Simulation in Progress.

A Simulation in an Experiment has ended. Clock is 48000.000000.

Simulation in Progress.

A Simulation in an Experiment has ended. Clock is 528000.000000.

05/20/10 15:18:04 "Run 8. Yield=.8736787710809414. S_1=6.000027138110013; S_2=4.999854398723966;"

Experiment ended.

Полученное уравнение поверхности отклика имеет вид:

Y = 28.4923 +0.0023674 A -9.46114 B -0.000108229 A B +2.11338 A^2 +0.946206 B^2

Время обслуживания 6 и 5 минут соответственно первым и вторым сотрудниками магазина включено в оптимальные условия. При этом оптимальное значение вероятности обслуживания заявок составит 0.8737.

Выводы

В ходе выполнения лабораторной работы был проведен анализ предметной области задачи. На основании проведенного анализа была построена модель двухканальной разомкнутой системы массового обслуживания MAG. Данная модель была смоделирована в среде GPSS World и исследована посредством пользовательского эксперимента.

По результатам дисперсионного и регрессионного анализов видно, что для обеспечения максимальной вероятности обслуживания заявок модель со временем обслуживания клиентов 6 первым продавцом и 5 минут вторым продавцом смоделирована оптимально.

Приложение А

Текст программы

Дисперсионный анализ

**********************************************

* Моделирование работы магазина *

**********************************************

INFORM QTABLE mag,0,10,70

GENERATE (Exponential (1,0,3));Поступление покупателей в магазин

QUEUE mag;Вход покупателей в очередь к сотруднику магазина

TRANSFER BOTH,SOT_1,SOT_2;Переход покупателя к свободному сотруднику магазина

SOT_1 SEIZE SOTRUDNIK_1;Определение занятости 1-го сотрудника магазина

DEPART mag;Выход покупателя из очереди от сотрудника магазина

ADVANCE 6,2;Обслуживание покупателя 1-ым сотрудником магазина

RELEASE SOTRUDNIK_1;Освобождение 1-го сотрудника

TRANSFER,NEXT;Переход к оператору с меткой NEXT

SOT_2 SEIZE SOTRUDNIK_2;Определение занятости 2-го сотрудника магазина

DEPART mag;Выход покупателя из очереди от сотрудника магазина

ADVANCE 5,2.989;Обслуживание покупателя 2-ым сотрудником магазина

RELEASE SOTRUDNIK_2;Освобождение 2-го сотрудника

NEXT SAVEVALUE Ave_Queue,QT$mag; Сохранение времени пребывания в очереди

TERMINATE;Выход покупателя из системы

GENERATE 480;Моделирование работы магазина в течение смены

TERMINATE 1

START 1

*******************************************************

* *

* MAG *

* Factorial Screening Experiment *

* *

*******************************************************

MAG_Results MATRIX,2,2

INITIAL MAG_Results,UNSPECIFIED

MAG_NextRunNumber EQU 0

EXPERIMENT MAG() BEGIN

/* Run 1 */

S_1 = 4;

S_2 = 2.011;

IF (StringCompare(DataType(MAG_Results[1,1]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Set the Run Number Variable at the beginning. */

MAG_NextRunNumber = 1;

/* Log the Run and Execute the Simulation */

MAG_GetResult();

MAG_Results[1,1] = N$SOT_1/N$SOT_2;

END;

/* Run 2 */

S_1 = 4;

S_2 = 7.989;

IF (StringCompare(DataType(MAG_Results[1,2]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Log the Run and Execute the Simulation */

MAG_GetResult();

MAG_Results[1,2] = N$SOT_1/N$SOT_2;

END;

/* Run 3 */

S_1 = 8;

S_2 = 2.011;

IF (StringCompare(DataType(MAG_Results[2,1]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Log the Run and Execute the Simulation */

MAG_GetResult();

MAG_Results[2,1] = N$SOT_1/N$SOT_2;

END;

/* Run 4 */

S_1 = 8;

S_2 = 7.989;

IF (StringCompare(DataType(MAG_Results[2,2]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Log the Run and Execute the Simulation */

MAG_GetResult();

