Моделирование системы обслуживания с отказами : Практическое задание по Информационное обеспечение, программирование

Рубрикатор

Информационное обеспечение, программирование

Практические задания

Моделирование системы обслуживания с отказами

Федеральное агентство по образованию

Государственное образовательное учреждение высшего профессионального образования

Ивановский государственный химико-технологический университет

Лабораторная работа №3

Вариант 1

Моделирование систем

Выполнили:

Романычева А.C. гр. 3/42

Стрельников А.А. гр. 3/42

Проверил: Смирнов С.С.

Иваново 2013

Задание

1.Построить модель одноканальной СМО с отказами с использованием блоков библиотеки SimEvents

2.Согласно варианту задания произвести модельные эксперименты и определить статистические характеристики СМО в стационарном режиме

.Результаты вычислений оформить в виде отчета с подробным описанием работы модели, используемых формул и с необходимым графическим материалом.

Одноканальная СМО с отказами представляет собой одну телефонную линию. Заявка (вызов), пришедшая в момент, когда линия занята, получает отказ. Заявки распределены по закону, наименование и параметры которого указаны в таблице вариантов. Продолжительность разговора распределена по закону, наименование и параметры которого указаны в таблице вариант. Определите вероятностные характеристики СМО в установившемся режиме работы.

Таблица 1

Варианты заданий

№ вариантаЗакон поступления заявокЗакон обслуживания заявокЗаконПараметр, минЗаконПараметр, мин1Экспоненциальный10Равномерный8 ± 3

Генератор поступления заявок

Задаем в блоке Time-Based Entity Generator:

Лямбда = 10

Облуживание заявок задаем в блоке Subsystem

По заданию у нас равномерное распределение в интервале от 5 до 11.

Блок Replicate отвечает за отказ от заявок.

Блок Entity Sink уничтожает отказанные заявки.Server собственно сам одноканальный сервер.

Время моделирование установлено 5000, чтобы показать, что СМО переходит в стационарный режим, из графика видно, что это так

Всего сгенерировано 509 заявок, из них обслужено 290 заявок.

Коэффициент использования обслуживающего устройства равен 0.4642.

Далее непосредственно мы определяем статистические характеристики СМО:

1.Абсолютную пропускную способность определим по формуле: А=?×q=5.697 обслуживаний в час.

2.Ротк=1-q= отказано 43%.

3.q мы высчитывали пропорцией между обслуженными и сгенерированными заявками, обслужено 57% заявок.

Вывод: В ходе работы построена СМО с отказами, и вычислены статистические характеристики.

модель одноканальный система отказ

Приложение 1

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Приложение 2

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" 0 8 ! ! & 4&]I;G1S . . 8 ( !@ "

" % $ ! 0 ) / _#@ #@ & "

" 8 !0 @ ! 0 $ 0 @ #P/PX #(!P "

" !@ @ 4 ( 0 $ ! 4 ! 5 0 .,! !"

");G!U=%1Y<&4 !826YP=71/<'1I;VY%;G1I='D !!='1R:6)U=&5.86UE60 "

" !!='1R:6)U=&5.86UE6 !0;&]T5'EP90 !!>&ES1W)I9 "

" !3:&]W0V]U;G10;&]T=&5D !!>&ES3&5G96YD !!>&ES6F"

"]O;0 !/<&5N4V-O<&5!=%-I;5-T87)T !&:6=U<F50;W-I=&EO;@ !"

"83&%B96P !4:71L90 !936EN "

" !936%X !836EN !836%X "

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"%R:V5R<P !,:6YE0V]L;W)S !83&EM:71%>&-E961E9$]P=&EO;@!"

