r❝❛❞♦ ❞✐s♣õ❡♠ ❞❡ ❝❛✐①❛s ♥♦r♠❛✐s ♣❛r❛ ♦ ❛t❡♥❞✐♠❡♥t♦✱ ❡ ♣❛r❛ ❛q✉❡❧❡ ❝♦♠ ♣♦✉❝♦s ✐t❡♥s✱ ♦ q✉❛❧ ♥❡❝❡ss✐t❛ ❞❡ ✉♠ t❡♠♣♦ ♠❡♥♦r ❞❡ s❡r✈✐ç♦✱ é ❞✐s♣♦♥✐❜✐❧✐③❛❞♦ ♦ s❡r✈✐ç♦ ❞❡ ❝❛✐①❛ rá♣✐❞♦✳
❉✐❛♥t❡ ❞❡st❡ ♦❜❥❡t✐✈♦ ✉s❛♠♦s ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❝♦♠♣♦s✐çã♦ ❞❡ ❞✐str✐❜✉✐çõ❡s ♣❛r❛ ♦❜t❡r ♥♦✈❛s ❞✐str✐❜✉✐çõ❡s ❞❡ s❡r✈✐ç♦✱ q✉❡ s✉r❣❡♠ ❛ ♣❛rt✐r ❞❛ ❝♦♠♣♦s✐çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥ tr✉♥❝❛❞❛ ♥♦ ♣♦♥t♦ ③❡r♦✱ ❞❡♥♦t❛❞❛ ♣♦r ❈❖▼P tr✉♥❝❛❞❛✱ ✉s❛❞❛ ♣❛r❛ ♠♦❞❡❧❛r ♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ♥♦ s✐st❡♠❛✱ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧ ♣❛r❛ ♦ ♠á①✐♠♦ ❡ ♦
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♠í♥✐♠♦ t❡♠♣♦s ❞❡ s❡r✈✐ç♦✳ ❉❡♥♦♠✐♥❛♠♦s t❛✐s ❞✐str✐❜✉✐çõ❡s ❞❡ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲ P♦✐ss♦♥✲●❡r❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼❆❳❈❖▼P● ❡ ▼í♥✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲ ●❡r❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼■◆❈❖▼P●✱ s❡♥❞♦ q✉❡ ❛♠❜❛s sã♦ tr✉♥❝❛❞❛s ♥♦ ♣♦♥t♦ ③❡r♦✳ ❈♦♠♦ ❞✐str✐❜✉✐çõ❡s ❣❡r❛✐s✱ ✉s❛♠♦s ❛s ❞✐str✐❜✉✐çõ❡s✿ ❡①♣♦♥❡♥❝✐❛❧✱ ❲❡✐❜✉❧❧ ❡ ❇✐r♥✲ ❜❛✉♠ ❙❛✉♥❞❡rs✳
❆ ❞✐str✐❜✉✐çã♦ ❈❖▼P é ✉♠ ♠♦❞❡❧♦ ♣❛rt✐❝✉❧❛r ❡ ❜❛st❛♥t❡ ✈❡rsát✐❧ ♣❛r❛ ❞❡s❝r❡✲ ✈❡r ♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛ ✭❈♦♥✇❛② ❛♥❞ ▼❛①✇❡❧❧✱ ✶✾✻✶✮ ✭✈❡r ❆♣ê♥❞✐❝❡ ✼✮✱ ♣♦✐s ♣♦ss✉✐ ✉♠ ♣❛râ♠❡tr♦ q✉❡ r❡♣r❡s❡♥t❛ ❛ ♣r❡ssã♦ ❡①❡r❝✐❞❛ ♥♦ s❡r✈✐❞♦r q✉❛♥❞♦ ♦❝♦rr❡ ✉♠ ❛✉♠❡♥t♦ ♦✉ ❞✐♠✐♥✉✐çã♦ ❞♦ ✢✉①♦ ❞❡ ✉s✉ár✐♦s✳
❈♦♥s✐❞❡r❛♠♦s três ✈❛r✐❛çõ❡s ❞❡st❡ ♣❛râ♠❡tr♦✿ ✭✐✮ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ❛ss✉♠❡ ♦ ✈❛❧♦r ③❡r♦✱ ❡♠ q✉❡ ♦ s❡r✈✐❞♦r ♥ã♦ ❛❧t❡r❛ ❛ t❛①❛ ❞❡ s❡r✈✐ç♦ ✭✐✐✮ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ❛ss✉♠❡ ♦ ✈❛❧♦r ✉♠✱ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛ s✐t✉❛çã♦ ❡♠ q✉❡ ❛ t❛①❛ ❞❡ s❡r✈✐ç♦ ❛✉♠❡♥t❛ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❡ ✢✉①♦ ❞❡ ✉s✉ár✐♦s ✭✐✐✐✮ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ t❡♥❞❡ ❛ ✐♥✜♥✐t♦✱ s❡♥❞♦ q✉❡ ❛ t❛①❛ ❞❡ s❡r✈✐ç♦ ❛✉♠❡♥t❛ ❛✐♥❞❛ ♠❛✐s✳
❖s ✈❛❧♦r❡s s✉♣r❛❝✐t❛❞♦s ♣❛r❛ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ❢♦r❛♠ ❡s❝♦❧❤✐❞♦s ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡❧❡s ❞❡s❝r❡✈❡r❡♠ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s ♥♦ s✐st❡♠❛ ❞❡ ♠♦❞❡❧♦s ❝❧áss✐❝♦s ❞❡ ✜❧❛s✳ ◗✉❛♥❞♦ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ❛ss✉♠❡ ♦ ✈❛❧♦r ③❡r♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❈❖▼P t♦r♥❛✲s❡ ❛ ❞✐str✐❜✉✐çã♦ ❣❡♦♠étr✐❝❛ ❡✱ ❛ss✐♠✱ t❡♠♦s ♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ M/M/1✱ ❡♠ q✉❡ ♦s t❡♠♣♦s ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ❡ ♦s t❡♠♣♦s ❞❡ s❡r✈✐ç♦ ♣♦ss✉❡♠ ❞✐str✐❜✉✐çã♦ ❡①♣♦♥❡♥❝✐❛❧✱ ❛ ❢♦r♠❛ ❞❡ ❛t❡♥❞✐♠❡♥t♦ é ♦ ♣r✐♠❡✐r♦ q✉❡ ❝❤❡❣❛ é ♦ ♣r✐♠❡✐r♦ ❛ s❡r ❛t❡♥❞✐❞♦ ❡ ❤á ❛♣❡♥❛s ✉♠ s❡r✈✐❞♦r✳ P❛r❛ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ❛ss✉♠✐♥❞♦ ♦ ✈❛❧♦r ✉♠✱ ❛ ❞✐str✐❜✉✐çã♦ ❈❖▼P t♦r♥❛✲s❡ ❛ ❞✐str✐❜✉✐çã♦ P♦✐ss♦♥✱ ❡✱ ❛ss✐♠✱ t❡♠♦s ♦ ♠♦❞❡❧♦M/M/∞✱ q✉❡ ❞✐❢❡r❡ ❞♦ ♠♦❞❡❧♦