MAG_Results[2,2] = N$SOT_1/N$SOT_2;

END;

/* Aliased Effects in Fractional Factorial Experiment */

SE_Effects(MAG_Results,"I");

END;

*******************************************************

* The Run Execution Procedure *

*******************************************************

PROCEDURE MAG_GetResult() BEGIN

/* Run Simulation and Log Results. */

/* Treatments have already been set for this run. */

TEMPORARY CurrentYield,ShowString,CommandString;

/* Run Procedure Call */

MAG_RUN(MAG_NextRunNumber);

CurrentYield = N$SOT_1/N$SOT_2;

ShowString = PolyCatenate("Run ",String(MAG_NextRunNumber),". ", "");

ShowString = PolyCatenate(ShowString," Yield=",String(CurrentYield),". ");

ShowString = PolyCatenate(ShowString," S_1=",String(S_1), ";");

ShowString = PolyCatenate(ShowString," S_2=",String(S_2), ";");

CommandString = PolyCatenate("SHOW """,ShowString,"""", "");

DoCommand(CommandString);

MAG_NextRunNumber = MAG_NextRunNumber + 1;

RETURN CurrentYield;

END;

*******************************************************

* Run Procedure *

*******************************************************

PROCEDURE MAG_RUN(Run_Number) BEGIN

DoCommand("CLEAR OFF"); /* Must use OFF to preserve results. */

/* EXPAND THIS RMULT IF YOU HAVE MORE RNGs. */

/* All Random Number Streams must have new seeds. */

TEMPORARY CommandString;

/* Evaluate before passing to DoCommand. */

CommandString = Catenate("RMULT ",Run_Number#111);

/* DoCommand compiles the string in Global Context. */

DoCommand(CommandString);

/* SET UP YOUR OWN RUN CONDITIONS. */

DoCommand("START 15,NP"); /* Get past the Startup Period. */

DoCommand("RESET"); /* Begin the Measurement Period. */

DoCommand("START 100,NP"); /* Run the Simulation. */

END;