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051,04)<4C(P,#9A7'1O;VQB;WA<9&5S7&1E<V)L:W-<9&5S7"

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"( !@ % $ ! 0 ) / _#@ $"

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}

Приложение 3

Model {"qwe1"7.50{00"""1.2"00

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}{RelationalOperator">="on"Logical (see Configuration Parameters:

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}{Step"1""0""1""-1"D onon

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}{UniformRandomNumber"-1""1""0""-1"D on

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}{Sum"Add1"3[2, 1][855, 412, 885, 443]onoff"Inherit via internal rule""sfix(16)""2^-10""Inherit: Inherit via internal rule"

}{Constant"Constant"6[20, 90, 50, 120]"sfix(16)""2^0"

}{Constant"Constant1"7[340, 650, 370, 680]"sfix(16)""2^0"

}{Constant"Constant2"8[175, 25, 205, 55]"sfix(16)""2^0"

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}{DigitalClock"Digital Clock"13[915, 418, 980, 442]on

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}{Reference"Entity Sink"16[0, 1, 0, 0, 0, 1][335, 568, 420, 622]"1""1.271"on"DataTag1""simeventssink1/Entity Sink""Entity Sink""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model"on"On"

}{DataTypeConversion"Int2Dbl"17[525, 69, 580, 101]"alternate""double""sfix(16)""2^0""double""Floor"

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}{Reference"Output Switch"34[0, 0, 0, 0, 0, 1, 1][500, 287, 600, 343]"1""1.370"on"DataTag2""simeventsrouting1/Output Switch""Output Switch""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""1""First port that is not blocked""34567""Attribute1"off"1"offoff"4100"off"Off""Off""Off""Off""1"

}{Display"Query's Average \nRound Time"37[1][325, 509, 410, 541]"1"off

}{Reference"Query's Full\nRound Time"38[1][360, 418, 445, 472]"1""1.271"on"DataTag3""simeventssink1/Signal Scope""Signal Scope""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Continuous""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""None"on" "" ""Time""des_figposition([5 60 25 25])"off"Limited""10000""Off"onon

}{Reference"Read Timer"39[0, 3, 0, 0, 0, 1, 1][115, 421, 200, 484]"0""1.205"on"DataTag4""simeventstiming1/Read Timer""Read Timer""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""T1""Error"off"On""Off""On""On"

}{RelationalOperator"Relational\nOperator"40[2, 1][465, 67, 495, 98]"alternate"offoff"boolean""boolean"

}{RelationalOperator"Relational\nOperator2"41[2, 1][505, 587, 535, 618]">"off"boolean""boolean"

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}{Reference"Single Server"43[1, 1, 0, 0, 0, 1, 1][310, 301, 395, 359]"1""1.208"on"DataTag6""simeventsserver1/Single Server""Single Server""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Signal port t""1""Weight""500"off"PriorityAttributeName""Ascending"off"ResidualServiceTime"onoff"Off""Off""Off""Off""Off""On""Off"

}{Step"Step"45[915, 360, 945, 390]on"1""0""0"off

}{Stop"Stop Simulation"46[585, 587, 620, 623]

}{SubSystem"Генератор времени\nмежду заявками"18[1, 1][210, 76, 300, 134]{"extended_custcode""Subsystem Initialize Function"" setCanModuleFloatingPointCallback \n(&GlobalModuleCAN_A,

CAN_IRQ_ERROR, can"

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}{Assertion"Assertion"20[350, 167, 410, 213]on

}{Assertion"Assertion1"21[350, 232, 410, 278]on

}{Constant"Constant"22[45, 80, 75, 110]off"sfix(16)""2^0"

}{Product"Divide"23[2, 1][175, 27, 205, 58]off"*/"off"Inherit via internal rule""sfix(16)""2^-10""Inherit: Inherit via internal rule""Floor"off

}{Reference"Lower Bound\non Arrival Rate"24[1, 1][250, 175, 280, 205]"1.216""simulink/Logic and Bit\nOperations/Compare\nTo Constant""Compare To Constant""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model"">""0""uint8"off

}{Math"Math\nFunction"25[1, 1][185, 120, 215, 150]"log""sfix(16)""2^0"

}{Product"Product"26[2, 1][260, 92, 290, 123]offoff"Inherit via internal rule""sfix(16)""2^0""Inherit: Inherit via internal rule"off

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}{UnaryMinus"Unary Minus"28[335, 95, 365, 125]off

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}{"Uniform Random\nNumber"1"Subtract"2

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}

}{"Rate"1[85, 0]{"Divide"2

}{[0, 140]{"Lower Bound\non Arrival Rate"1

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}{"Divide"1[15, 0; 0, 55]"Product"1