▼✴▼✴✶ ♣❡❧♦ ♥ú♠❡r♦ ❞❡ s❡r✈✐❞♦r❡s✳ P❛r❛ ♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ t❡♥❞❡♥❞♦ ❛ ✐♥✜♥✐t♦ ♦❜t❡♠♦s ❛ ❞✐str✐❜✉✐çã♦ ❇❡r♥♦✉❧❧✐ ✭❈♦♥✇❛② ❛♥❞ ▼❛①✇❡❧❧✱ ✶✾✻✶✮✳
✸
▼á①✐♠♦✲❇❡r♥♦✉❧❧✐✲❣❡r❛❧✱ ❞❡♥♦t❛❞❛ ❞❡ ▼❆❳❇●✱ ❡ ❞✐str✐❜✉✐çã♦ ▼í♥✐♠♦✲❇❡r♥♦✉❧❧✐✲●❡r❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ▼■◆❇●✳ ◆♦ ú❧t✐♠♦ ❝❛s♦✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ❛s ❞✐str✐❜✉✐çõ❡s sã♦ s❡♠❡❧❤❛♥t❡s ❡ ❝♦✐♥❝✐❞❡♠ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧✳
❈♦♠♦✱ ✉s❛♠♦s três ❞✐str✐❜✉✐çõ❡s ❝♦♠♦ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧ ♣❛r❛ ♦❜t❡r ♥♦✈♦s ♠♦✲ ❞❡❧♦s ❞❡ s❡r✈✐ç♦✿ ❡①♣♦♥❡♥❝✐❛❧✱ ❲❡✐❜✉❧❧ ❡ ❇✐r♥❜❛✉♠ ❙❛✉♥❞❡rs✱ ❡♥tã♦✱ ♦❜t❡♠♦s s❡✐s ♥♦✲ ✈❛s ❞✐str✐❜✉✐çõ❡s ❛ ♣❛rt✐r ❞❛s ❞✐str✐❜✉✐çõ❡s ▼❆❳❈❖▼P● ❡ ▼■◆❈❖▼P● q✉❡ ❢♦r❛♠ ♥♦♠❡❛❞❛s ❝♦♠♦ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❡①♣♦♥❡♥❝✐❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐✲ çã♦ ▼❆❳❈❖▼P❊✱ ❞✐str✐❜✉✐çã♦ ▼í♥✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❡①♣♦♥❡♥❝✐❛❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼■◆❈❖▼P❊✱ ❞✐str✐❜✉✐çã♦ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❲❡✐❜✉❧❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼❆❳❈❖▼P❲✱ ❞✐str✐❜✉✐çã♦ ▼í♥✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲ ❲❡✐❜✉❧❧✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼■◆❈❖▼P❲✱ ❞✐str✐❜✉✐çã♦ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲ P♦✐ss♦♥✲❇✐r♥❜❛✉♠✲❙❛✉♥❞❡rs✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼❆❳❈❖▼P❇❙ ❡ ❛ ❞✐str✐❜✉✐çã♦ ▼í♥✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❇✐r♥❜❛✉♠✲❙❛✉♥❞❡rs✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ▼■◆✲ ❈❖▼P❇❙✳
❆ ❡s❝♦❧❤❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ ❢♦✐ ❢❡✐t❛ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♠❡❧❤♦r ❞❡s❝r❡✈❡r s❡r✈✐❞♦r❡s ❤✉♠❛♥♦s ❡ ✈❡♠ s❡♥❞♦ ❛♠♣❧❛♠❡♥t❡ ✉s❛❞❛ ✭❋❡❧❞♠❛♥♥ ❛♥❞ ❲❤✐tt✱ ✶✾✾✽✮✳ ❊ ❛ ❞✐str✐❜✉✐çã♦ ❇✐r♥❜❛✉♠ ❙❛✉♥❞❡rs ❢♦✐ ✉s❛❞❛ ♣♦✐s ❞❛❞♦s r❡❛✐s ❛♣r❡s❡♥t❛r❡♠ s❡r✈✐ç♦s ❝♦♠ ❡st❛ ❞✐str✐❜✉✐çã♦ ❡ ♥ã♦ ❢♦✐ ❡♥❝♦♥tr❛❞♦ ♥❡♥❤✉♠ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ❝♦♠ ♦ ✉s♦ ❞❡st❛ ❞✐str✐❜✉✐çã♦✱ ❡ ❡ss❛ ❢♦✐ ✉♠❛ ❞❛s ♠♦t✐✈❛çõ❡s ❞❡ ❛❞♦t❛r♠♦s ❡st❛ ❞✐str✐❜✉✐çã♦✳