*******************************************************

Приложение Б

Текст программы

Регрессионный анализ

**********************************************

* Моделирование работы магазина *

**********************************************

INFORM QTABLE mag,0,10,70

GENERATE (Exponential (1,0,3));Поступление покупателей в магазин

QUEUE mag;Вход покупателей в очередь к сотруднику магазина

TRANSFER BOTH,SOT_1,SOT_2;Переход покупателя к свободному сотруднику магазина

SOT_1 SEIZE SOTRUDNIK_1;Определение занятости 1-го сотрудника магазина

DEPART mag;Выход покупателя из очереди от сотрудника магазина

ADVANCE 6,2;Обслуживание покупателя 1-ым сотрудником магазина

RELEASE SOTRUDNIK_1;Освобождение 1-го сотрудника

TRANSFER,NEXT;Переход к оператору с меткой NEXT

SOT_2 SEIZE SOTRUDNIK_2;Определение занятости 2-го сотрудника магазина

DEPART mag;Выход покупателя из очереди от сотрудника магазина

ADVANCE 5,2.989;Обслуживание покупателя 2-ым сотрудником магазина

RELEASE SOTRUDNIK_2;Освобождение 2-го сотрудника

NEXT SAVEVALUE Ave_Queue,QT$mag; Сохранение времени пребывания в очереди

TERMINATE;Выход покупателя из системы

GENERATE 480;Моделирование работы магазина в течение смены

TERMINATE 1

START 1

*******************************************************

* *

* mag_Opt *

* Response Surface Exploration *

* *

*******************************************************

mag_Opt_RunMatrix MATRIX,24,2

INITIAL mag_Opt_RunMatrix,UNSPECIFIED

mag_Opt_RunYields MATRIX,24,1

INITIAL mag_Opt_RunYields,UNSPECIFIED

mag_Opt_TreatmentLevels MATRIX,2,1

INITIAL mag_Opt_TreatmentLevels,UNSPECIFIED

mag_Opt_TreatmentHalfRange MATRIX,2,1

INITIAL mag_Opt_TreatmentHalfRange,UNSPECIFIED

mag_Opt_MovementVector MATRIX,2,1

INITIAL mag_Opt_MovementVector,UNSPECIFIED

mag_Opt_BestYields MATRIX,2,1

INITIAL mag_Opt_BestYields,UNSPECIFIED

mag_Opt_CurrentBestTC MATRIX,2,1

INITIAL mag_Opt_CurrentBestTC,UNSPECIFIED

mag_Opt_OptimumTC MATRIX,2,1

INITIAL mag_Opt_OptimumTC,UNSPECIFIED

mag_Opt_NextRunNumber EQU 0

mag_Opt_RunIndex EQU 0

EXPERIMENT mag_Opt() BEGIN

TEMPORARY Moving,InitialMove,OptimumType,CurrentYield,TRUE,FALSE;

TEMPORARY FitCode,LackOfFit,DirectionFound,OptimumPredicted,OptimumContained;

/* Return codes from surface fit. */

TRUE=1;FALSE=0;FitCode=TRUE;InitialMove=FALSE;

LackOfFit=1;DirectionFound=2;OptimumPredicted=3;OptimumContained=4;

OptimumType = 1; /* Look for Maximum */

mag_Opt_DirectionLimit = 2;

mag_Opt_NextRunNumber = 1;

mag_Opt_TreatmentLevels[1,1] = ((8)+(4))/2;

mag_Opt_TreatmentHalfRange[1,1] = ((8)-(4))/2;

mag_Opt_TreatmentLevels[2,1] = ((7.989)+(2.011))/2;

mag_Opt_TreatmentHalfRange[2,1] = ((7.989)-(2.011))/2;

Moving = TRUE;

WHILE ((Moving'E'TRUE)'AND'(mag_Opt_DirectionLimit>0)) DO BEGIN

/* Repeat for each direction */

/* Set up the ascent vector. */

/* Run the unaugmented factorial experiment. */

DoCommand("INITIAL mag_Opt_RunYields,UNSPECIFIED");

mag_Opt_FullPlusCenter();

/* If we have moved, run the augmented experiment. */

IF (InitialMove'E'TRUE) THEN mag_Opt_Augmented();

FitCode = RSM_FitSurfaceToData(mag_Opt_RunMatrix,mag_Opt_RunYields,mag_Opt_TreatmentLevels,

mag_Opt_TreatmentHalfRange,OptimumType,mag_Opt_BestYields,

mag_Opt_CurrentBestTC,mag_Opt_MovementVector,mag_Opt_OptimumTC);

IF (FitCode'LE'LackOfFit) THEN BEGIN

/* Factorial experiment fails. Try the augmented. */

mag_Opt_Augmented();

FitCode = RSM_FitSurfaceToData(mag_Opt_RunMatrix,mag_Opt_RunYields,mag_Opt_TreatmentLevels,

mag_Opt_TreatmentHalfRange,OptimumType,mag_Opt_BestYields,

mag_Opt_CurrentBestTC,mag_Opt_MovementVector,mag_Opt_OptimumTC);

END;

IF (FitCode'LE'LackOfFit) THEN BEGIN

/* All Models Fail. RSM Fails.*/

DoCommand("SHOW ""ERROR: Response Surface Fails. Optimum not found.""");

RETURN 0;

END;

IF (FitCode'L'OptimumContained) THEN BEGIN

/* The Move Vector is in place.*/

mag_Opt_Move(OptimumType);

InitialMove=TRUE;

/* Reset the Experimental Region, */

mag_Opt_TreatmentLevels[1,1] = mag_Opt_CurrentBestTC[1,1];

/* Don't exceed limits. */

IF (mag_Opt_TreatmentLevels[1,1]'LE'((7.989)+1.000000)) THEN BEGIN

mag_Opt_TreatmentLevels[1,1] = (7.989) + 1.000000;

END;

IF (mag_Opt_TreatmentLevels[1,1]'GE'((8)-1.000000)) THEN BEGIN

mag_Opt_TreatmentLevels[1,1] = (8) - 1.000000;

END;

mag_Opt_TreatmentLevels[2,1] = mag_Opt_CurrentBestTC[2,1];