}{"Lower Bound\non Arrival Rate"1"Assertion"1

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}{SubSystem"Генератор времени\nмежду заявками1"247[0, 1][70, 221, 160, 279]{"extended_custcode""Subsystem Initialize Function"" setCanModuleFloatingPointCallback \n(&GlobalModuleCAN_A,

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Name"Генератор времени\nмежду заявками1"

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}{Constant"Constant4"264[15, 70, 45, 100]off"5""sfix(16)""2^0"

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}{"Add"1[0, 20]"Product"1

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Name "Количество заявок для эксперимента"

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Name "Начальное время заявки в системе"

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}{Reference"Поступившие заявки"12[1][705, 13, 790, 67]"1""1.271"on"DataTag8""simeventssink1/Signal Scope""Signal Scope""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Stair""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""."on" "" ""Time""des_figposition([5 60 25 25])"off"Limited""10000""Off"onon

}{Reference"Формирование\nзаявок"47[1, 1, 0, 0, 0, 0, 1][335, 77, 420, 133]"1""1.358"on"DataTag9""des_ddg_create""DataTag10""simeventsgenerators1/Entity Generators/Time-Based\nEntity

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}{Reference"Шлюз разрешения"15[1, 0, 0, 0, 0, 1, 1][595, 77, 680, 133]"1""1.140"on"DataTag11""simeventsgates1/Enabled Gate""Enabled Gate""FromPortIcon""-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model"off"2000""Off"

}{"Формирование\nзаявок"1"Relational\nOperator"2

}{

SrcBlock "Интенсивность потока\nзаявок"1[0, 0]"Генератор времени\nмежду заявками"1

}{"Генератор времени\nмежду заявками"

SrcPort 1[0, 0]"Формирование\nзаявок"1

}{"Constant"1

DstBlock "Интенсивность потока\nзаявок"1

}{"Connection""Single Server"RConn1[75, 0]"Output Switch"LConn1

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}

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}{"Add1"1[0, -65]"Divide"2

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}{"Connection""Шлюз разрешения"

SrcPort RConn1[80, 0]"Начальное время заявки в системе"LConn1

}{"Начальное время заявки в системе"

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" $ 0 @ 7)0 X X !@ @ & 4 ( 0 $ ! D ( "

" %(B4 . . 8 ( !@ % $ ! 0 ) $ !4(E #@ #@ & "

" 8 !0 @ ! 0 $ 0 @ ! 5B)0 X X !@ @ & 4 ( 0 "

" $ ! D ( %@B4 . . 8 ( !@ % $ ! 0 ) "

" !:(E #@ $ & 8 !0 @ ! @ $ 0 ! 8)0 !B(E #@"

" # & 8 !0 @ $ 0 . , 8 ( !@ % "

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" * # & ! !0 @ ! 0 $ #@ ' # & ( !0 @ ! 0 "

" $ !0 $ ! ! 0 &UA=&QA8G)O;W0 !S97!A<F%T;W( <V5N=&EN96P &9U;F-T:6]N7VAA;"

"F1L90 . 0 8 ( ! % $ , 0 0 # $,Z7$UA=&QA8C<Q, . , "

"8 ( ! % $ ! 0 0 $ 7 X P !@ @ $ 4 ( 0 $"

" ! ! 0! #@ #@ & ( !0 @ ! 0 $ !0 $ H ! * &9"

"U;F-T:6]N !T>7!E 9FEL90 '!A<F5N=&%G90 . 4 8 ( ! % $ ; 0 "

" 0 &P '5P9&%T95]L:6YE<U]D:7-C<F5T95]S=&%T90 #@ $ & 0 !0 @ ! #@ $ "

" $ X !S8V]P961F=6YC=&EO;@ #@ & & 0 !0 @ ! +0 $ $ T "

" !#.EQ-871L86(W,3!<=&]O;&)O>%QD97-<9&5S8FQK<UQD97-?<V-O<&4R+G . R 8 ( 0 % $ "

" 0 . 4 8 ( ! % $ ; 0 0 &P '5P9&%T95]L:6YE<U]D:7"