❈♦♠ ❛ ❝♦♥tr✉çã♦ ❞❡st❛s ♥♦✈❛s ❞✐str✐❜✉✐çõ❡s ❞❡ s❡r✈✐ç♦ ♣❛r❛ ♦ ♠á①✐♠♦ ❡ ♦ ♠í♥✐♠♦ t❡♠♣♦s ❞❡ s❡r✈✐ç♦ s✉r❣❡♠ ♥♦✈♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛✳ ❚❛✐s ♠♦❞❡❧♦s sã♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴●✴✶ ✭●r♦ss ❛♥❞ ❍❛rr✐s✱ ✶✾✾✽✮✱ ♥❛ q✉❛❧ ❛s ❝❤❡❣❛❞❛s ❞♦s ✉s✉ár✐♦s s❡❣✉❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥✱ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ é ❣❡r❛❧✱ ♣♦ss✉✐ ❛♣❡♥❛s ✉♠ s❡r✈✐❞♦r ❡ ♦ ❛t❡♥❞✐♠❡♥t♦ é ♣♦r ♦r❞❡♠ ❞❡ ❝❤❡❣❛❞❛✱ s❡♥❞♦ q✉❡✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛ss✉♠✐♠♦s ❝♦♠♦ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧ ❛s ❞✐str✐❜✉✐çõ❡s ▼❆❳❈❖▼P● ❡ ▼■◆❈❖▼P●✳ ❉❡st❛ ❢♦r♠❛ ♦❜t❡♠♦s ♦s s❡❣✉✐♥t❡s ♠♦❞❡❧♦s ❞❡ ✜❧❛ ▼✴▼❆❳❈❖▼P●✴✶ ❡ ▼✴▼■◆❈❖▼P●✴✶✱ ♣❛r❛ ♦ ♠á①✐♠♦ ❡ ♦ ♠í♥✐♠♦ t❡♠♣♦s ❞❡ s❡r✈✐ç♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
✹
s❡r✈✐ç♦ ❝♦♠ t❛①❛ ❞❡ s❡r✈✐ç♦ ❞❡s❝♦♥❤❡❝✐❞❛✳ ■②❡r ❛♥❞ ▼❛♥❥✉♥❛t❤ ✭✷✵✵✻✮ ❡st✉❞❛r❛♠ ♠♦❞❡❧♦s ❞❡ ✜❧❛s ❡♠ q✉❡ ❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❝♦♥❥✉♥t❛ ❞♦ t❡♠♣♦ ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ❡ ❞♦ s❡r✈✐ç♦ sã♦ ❞❡s❝r✐t❛s ♣❡❧❛ ❝♦♠♣♦s✐çã♦ ❞❡ ♠✐st✉r❛s ✜♥✐t❛s ❞❡ ❞❡♥s✐❞❛❞❡s ❡①♣♦♥❡♥❝✐❛✐s✳ ❈♦r❞❡✐r♦ ❡t ❛❧✳ ✭✷✵✶✷✮ ✐♥tr♦❞✉③✐r❛♠ ✉♠❛ ♥♦✈❛ ❞✐str✐❜✉✐çã♦ ❝❤❛♠❛❞❛ ❞✐str✐❜✉✐çã♦ ❡①♣♦♥❡♥❝✐❛❧✲❈♦♥✇❛②✲ ▼❛①✇❡❧❧✲P♦✐ss♦♥✱ ❞❡♥♦t❛❞❛ ♣♦r ❞✐str✐❜✉✐çã♦ ❊❈❖▼P✳ Pr❛❞♦ ❡t ❛❧✳ ✭✷✵✶✺✮ ❛♣r❡s❡♥t❛r❛♠ ✉♠❛ ♥♦✈❛ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ ❞❡♥♦♠✐♥❛❞❛ ▼á①✐♠♦✲❈♦♥✇❛②✲▼❛①✇❡❧❧✲P♦✐ss♦♥✲❲❡✐❜✉❧❧ ❝♦♠ t❛①❛ ❞❡ s❡r✈✐ç♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✳
❆ ❧✐t❡r❛t✉r❛ é ✈❛st❛ ♣❛r❛ ♠♦❞❡❧♦s ❝♦♠ t❛①❛ ❞❡ s❡r✈✐ç♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✱ ♣♦❞❡♠♦s ❝✐t❛r ♦s s❡❣✉✐♥t❡s ❛rt✐❣♦s✿ ❲❤✐tt ✭✶✾✽✾✮ ✐♥✈❡st✐❣♦✉ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴▼✴✶ ❝♦♠ ♦ ❝r❡s❝❡♥t❡ ❛✉♠❡♥t♦ ❞❛ t❛①❛ ❞❡ ❝❤❡❣❛❞❛✳ ❆❞❛♥ ❛♥❞ ❑✉❧❦❛r♥✐ ✭✷✵✵✸✮ ❡st✉❞❛r❛♠ ✉♠ s✐st❡♠❛ ❝♦♠ ✉♠ ú♥✐❝♦ s❡r✈✐❞♦r✱ ♥❛ q✉❛❧ ♦s t❡♠♣♦s ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ❡ t❡♠♣♦s ❞❡ s❡r✈✐ç♦s ❞❡♣❡♥❞❡♠ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈ ❞✐s❝r❡t❛✳ ❱❛♥ ❍♦✉❞t ❡t ❛❧✳ ✭✷✵✵✸✮ ❛♣r❡s❡♥t❛r❛♠ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❛tr❛s♦ ❞❡ ✉s✉ár✐♦s ❝♦♠ ✐♠♣❛❝✐ê♥❝✐❛ ❡ ♣❛❝✐ê♥❝✐❛✱ s❡❣✉♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ❝♦♠ t❡♠♣♦ ❞✐s❝r❡t♦✱ ♥❛ q✉❛❧ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ ❞❡♣❡♥❞❡ ❞♦ t❡♠♣♦ ❞❡ ❡s♣❡r❛ ❞♦ ✉s✉ár✐♦✳ ❇❡❦❦❡r ❡t ❛❧✳ ✭✷✵✵✹✮ ❡st✉❞❛r❛♠ ♠♦❞❡❧♦s ❞❡ ✜❧❛ ❝♦♠ ❝❛r❣❛ ❞❡ tr❛❜❛❧❤♦ ❞❡♣❡♥❞❡♥t❡ ❞❛ ❝❤❡❣❛❞❛ ❡ ❞❛ r❛♣✐❞❡③ ❞♦ s❡r✈✐ç♦✳ ❑♦♦❧❡ ❡t ❛❧✳ ✭✷✵✵✺✮ ❡st✉❞❛r❛♠ ♦ ✐♠♣❛❝t♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ ♥❛ ❞✐str✐❜✉✐çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ♠á①✐♠♦ ❞❛ ✜❧❛ ❞❡ ❡s♣❡r❛ ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ♦❝✉♣❛❞♦ ❞♦ ♠♦❞❡❧♦ Mx✴●✴✶✱ ♥❛ q✉❛❧ x r❡♣r❡s❡♥t❛ ❛s ❝❤❡❣❛❞❛s ❡♠ ❜❧♦❝♦s✳ ▲❡❡ ❛♥❞ ❑✐♠ ✭✷✵✵✻✮