IF (mag_Opt_TreatmentLevels[2,1]'LE'((2.011)+1.000000)) THEN BEGIN

mag_Opt_TreatmentLevels[2,1] = (2.011) + 1.000000;

END;

IF (mag_Opt_TreatmentLevels[2,1]'GE'((4)-1.000000)) THEN BEGIN

mag_Opt_TreatmentLevels[2,1] = (4) - 1.000000;

END;

mag_Opt_DirectionLimit = mag_Opt_DirectionLimit-1;

END;

ELSE Moving = FALSE;

END;

IF (FitCode<OptimumContained) THEN BEGIN

/* Fit the augmented model. */

DoCommand("INITIAL mag_Opt_RunYields,UNSPECIFIED");

mag_Opt_FullPlusCenter();

mag_Opt_Augmented();

FitCode = RSM_FitSurfaceToData(mag_Opt_RunMatrix,mag_Opt_RunYields,mag_Opt_TreatmentLevels,

mag_Opt_TreatmentHalfRange,OptimumType,mag_Opt_BestYields,

mag_Opt_CurrentBestTC,mag_Opt_MovementVector,mag_Opt_OptimumTC);

END;

IF (FitCode<OptimumPredicted) THEN BEGIN

/* All Models Fail. RSM Fails.*/

DoCommand("SHOW ""ERROR: Response Surface Fails. Optimum not found.""");

END;

IF (FitCode'GE'OptimumPredicted) THEN BEGIN

/* Verify the Optimum.*/

IF ((OptimumType#mag_Opt_BestYields[2,1])>(OptimumType#mag_Opt_BestYields[1,1])) THEN BEGIN

DoCommand("SHOW ""Running the predicted Optimum.""");

S_1 = mag_Opt_OptimumTC[1,1];

S_2 = mag_Opt_OptimumTC[2,1];

/* Do the Simulation */

CurrentYield = mag_Opt_GetResult();

IF ((OptimumType#CurrentYield)>(OptimumType#mag_Opt_BestYields[1,1])) THEN BEGIN

mag_Opt_BestYields[1,1]=CurrentYield;

mag_Opt_CurrentBestTC[1,1] = S_1;

mag_Opt_CurrentBestTC[2,1] = S_2;

END;

END;

END;

END;

*******************************************************

* Move Procedure *

* *

* OptimumType = 1 - Maximize *

* = -1 - Minimize *

*******************************************************

PROCEDURE mag_Opt_Move(OptimumType) BEGIN

/* RSM_FitSurfaceToData must return a code > 0 before moving. */

TEMPORARY CurrentYield,KeepMoving,TRUE,FALSE;

TRUE=1;FALSE=0;KeepMoving=TRUE;

DoCommand("INITIAL mag_Opt_RunYields,UNSPECIFIED ");

DoCommand("SHOW ""Moving...""");

/* Backup a half step so that the first step is a small one. */

S_1 = mag_Opt_CurrentBestTC[1,1]-mag_Opt_MovementVector[1,1]/2;

S_2 = mag_Opt_CurrentBestTC[2,1]-mag_Opt_MovementVector[2,1]/2;

WHILE (KeepMoving) DO BEGIN

S_1 = S_1 + mag_Opt_MovementVector[1,1];

S_2 = S_2 + mag_Opt_MovementVector[2,1];

/* Don't exceed limits. */

IF ((S_1)'LE'((7.989)+1.000000)) THEN BEGIN

S_1 = 7.989 + 1.000000;

KeepMoving = FALSE;

END;

IF ((S_1)'GE'((8)-1.000000)) THEN BEGIN

S_1 = 8 - 1.000000;

KeepMoving = FALSE;

END;

IF ((S_2)'LE'((2.011)+1.000000)) THEN BEGIN

S_2 = 2.011 + 1.000000;

KeepMoving = FALSE;

END;

IF ((S_2)'GE'((4)-1.000000)) THEN BEGIN

S_2 = 4 - 1.000000;

KeepMoving = FALSE;

END;

/* Do the Simulation */

mag_Opt_RunIndex = 1; /* Don't let the Run Index Advance */

CurrentYield = mag_Opt_GetResult();