"-C<F5T95]S=&%T90 #@ $ & 0 !0 @ ! @ $ $ H !D97-?<V-O<&4R "

" #@ #@ & 8 !0 @ ! 0 $ 0 @ #P/PX !( !@ @ "

" $ 4 ( 0 !< ! ! 7 0W)E871E7V]R7U)E<W1A<G1?4V-O<&4 #@ #@ & 8 "

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" D ( . . 8 ( !@ % $ ! 0 ) "

" #@ # & 0 !0 @ ! ! $ $ $ &YO;F4. . 8 ( !@ % "

" $ ! 0 ) "

}

Приложение 4

Model {"r1"6.40{00"""1.1"00

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$ObjectID 11"1.2.0""SimEvents""0""123456789""0"0000

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}{Sum"rectangular""++"on"Same as first input""sfix(16)""2^0"off"Floor""-1"

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}{UniformRandomNumber"-1""1""0""-1"D on

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}{"center""middle""black""white"off"Arial"10"normal""normal"

}{"Arial"9"normal""normal"

}{"r1"[2, 78, 1005, 718]onoff200"white""landscape""auto""A4""centimeters"[0.500000, 0.500000, 0.500000, 0.500000]1off"100""simulink-default.rpt"{Display"Absolute Bandwidth"[1][660, 365, 750, 395]"1"off

}{Sum"Add"[2, 1][160, 242, 190, 273]"+-"off"Inherit via internal rule""2^-10"

}{Sum"Add1"[2, 1][860, 437, 890, 468]"left"off"Inherit via internal rule""2^-10"

}{Sum"Add2"[2, 1][335, 277, 365, 308]off"Inherit via internal rule""2^-10"

}{Constant"Constant"[15, 85, 45, 115]"1"D on"Sample based""Inherit from 'Constant value'""sfix(16)""Use specified scaling""2^0""inf""inf"

}{Constant"Constant1"[310, 820, 340, 850]"1"D on"Sample based""Inherit from 'Constant value'""sfix(16)""Use specified scaling""2^0""inf""inf"

}{Constant"Constant2"[260, 20, 290, 50]"1"D on"Sample based""Inherit from 'Constant value'""sfix(16)""Use specified scaling""2^0""inf""inf"

}{Constant"Constant3"[50, 200, 80, 230]off"11"D on"Sample based""Inherit from 'Constant value'""sfix(16)""Use specified scaling""2^0""inf""inf"

}{Constant"Constant4"[50, 250, 80, 280]off"5"D on"Sample based""Inherit from 'Constant value'""sfix(16)""Use specified scaling""2^0""inf""inf"

}{Reference"Departures from \nthe System1"[1][500, 663, 585, 717]"1"on"DataTag0""simeventssink1/Signal Scope""Signal Scope"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Stair""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""."on" "" ""Time""des_figposition([5 60 25 25])"off"Off"onon

}{Reference"Departures to\n the System"[1][710, 13, 795, 67]"1"on"DataTag1""simeventssink1/Signal Scope""Signal Scope"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Stair""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""."on" "" ""Time""des_figposition([5 60 25 25])"off"Off"onon

}{DigitalClock"Digital Clock"[920, 443, 985, 467]"left"

}{Product"Divide"[2, 1][765, 435, 800, 470]"left""*/"off"Inherit via internal rule""2^-10""Floor"

}{Reference"Enabled Gate"[1, 0, 0, 0, 0, 1, 1][590, 72, 675, 128]"1"on"DataTag2""simeventsgates1/Enabled Gate""Enabled Gate"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model"off"2000""Off"

}{Reference"Entity Sink"[0, 1, 0, 0, 0, 1][305, 738, 390, 792]"1"on"DataTag3""simeventssink1/Entity Sink""Entity Sink"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model"on"On"

}{DataTypeConversion"Int2Dbl"[520, 64, 575, 96]"alternate""double""Floor"

}{Reference"NumOfQueries"[1, 1][395, 819, 450, 851]"simulink/Math\nOperations/Slider\nGain""Slider Gain"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""1""20""50"

}{Reference"NumOfQueries1"[1, 1][350, 18, 410, 52]"simulink/Math\nOperations/Slider\nGain""Slider Gain"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""1""20""50"