❝♦♥s✐❞❡r❛r❛♠ ♦ ♠♦❞❡❧♦ ❞❡ ▼✴●✴✶✱ ♥♦ q✉❛❧ ❛ r❛♣✐❞❡③ ❞♦ s❡r✈✐❞♦r ❞❡♣❡♥❞❡ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ tr❛❜❛❧❤♦ ♣r❡s❡♥t❡ ♥♦ s✐st❡♠❛✱ ❡ ❛ ♣♦❧ít✐❝❛ ❞❡ s❡r✈✐ç♦ é ❞❛❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ❡st♦q✉❡✳ ❈r✉③ ❛♥❞ ❙♠✐t❤ ✭✷✵✵✼✮ ♣r♦♣✉s❡r❛♠ ✉♠❛ ❛♥á❧✐s❡ ❛♣r♦①✐♠❛❞❛ ♣❛r❛ r❡❞❡s ❞❡ ✜❧❛s ❛❜❡rt❛s ❝♦♠ ❞✐str✐❜✉✐çã♦ ▼❛r❦♦✈✐❛♥❛ ♣❛r❛ ♦ t❡♠♣♦ ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ❡ ❝♦♠ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛ ❝♦♠cs❡r✈✐❞♦r❡s ❡♠ ♣❛r❛❧❡❧♦✳ ❘❛♠s❛② ✭✷✵✵✼✮ ❡♥❝♦♥tr♦✉
✺
s❡❧❡çã♦ ❞❡ r♦t❛✳ ❇❡❦❦❡r ❡t ❛❧✳ ✭✷✵✶✶✮ ❡st✉❞❛r❛♠ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ t❡♠♣♦ ❞❡ ❡s♣❡r❛ ♥❛ ✜❧❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ s❡r✈✐ç♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ ♣r✐♠❡✐r♦ ✉s✉ár✐♦ ♥❛ ✜❧❛✳ ❙✐♥❣❤ ❡t ❛❧✳ ✭✷✵✶✷✮ ❡st✉❞❛r❛♠ s✐st❡♠❛s ❞❡ ✜❧❛s ❝♦♠ ✉♠ ú♥✐❝♦ s❡r✈✐❞♦r✱ ❡♠ q✉❡ ❛s ❝❤❡❣❛❞❛s s❡❣✉❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ P♦✐ss♦♥ ❝♦♠ t❛①❛s ❞❡ ❝❤❡❣❛❞❛ ✈❛r✐❛♥❞♦ ❡ ❝♦♠ ❞✐str✐❜✉✐çã♦ ❣❡r❛❧ ♣❛r❛ ♦ t❡♠♣♦ ❞❡ s❡r✈✐ç♦✳ ❚❡③❝❛♥ ✭✷✵✶✷✮ ❡st✉❞♦✉ ✉♠ ❝♦♥tr♦❧❡ ót✐♠♦ ❞❡ s❡r✈✐❞♦r❡s ❤❡t❡r♦❣ê♥❡♦s ❝♦♠ ❞✐str✐❜✉✐çã♦ ❞❡ s❡r✈✐ç♦ ❞❛❞❛ ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ❤✐♣❡r✲❡①♣♦♥❡♥❝✐❛❧✱ ❞❡♥♦t❛❞❛ ❞❡H∗✳
❆ ❧✐♠✐t❛çã♦ ❡♥❝♦♥tr❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛ ♥♦ ❡st✉❞♦ ❞❡ ♥♦✈♦s ♠♦❞❡❧♦s ❞❡ s❡r✈✐ç♦ t❛♠✲ ❜é♠ ❢♦✐ ✉♠❛ ❞❛s ♠♦t✐✈❛çõ❡s ❞❡st❡ tr❛❜❛❧❤♦✳ ■st♦ ♦❝♦rr❡✱ ❞❡✈✐❞♦ ❛ ❞✐✜❝✉❧❞❛❞❡ ❞❡ ❡♥❝♦♥tr❛r ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ♥❛ ♦❝♦rrê♥❝✐❛ ❞❛ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ s❡r✈✐ç♦ ❡ ❝❤❡❣❛❞❛s✱ ♣r✐♥✲ ❝✐♣❛❧♠❡♥t❡✱ q✉❛♥❞♦ r❡❧❛①❛♠♦s ❛ s✉♣♦s✐çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❡①♣♦♥❡♥❝✐❛❧ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ s❡r✈✐ç♦ ❡✴♦✉ t❡♠♣♦s ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ✭●r♦ss ❛♥❞ ❍❛rr✐s✱ ✶✾✾✽✮ ❡ ✭❲♦❧✛✱ ✶✾✽✾✮✳ ❖ r❡❧❛①❛♠❡♥t♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❡①♣♦♥❡♥❝✐❛❧ ❢❛③ ❝♦♠ q✉❡ ♦ t❡♠♣♦ ♣❛r❛ ❝♦♠♣❧❡t❛r ♦ s❡r✈✐ç♦ ♥ã♦ ♣♦ss❛ s❡r ❞❡t❡r♠✐♥❛❞♦✱ ❞❛❞♦ q✉❡ s✉❛ ❞✐str✐❜✉✐çã♦ ♥ã♦ t❡♠ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❛ ♣r♦♣r✐✲ ❡❞❛❞❡ ❞❡ ❢❛❧t❛ ❞❡ ♠❡♠ór✐❛✱ ❡ ♥❡st❡ ❝❛s♦ ♦s s✐st❡♠❛s ♥ã♦ sã♦ ▼❛r❦♦✈✐❛♥♦s✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❞❡♣❡♥❞ê♥❝✐❛ é ♠✉✐t❛s ✈❡③❡s ✐❣♥♦r❛❞❛ ♥❛ t❡♦r✐❛ ❞❛s ✜❧❛s ❡♠ r❛③ã♦ ❞❛ ❞✐✜❝✉❧❞❛❞❡ ❥á ❝✐t❛❞❛ ✭❈✐✈❡❧❡❦ ❡t ❛❧✳✱ ✷✵✵✾✮✳
❆ ♣r❡s❡♥t❡ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ é ♦r❣❛♥✐③❛❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
◆♦ ❈❛♣ít✉❧♦ ✷✱ ❛♣r❡s❡♥t❛♠♦s ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❛ t❡♦r✐❛ ❞❛s ✜❧❛s✱ ❛s✲ s✐♠ ❝♦♠♦✱ ❛ ♣r♦♣r✐❡❞❛❞❡ P♦✐ss♦♥ ❆rr✐✈❛❧ ❙❡❡ ❚✐♠❡ ❆✈❡r❛❣❡s✱ ❞❡♥♦t❛❞❛ ❝♦♠♦ ♣r♦♣r✐❞❛❞❡ P❆❙❚❆✳ ❊st❛ ♣r♦♣r✐❡❞❛❞❡ é ✐♠♣♦rt❛♥t❡ ♥❛ ♦❜t❡♥çã♦ ❞❛s ❞✐str✐❜✉✐çõ❡s ❞♦ t❡♠♣♦ ❞❡ ❡s✲ ♣❡r❛ ♥❛ ✜❧❛ ❡ ♥♦ s✐st❡♠❛✳ ▼♦str❛♠♦s✱ t❛♠❜é♠✱ ♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ M/G/1 q✉❡ é ❞❡ ♥♦ss♦ ✐♥t❡r❡ss❡✱ ♣♦✐s ♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s ♥❡st❡ tr❛❜❛❧❤♦ sã♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❡st❡ ♠♦❞❡❧♦✳
✻
◆♦s ❈❛♣ít✉❧♦s ✹✱ ✺ ❡ ✻ ❛♣r❡s❡♥t❛♠♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s ♠♦❞❡❧♦s ▼✴▼❆❳❈❖▼P❊✴✶ ❡ ▼✴▼■◆❈❖▼P❊✴✶✱ ♠♦❞❡❧♦s ▼✴▼❆❳❈❖▼P❲✴✶ ❡ ▼✴▼■◆❈❖▼P❲✴✶ ❡ ♦s ♠♦❞❡❧♦s ▼✴▼❆❳❈❖▼P❇❙✴✶ ❡ ▼✴▼■◆❈❖▼P❇❙✴✶✱ ❛❧é♠ ❞♦s ♠♦❞❡❧♦s ♣❛rt✐❝✉❧❛r❡s ✜①❛♥❞♦ ♦s ✈❛❧♦r❡s ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♣r❡ssã♦ ♣❛r❛ ❝❛❞❛ ✉♠ ❞❡st❡s ♠♦❞❡❧♦s✳ ❆♣r❡s❡♥t❛♠♦s ❛s ♣r♦♣r✐❡✲ ❞❛❞❡s ❞❡st❡s ♠♦❞❡❧♦s✱ ❝♦♠♦ ❛s ❡①♣r❡ssõ❡s ♣❛r❛ ❛s ❢✉♥çõ❡s ❞❡ ❞❡♥s✐❞❛❞❡ ❞❛s ❞✐str✐❜✉✐çõ❡s ❞♦s t❡♠♣♦s ❞❡ s❡r✈✐ç♦ ❡ s❡✉s ♠♦♠❡♥t♦s✱ ❡✱ ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s ♥♦ s✐st❡♠❛ ❡ ❞♦ t❡♠♣♦ ❞❡ ❡s♣❡r❛ ♥❛ ✜❧❛✳ ❯s❛♠♦s ♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐✲ ❧❤❛♥ç❛ ♣❛r❛ ❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞♦s ♠♦❞❡❧♦s✳ P❛r❛ ✐❧✉str❛r ♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s✱ ❞❛❞♦s s✐♠✉❧❛❞♦s ❡ ❞❛❞♦s r❡❛✐s ❢♦r❛♠ ✉t✐❧✐③❛❞♦s✳
❈❛♣ít✉❧♦ ✷
■♥tr♦❞✉çã♦ ❛ t❡♦r✐❛ ❞❛s ✜❧❛s
◆❡st❡ ❝❛♣ít✉❧♦✱ ❛♣r❡s❡♥t❛♠♦s ❛♣❡♥❛s ✉♠ ❜r❡✈❡ r❡❧❛t♦ s♦❜r❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❞❛ t❡♦r✐❛ ❞❛s ✜❧❛s✳ P❛r❛ ♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s✱ ❡①✐st❡ ✉♠ ✈❛st♦ ♠❛t❡r✐❛❧ ❞✐s♣♦♥í✈❡❧✱ ❞❡♥tr❡ ♦s q✉❛✐s ♣♦❞❡♠♦s ❝✐t❛r ❛s ♣r✐♥❝✐♣❛✐s r❡❢❡rê♥❝✐❛s ❞❡st❡ tr❛❜❛❧❤♦✱ ✭❲♦❧✛✱ ✶✾✽✾✮✱ ✭●r♦ss ❛♥❞ ❍❛rr✐s✱ ✶✾✾✽✮ ❡ ✭P✐♥s❦② ❛♥❞ ❑❛r❧✐♥✱ ✷✵✶✵✮✳ ❊♠ s❡❣✉✐❞❛✱ ♠♦str❛♠♦s ❛ ♣r♦♣r✐❡❞❛❞❡ P♦✐ss♦♥ ❆rr✐✈❛❧s s❡❡ ❚✐♠❡ ❆✈❡r❛❣❡✱ ❞❡♥♦t❛❞❛ ♣♦r P❆❙❚❆✱ q✉❡ é ✉♠❛ ♣r♦♣r✐❡❞❛❞❡ ✐♠♣♦rt❛♥t❡ ❡ ♠✉✐t♦ ✉s❛❞❛ ♥❛ t❡♦r✐❛ ❞❛s ✜❧❛s ✭❲♦❧✛✱ ✶✾✽✾✮✱ ❡✱ ✜♥❛❧♠❡♥t❡✱ ♦ ♠♦❞❡❧♦ ❞❡ ✜❧❛ ▼✴●✴✶✱ q✉❡ é ❞❡ ♥♦ss♦ ✐♥t❡r❡ss❡ ♣♦✐s ♦s ♠♦❞❡❧♦s ♣r♦♣♦st♦s ♥❡st❡ tr❛❜❛❧❤♦ sã♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❡st❡ ♠♦❞❡❧♦✳
✷✳✶
■♥tr♦❞✉çã♦ ❛♦ ❝♦♥❝❡✐t♦ ❞❡ ✜❧❛
❯♠ ♠♦❞❡❧♦ ♦✉ s✐st❡♠❛ ❞❡ ✜❧❛ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ✉s✉ár✐♦s ❝❤❡✲ ❣❛♠ ♣❛r❛ r❡❝❡❜❡r ✉♠ ❝❡rt♦ s❡r✈✐ç♦ ❡✱ ❞❡✈✐❞♦ à ✐♠♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛t❡♥❞✐♠❡♥t♦ ✐♠❡❞✐❛t♦✱ ❢♦r♠❛♠ ✉♠❛ ✜❧❛ ❞❡ ❡s♣❡r❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦s t❡r♠♦s ✉s✉ár✐♦s ❡ s❡r✈✐ç♦ sã♦ ✉s❛❞♦s ❡♠ ✉♠ s❡♥t✐❞♦ ❛♠♣❧♦✳ P♦❞❡♠♦s ❡st❛r ♥♦s r❡❢❡r✐♥❞♦ ❛ ❝❛rr♦s q✉❡ ❝❤❡❣❛♠ ❛ ✉♠ ♣♦st♦ ❞❡ s❡r✈✐ç♦✱ ♠áq✉✐♥❛s q✉❡ ❡s♣❡r❛♠ ♣❛r❛ s❡r❡♠ ❝♦♥s❡rt❛❞❛s ♦✉ ♠❡♥s❛❣❡♥s q✉❡ sã♦ tr❛♥s♠✐t✐❞❛s ♣♦r ❝❛♥❛✐s ❞❡ ❝♦♠✉♥✐❝❛çã♦✳
❖ ♦❜❥❡t✐✈♦ ❞♦ ❡st✉❞♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✜❧❛ é ❛ ♠❡❧❤♦r✐❛ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♠❡❧❤♦r ✉t✐❧✐③❛çã♦ ❞♦s r❡❝✉rs♦s ❞♦s s❡r✈✐ç♦s ❞✐s♣♦♥í✈❡✐s✱ ♠❡♥♦r t❡♠♣♦ ❞❡ ❡s♣❡r❛ ❡ ♠❛✐♦r r❛♣✐❞❡③ ♥♦ ❛t❡♥❞✐♠❡♥t♦✳ ❖ ♣✐♦♥❡✐r♦ ♥❡st❡ ❡st✉❞♦ ❢♦✐ ❆✳ ❑✳ ❊r❧❛♥❣