}{Reference"Output Switch"[0, 0, 0, 0, 0, 1, 1][475, 427, 575, 483]"1"on"DataTag4""simeventsrouting1/Output Switch""Output Switch"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""1""First port that is not blocked""34567""Attribute1"off"4100""Off""Off"

}{Product"Product"[2, 1][255, 272, 285, 303]off"Inherit via internal rule"

}{Display"Query's Average \nRound Time1"[1][295, 679, 380, 711]"1"off

}{Reference"Query's Full\nRound Time1"[1][330, 588, 415, 642]"1"on"DataTag5""simeventssink1/Signal Scope""Signal Scope"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Continuous""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""None"on" "" ""Time""des_figposition([5 60 25 25])"off"Off"onon

}{Reference"Read Timer"[0, 3, 0, 0, 0, 1, 1][120, 539, 205, 606]"0"on"DataTag6""simeventstiming1/Read Timer""Read Timer"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""T1""Error"off"On""Off""On""On"

}{RelationalOperator"Relational\nOperator"[460, 62, 490, 93]"alternate"offoff"Boolean"

}{RelationalOperator"Relational\nOperator2"[475, 757, 505, 788]">"off"Boolean"

}{Reference"Server Utilization"[1][320, 353, 405, 407]"left""1"on"DataTag7""simeventssink1/Signal Scope""Signal Scope"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Continuous""Signal""1""Count""Event time""Event time""Count"on"0""10""Stretch axis limits""0""10""Stretch axis limits"on"off"" ""b""-""None"off" "" ""Time""des_figposition([5 60 25 25])"off"Off"onon

}{Reference"Single Server"[1, 1, 0, 0, 0, 1, 1][320, 426, 405, 484]"1"on"DataTag8""simeventsserver1/Single Server""Single Server"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""Signal port t""1""Weight""500"off"PriorityAttributeName""Ascending"off"ResidualServiceTime"on"Off""Off""Off""Off""Off""On"

}{Reference"Start Timer"[0, 1, 0, 0, 0, 1, 1][785, 77, 870, 133]"0"on"DataTag9""simeventstiming1/Start Timer""Start Timer"on"-1"off"Inherit from model""Inherit from model""Inherit from model""Inherit from model""Inherit from model""T1""Warn and continue""On"

}{Step"Step"[920, 385, 950, 415]"left""1""0""0"off

}{Stop"Stop Simulation"[555, 757, 590, 793]

}{UniformRandomNumber"Uniform Random\nNumber"[55, 299, 85, 331]"0""1000""0"

}{From"From_SS_ec_2"[50, 930, 260, 960]"simeventstagdbc13581fdf0508f"

}{From"From_SS_mr_1"[50, 130, 260, 160]"simeventstaga16f24ffe3f2070e"

}{From"From_SS_mr_2"[50, 180, 260, 210]"simeventstage4c3f29d83f3b63f"

}{From"From_SS_mr_3"[50, 230, 260, 260]"simeventstag393c2e71a468762"

}{From"From_SS_mr_4"[50, 280, 260, 310]"simeventstag8ae185563cbabb4"

}{From"From_SS_mr_5"[50, 330, 260, 360]"simeventstag1c5db8bb6045b7e1"

}{Goto"Goto_SS_ec_1"[400, 480, 610, 510]"simeventstag2d2cb5f53746c881""global"

}{Goto"Goto_SS_ec_2"[400, 530, 610, 560]"simeventstag2d8317011a7e3b3a""global"

}{Goto"Goto_SS_ec_3"[400, 580, 610, 610]"simeventstagd4d58db8f2ed867d""global"

}{Goto"Goto_SS_ec_4"[400, 630, 610, 660]"simeventstag1dec61d9a6b93ab1""global"

}{Goto"Goto_SS_ec_5"[400, 680, 610, 710]"simeventstaga678993e48b2feba""global"

}{Goto"Goto_SS_ec_6"[400, 730, 610, 760]"simeventstag3777289921711818""global"

}{Goto"Goto_SS_ec_7"[400, 780, 610, 810]"simeventstag19abf540d0e48912""global"