✽
q✉❡✱ ❝♦♠♦ ❡♥❣❡♥❤❡✐r♦ ❞❛ ❝♦♠♣❛♥❤✐❛ ❞✐♥❛♠❛rq✉❡s❛ ❞❡ t❡❧❡❢♦♥❡s✱ ❡st✉❞♦✉ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❞❡ ❧✐♥❤❛s ✭❇r♦❝❦♠❡②❡r ❡t ❛❧✳✱ ✶✾✹✽✮✳ ❆ ♣❛rt✐r ❞❛í✱ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ár❡❛s t❡♠ ✉t✐❧✐③❛❞♦ ❡st❛ ❢❡rr❛♠❡♥t❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ♥♦ ✢✉①♦ ❞❡ trá❢❡❣♦ ❞❡ ✈❡í❝✉❧♦s ❡ ❡♠ ❝❡♥tr❛✐s ❞❡ ❛t❡♥❞✐♠❡♥t♦✳
✷✳✶✳✶ Pr✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ✜❧❛
❆❧❣✉♠❛s ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❜ás✐❝❛s ❞❡ ✉♠❛ ✜❧❛✱ ❝♦♠♦ ❝❤❡❣❛❞❛s✱ s❡r✈✐ç♦s✱ ❞✐s❝✐✲ ♣❧✐♥❛ ❞❡ ❛t❡♥❞✐♠❡♥t♦ ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡s♣❡r❛ sã♦✱ ❜r❡✈❡♠❡♥t❡✱ ❞❡s❝r✐t❛s ❛ s❡❣✉✐r✳ P❛r❛ ♠❛✐♦r❡s ❞❡t❛❧❤❡s ✈❡❥❛♠ ✭P✐♥s❦② ❛♥❞ ❑❛r❧✐♥✱ ✷✵✶✵✮✳
• ❖ ♣r♦❝❡ss♦ ❞❡ ❝❤❡❣❛❞❛ é ❛ ❞❡s❝r✐çã♦ ❞❡ ❝♦♠♦ ♦s ✉s✉ár✐♦s ♣r♦❝✉r❛♠ ♦ s❡r✈✐ç♦✳ ❙❡
❡❧❡s ❝❤❡❣❛♠ ❛ ✐♥t❡r✈❛❧♦s ✜①♦s ❞❡ t❡♠♣♦✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❝❤❡❣❛❞❛ é ❞✐t♦ ❝♦♥st❛♥t❡ ♦✉ ❞❡t❡r♠✐♥íst✐❝♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ s❡ ❛s ❝❤❡❣❛❞❛s sã♦ ❛❧❡❛tór✐❛s ♥♦ t❡♠♣♦✱ ❡❧❛s ❢♦r♠❛♠ ✉♠ ♣r♦❝❡ss♦ ❡st♦❝ást✐❝♦ ❡ é ♥❡❝❡ssár✐♦ ❞❡s❝r❡✈❡r s✉❛s ♣r♦♣r✐❡❞❛❞❡s ♣r♦❜❛❜✐❧íst✐❝❛s✳ ❆ s✉♣♦s✐çã♦ ♠❛✐s ❝♦♠✉♠ é q✉❡ ❛s ❝❤❡❣❛❞❛s ❢♦r♠❛♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ r❡♥♦✈❛çã♦ ✭P✐♥s❦② ❛♥❞ ❑❛r❧✐♥✱ ✷✵✶✵✮✱ ✐st♦ é✱ ♦s ✐♥t❡r✈❛❧♦s ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ✐❞❡♥t✐❝❛♠❡♥t❡ ❞✐str✐❜✉í❞♦s✳ ❊♠ ❣❡r❛❧✱ é t❛♠❜é♠ ❛ss✉♠✐❞♦ ❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♠ r❡❧❛çã♦ ❛♦ s❡r✈✐ç♦✳ ❚❛♠❜é♠ s❡ ❢❛③ ♥❡❝❡ssár✐♦ s❛❜❡r s❡ ❛s ❝❤❡❣❛❞❛s sã♦ ✉♥✐tár✐❛s ♦✉ ❡♠ ❜❧♦❝♦s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞❛ ❝❤❡❣❛❞❛ ❞❡ ♣❛ss❛❣❡✐r♦s ❞❡ ✉♠ ✈ô♦ ❡♠ ✉♠ ❛❡r♦♣♦rt♦✳
• ❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❝❤❡❣❛❞❛✱ ♣♦❞❡♠♦s ❝♦♥s✐❞❡r❛r ♦ ♣r♦❝❡ss♦ ❞❡
s❡r✈✐ç♦ ❝♦♠♦ s❡♥❞♦ ❞❡t❡r♠✐♥íst✐❝♦ ♦✉ ❛❧❡❛tór✐♦✳ ❆ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ s❡r✈✐ç♦ ♣♦❞❡ ❞❡♣❡♥❞❡r ❞♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛ ♦✉✱ ❛té ♠❡s♠♦✱ ❞♦ t✐♣♦ ❞❡ ✉s✉ár✐♦ ❛ s❡r s❡r✈✐❞♦✳ ❆ ❤✐♣ót❡s❡ ♠❛✐s s✐♠♣❧❡s é ❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ s❡r✈✐ç♦s ❡ ❝❤❡❣❛❞❛s✳ ❖ ♥ú♠❡r♦ ❞❡ s❡r✈✐❞♦r❡s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❛t❡♥❞❡r ❛ ✉♠❛ ♠❡s♠❛ ✜❧❛ t❛♠❜é♠ ❞❡✈❡ s❡r ❡s♣❡❝✐✜❝❛❞♦✳ ◆❡ss❡ ❝❛s♦✱ é ❝♦♠✉♠ ♠❡♥❝✐♦♥❛r q✉❡ ♦s s❡r✈✐❞♦r❡s ❡stã♦ ❡♠ ♣❛r❛❧❡❧♦ ♥✉♠❛ r❡❢❡rê♥❝✐❛ ❛ ❡st❛r❡♠ ❛t❡♥❞❡♥❞♦ ✉♠❛ ♠❡s♠❛ ✜❧❛✳
• ❆ ❞✐s❝✐♣❧✐♥❛ ❞❛ ✜❧❛ s❡ r❡❢❡r❡ ❛ ♠❛♥❡✐r❛ ❝♦♠♦ ♦s ✉s✉ár✐♦s s❡rã♦ s❡❧❡❝✐♦♥❛❞♦s ♣❛r❛
✾
❞✐s❝✐♣❧✐♥❛s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ▲■❋❖ ✭❞♦ ✐♥❣❧ês✱ ❧❛st ✐♥ ✜st ♦✉t✮✱ ❡♠ q✉❡ ♦ ú❧t✐♠♦ q✉❡ ❝❤❡❣❛ é ♦ ♣r✐♠❡✐r♦ ❛ s❡r ❛t❡♥❞✐❞♦✱ ❡ ❛ s❡❧❡çã♦ ❛❧❡❛tór✐❛ ❞♦s ✉s✉ár✐♦s ♥❛ ✜❧❛✱ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❙✐r♦ ✭❞♦ ✐♥❣❧ês s❡r✈❡ ✐♥ r❛♥❞♦♠ ♦r❞❡r✮✳ ❆ ❞✐s❝✐♣❧✐♥❛ ❞❡ ❛t❡♥❞✐♠❡♥t♦ ♣♦❞❡ ❛✐♥❞❛ ❡st❛❜❡❧❡❝❡r ♣r✐♦r✐❞❛❞❡s ❡♥tr❡ ♦s ✉s✉ár✐♦s✱ ❞❡ ♠♦❞♦ ❛ ❛t❡♥❞❡r ♣r✐♠❡✐r♦ ♦s ✉s✉ár✐♦s ❝♦♠ ❛❧t❛ ♣r✐♦r✐❞❛❞❡✳ ❊♠ ❛❧❣✉♥s ♠♦❞❡❧♦s✱ ♦ s❡r✈✐ç♦ ♣♦❞❡ s❡r ✐♥t❡rr♦♠♣✐❞♦ ♣❛r❛ ❞❛r ❧✉❣❛r ❛ ✉♠ ✉s✉ár✐♦ ❞❡ ♣r✐♦r✐❞❛❞❡ ♠❛✐s ❛❧t❛✳
• ❆ ❝❛♣❛❝✐❞❛❞❡ ❞❛ ✜❧❛ é ❛ ❧✐♠✐t❛çã♦ ❢ís✐❝❛ ♥♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s q✉❡ ♣♦❞❡♠ ❡s♣❡r❛r
♥♦ s✐st❡♠❛✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♠ ✉♠❛ s❛❧❛ ❞❡ ❡s♣❡r❛ ♣❛r❛ ✉♠❛ ❝♦♥s✉❧t❛ ♠é❞✐❝❛✳ ❙❡ ❛ ❝❛♣❛❝✐❞❛❞❡ t♦t❛❧ ❡st✐✈❡r ♦❝✉♣❛❞❛✱ ♦ ✉s✉ár✐♦ ♥ã♦ ♣♦❞❡rá ❡♥tr❛r ♥♦ s✐st❡♠❛ ❡ s❡rá ♣❡r❞✐❞♦ ♦✉ ❞❡s✈✐❛❞♦ ♣❛r❛ ♦✉tr♦ ❝❡♥tr♦ ❞❡ s❡r✈✐ç♦✳ ❊ss❛ ❧✐♠✐t❛çã♦ s❡ r❡❧❛❝✐♦♥❛ ❝♦♠ ❛ ❝❤❡❣❛❞❛✱ ♠❛s ❛ ❞❡❝✐sã♦ ❞❡ s❡ ✐♥t❡❣r❛r à ✜❧❛ ♥ã♦ é ❞♦ ✉s✉ár✐♦ ❡ s✐♠ ❞♦ s✐st❡♠❛ ❞❡ s❡r✈✐ç♦✳ ❆ ❝❛♣❛❝✐❞❛❞❡ ❞❛ ✜❧❛ t❛♠❜é♠ ♣♦❞❡ s❡r ✐♥✜♥✐t❛✱ ♥❡st❡ ❝❛s♦✱ ♦ s✐st❡♠❛ ♥ã♦ ♣♦ss✉✐ s❛❧❛ ❞❡ ❡s♣❡r❛ ❧✐♠✐t❛❞❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❛❝❡ss♦s ❛ ✇❡❜ s✐t❡ ❡ t❡❧❡❢ô♥✐❛✳
❆ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ✉♠❛ ✜❧❛✱ ❡♠ ❣❡r❛❧✱ é ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦ ❛ ♥♦t❛çã♦ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❑❡♥❞❛❧❧ ✭✶✾✺✸✮✱ ❛ q✉❛❧ ✉t✐❧✐③❛ sí♠❜♦❧♦s ❡ ❜❛rr❛s t❛❧ ❝♦♠♦ A/B/H/C/Z✱ s❡♥❞♦ q✉❡ A
✐♥❞✐❝❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s✱ B ✐♥❞✐❝❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡
s❡r✈✐ç♦✱ H ♦ ♥ú♠❡r♦ ❞❡ s❡r✈✐❞♦r❡s✱ C ❛ ❝❛♣❛❝✐❞❛❞❡ ❞♦ s✐st❡♠❛ ❡ Z é ❛ ❞✐s❝✐♣❧✐♥❛ ❞❛ ✜❧❛✳
❆ ♦♠✐ssã♦ ❞❡ C ❡Z ♥❛ r❡♣r❡s❡♥t❛çã♦ ❛❝✐♠❛✱ ✐♥❞✐❝❛ q✉❡ ❛ ✜❧❛ t❡♠ ❝❛♣❛❝✐❞❛❞❡ ✐♥✜♥✐t❛ ❡ ❛
✶✵
❚❛❜❡❧❛ ✷✳✶✿ ◆♦t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ✜❧❛s
❈❛r❛❝t❡ríst✐❝❛s ❙í♠❜♦❧♦s ❙✐❣♥✐✜❝❛❞♦
▼ ❡①♣♦♥❡♥❝✐❛❧
❉✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❡♥tr❡ ❛s ❝❤❡❣❛❞❛s ✭❆✮ ❉ ❞❡t❡r♠✐♥íst✐❝❛
Ek ❊r❧❛♥❣ ❞♦ t✐♣♦ k
●■ ❣❡r❛❧ ✐♥❞❡♣❡♥❞❡♥t❡ ❉✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ s❡r✈✐ç♦ ✭❇✮ ▼ ❡①♣♦♥❡♥❝✐❛❧
❉ ❞❡t❡r♠✐♥íst✐❝❛
Ek ❊r❧❛♥❣ ❞♦ t✐♣♦ k
● ❣❡r❛❧ ✐♥❞❡♣❡♥❞❡♥t❡ ◆ú♠❡r♦ ❞❡ s❡r✈✐❞♦r❡s ✭❍✮ 1,2, . . . ,∞
❈❛♣❛❝✐❞❛❞❡ ❞♦ s✐st❡♠❛ ✭❈✮ 1,2, . . . ,∞
❉✐s❝✐♣❧✐♥❛ ✭❩✮ ❋■❋❖ ♣r✐♠❡✐r♦ q✉❡ ❝❤❡❣❛✱
é ♦ ♣r✐♠❡✐r♦ ❛ s❡r ❛t❡♥❞✐❞♦ ▲■❋❖ ú❧t✐♠♦ q✉❡ ❝❤❡❣❛✱
é ♦ ♣r✐♠❡✐r♦ ❛ s❡r ❛t❡♥❞✐❞♦
✷✳✷ Pr♦♣r✐❡❞❛❞❡ P❛st❛
❱❛♠♦s ❢❛③❡r ✉♠ ❜r❡✈❡ r❡❧❛t♦ s♦❜r❡ ♣r♦♣r✐❡❞❛❞❡ P❆❙❚❆✱ ❝✉❥❛ ♣r♦✈❛ ♣♦❞❡♠♦s ❡♥❝♦♥tr❛r ❡♠ ❲♦❧✛ ✭✶✾✽✾✮✳ ❆ ♣r♦♣r✐❡❞❛❞❡ P❆❙❚❆ é ✉♠❛ ❛❜r❡✈✐❛t✉r❛ ❞❡ P♦✐ss♦♥ ❆rr✐✈❛❧s ❙❡❡ ❚✐♠❡ ❆✈❡r❛❣❡s✳ ❊ss❡ r❡s✉❧t❛❞♦ ✐♥❞✐❝❛ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s ♥♦ s✐st❡♠❛ ❡♠ t❡♠♣♦ ❝♦♥tí♥✉♦ é ✐❣✉❛❧ àq✉❡❧❛ ♦❜t✐❞❛ ♦❜s❡r✈❛♥❞♦✲s❡ ♦ s✐st❡♠❛ ♥♦s ✐♥st❛♥t❡s ✐♠❡❞✐❛t❛♠❡♥t❡ ♣r❡❝❡❞❡♥t❡s ❛ ✉♠❛ ❝❤❡❣❛❞❛✳ ■st♦ é✱ ❡♠ r❡❣✐♠❡ ❡st❛❝✐♦♥ár✐♦✱ ♦s ✉s✉ár✐♦s q✉❡ ❝❤❡❣❛♠ ✧❡①❡r❣❛♠✧♦ s✐st❡♠❛ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠ t❡♠♣♦ ❝♦♥tí♥✉♦✳ ❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❝❤❡❣❛❞❛ ❡♥❝♦♥tr❛r ♦ s✐st❡♠❛ ♥✉♠ ♣❛rt✐❝✉❧❛r ❡st❛❞♦ é ✉♠❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥t❡r❡ss❡ ♥♦ ❡st✉❞♦ ❞❡ ✜❧❛s ❡✱ ❡♠ ❡s♣❡❝✐❛❧✱ s❡rá ♥❡❝❡ssár✐❛ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❡s♣❡r❛ ♥❛ ✜❧❛ ❡ ♥♦ s✐st❡♠❛✳
❙❡❥❛πna(t) ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❝❤❡❣❛❞❛ ♥♦ ✐♥st❛♥t❡ t ❡♥❝♦♥tr❛r ♦ s✐st❡♠❛ ♥♦
❡st❛❞♦ n✱ ❡♠ q✉❡ ♦ s✉♣❡r❡s❝r✐t♦ a ✈❡♠ ❞❡ ❛rr✐✈❛❧✱ ❞♦ t❡r♠♦ ❡♠ ✐♥❣❧❡s ♣❛r❛ ❝❤❡❣❛❞❛✳ ❖
✉s✉ár✐♦✱ q✉❡ ❡stá ❝❤❡❣❛♥❞♦ ❡♠t ♥ã♦ é ❝♦♠♣✉t❛❞♦ ♥♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛ ❡✱ ♣♦r ❡ss❛ r❛③ã♦✱ πa
✶✶
t❡r✐♦r❡s ❛ ✉♠❛ ❝❤❡❣❛❞❛ ♦✉ ❞✐str✐❜✉✐çã♦ ✐♠❡rs❛ ♥♦s ✐♥st❛♥t❡s ❞❡ ❝❤❡❣❛❞❛✳ ■r❡♠♦s ❞❡s✐❣♥❛r ♣♦r πa
n ❛ ❝♦rr❡s♣♦♥❞❡♥t❡ ❞✐str✐❜✉✐çã♦ ❡st❛❝✐♦♥ár✐❛✳ ❆ ♣r✐♠❡✐r❛ ✈✐st❛✱ ♣♦❞❡rí❛♠♦s s✉♣♦r
q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❡♠ t❡♠♣♦ ❝♦♥tí♥✉♦ πn ❞❡✈❡r✐❛ s❡♠♣r❡ s❡r ✐❣✉❛❧ ❛ πna ♣❛r❛ t♦❞♦s ♦s
s✐st❡♠❛s ❞❡ ✜❧❛s✳ ❊♥tr❡t❛♥t♦✱ ✐ss♦ ♥ã♦ ❛❝♦♥t❡❝❡✱ ❝♦♠♦ ♣♦❞❡♠♦s ✈❡r ♥♦ ❡①❡♠♣❧♦ ❛ s❡❣✉✐r✳
• ❊①❡♠♣❧♦
❈♦♥s✐❞❡r❡ ✉♠❛ ✜❧❛ ❉✴❉✴✶✱ ❡♠ q✉❡ ❛s ❝❤❡❣❛❞❛s ❡ s❡r✈✐ç♦s sã♦ ❞❡t❡r♠✐♥íst✐❝♦s✱ ✐st♦ é✱ ❛s ❝❤❡❣❛❞❛s sã♦ ❡s♣❛ç❛❞❛s ✐❣✉❛❧♠❡♥t❡ ❛ ❝❛❞❛ x s❡❣✉♥❞♦s ❡ ♦ s❡r✈✐ç♦ t❡♠ ❛ ❞✉r❛çã♦ ❞❡
❡①❛t❛♠❡♥t❡y s❡❣✉♥❞♦s✳ P❛r❛ ❣❛r❛♥t✐r ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ s✐st❡♠❛ ❝♦♥s✐❞❡r❛♠♦s q✉❡y < x✱
♦✉ s❡❥❛✱ ♦ s❡r✈✐ç♦ é ♠❛✐s rá♣✐❞♦ q✉❡ ♦ ✐♥t❡r✈❛❧♦ ❡♥tr❡ ❝❤❡❣❛❞❛s✳ ❉❡ss❛ ❢♦r♠❛✱ ❛♣ós ♦ ❡q✉✐❧í❜r✐♦ ❞♦ s✐st❡♠❛ s❡r ❛t✐♥❣✐❞♦✱ ♦ ✉s✉ár✐♦ q✉❡ ❝❤❡❣❛ ❡♥❝♦♥tr❛ ❛ ✜❧❛ ✈❛③✐❛ ❡ t❡r❡♠♦s ❡ t❡r❡♠♦s πa
0 ❡ πka = 0✱∀k ≥ 1✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❢r❛çã♦ ❞♦ t❡♠♣♦ q✉❡ ♦ s✐st❡♠❛ ❝♦♥té♠
✉♠ ✉s✉ár✐♦ é y/x✳ ◆♦ r❡st❛♥t❡ ❞♦ t❡♠♣♦ ♦ s✐st❡♠❛ ❡st❛rá ✈❛③✐♦✱ ❛ss✐♠✱ π0 = 1−y/x✱
π1 =y/x ❡ πk = 0✱ ∀k≥2✳ ❚❡♠♦s ❛ss✐♠ ✉♠ ❡①❡♠♣❧♦ ❡♠ q✉❡ πn6=πn1✳
❚❡♦r❡♠❛ ✷✳✶ ◆❛ ✜❧❛ M/M/1✱ ❡♠ r❡❣✐♠❡ ❡st❛❝✐♦♥ár✐♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡
✉s✉ár✐♦s ♥♦ s✐st❡♠❛✱ ♥♦s ✐♥st❛♥t❡s ❞❡ ❝❤❡❣❛❞❛✱ ❝♦✐♥❝✐❞❡ ❝♦♠ ❛ ❞✐str✐❜✉✐çã♦ ❡♠ t❡♠♣♦ ❝♦♥tí♥✉♦✱ ✐st♦ é✱ πn =πa
n ❡♠ q✉❡ πna(t)✳
Pr♦✈❛✿ ❊♠ ❡q✉✐❧í❜r✐♦✱ πn(t) = πa
n(t)✱ ∀t✱ ✐♠♣❧✐❝❛♥❞♦ q✉❡ ❛s r❡s♣❡❝t✐✈❛s ❞✐str✐✲
❜✉✐çõ❡s ❡st❛❝✐♦♥ár✐❛s sã♦ ✐❣✉❛✐s✳ ❖ ❡✈❡♥t♦ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛ ✉♠❛ ❝❤❡❣❛❞❛ ♥♦ ✐♥t❡r✈❛❧♦ (t, t+ ∆t)s❡rá r❡♣r❡s❡♥t❛❞♦ ♣♦r A(t, t+ ∆t)✳ ❊♥tã♦
πa
n = lim
∆→0
P[N(t) =n|A(t, t+ ∆t)]
= lim ∆→0
P[N(t) =n] =πn(t),
♦♥❞❡ ❛♣❧✐❝❛♠♦s ❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞♦ ❡✈❡♥t♦A(t, t+ ∆t)❡♠ r❡❧❛çã♦ ❛♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s ♥♦ s✐st❡♠❛ ♥♦ ✐♥st❛♥t❡ t✳ ❖❜s❡r✈❡ q✉❡ ✐st♦ é ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ❞✐r❡t❛ ❞❛s ❝❤❡❣❛❞❛s