IF ((OptimumType#CurrentYield)>(OptimumType#mag_Opt_BestYields[1,1])) THEN BEGIN

mag_Opt_BestYields[1,1]=CurrentYield;

mag_Opt_CurrentBestTC[1,1] = S_1;

mag_Opt_CurrentBestTC[2,1] = S_2;

END;

ELSE BEGIN

/* We have passed the optimum. */

KeepMoving = FALSE;

END;

END;

DoCommand("SHOW ""Move ending.""");

END;

*******************************************************

* *

* mag_Opt_FullPlusCenter *

* *

*******************************************************

PROCEDURE mag_Opt_FullPlusCenter() BEGIN

/* Full Factorial Experiment Using Previous Results */

TEMPORARY CurrentYield,IndexI,IndexJ;

mag_Opt_RunIndex = 1;

IndexI=1;

WHILE (IndexI<3) DO BEGIN

IndexJ=1;

WHILE (IndexJ<3) DO BEGIN

/*********************************************/

IF (StringCompare(DataType(mag_Opt_RunYields[mag_Opt_RunIndex,1]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Run Procedure Call */

IF (IndexI'E'1) THEN S_1 = mag_Opt_TreatmentLevels[1,1]-mag_Opt_TreatmentHalfRange[1,1];

ELSE S_1 = mag_Opt_TreatmentLevels[1,1]+mag_Opt_TreatmentHalfRange[1,1];

IF (IndexJ'E'1) THEN S_2 = mag_Opt_TreatmentLevels[2,1]-mag_Opt_TreatmentHalfRange[2,1];

ELSE S_2 = mag_Opt_TreatmentLevels[2,1]+mag_Opt_TreatmentHalfRange[2,1];

/* Do the Simulation */

mag_Opt_GetResult();

END;

/*********************************************/

IndexJ = IndexJ+1;

END;

IndexI = IndexI+1;

END;

/*********************************************/

/* Evaluate 3 Center Points */

/*********************************************/

mag_Opt_CenterTheFactors();

IndexI=1;

WHILE (IndexI<4) DO BEGIN

IF (StringCompare(DataType(mag_Opt_RunYields[mag_Opt_RunIndex,1]),"UNSPECIFIED")'E'0)

THEN BEGIN

/* Do the Simulation */

mag_Opt_GetResult();

END;

IndexI = IndexI+1;

END;

END;

*******************************************************

* *

* mag_Opt_Augmented *

* *

*******************************************************

PROCEDURE mag_Opt_Augmented() BEGIN

/* Augmented Experiment */

/* Add the Augmentation Points. */

mag_Opt_CenterTheFactors();

S_1 = mag_Opt_TreatmentLevels[1,1] + 1.000000 # mag_Opt_TreatmentHalfRange[1,1];

mag_Opt_GetResult();

S_1 = mag_Opt_TreatmentLevels[1,1] - 1.000000 # mag_Opt_TreatmentHalfRange[1,1];

mag_Opt_GetResult();

mag_Opt_CenterTheFactors();

S_2 = mag_Opt_TreatmentLevels[2,1] + 1.000000 # mag_Opt_TreatmentHalfRange[2,1];

mag_Opt_GetResult();

S_2 = mag_Opt_TreatmentLevels[2,1] - 1.000000 # mag_Opt_TreatmentHalfRange[2,1];

mag_Opt_GetResult();

END;

*******************************************************

* *

* mag_Opt_CenterTheFactors *

* *

*******************************************************

PROCEDURE mag_Opt_CenterTheFactors() BEGIN

/* Return all Treatment Levels to the Center Point */

S_1 = mag_Opt_TreatmentLevels[1,1];

S_2 = mag_Opt_TreatmentLevels[2,1];

END;

*******************************************************

* The Run Execution Procedure *

*******************************************************

PROCEDURE mag_Opt_GetResult() BEGIN

/* Run Simulation and Log Results. */

/* Treatments have already been set for this run. */

TEMPORARY CurrentYield,ShowString,CommandString;

/* Run Procedure Call */

mag_Opt_RUN(mag_Opt_NextRunNumber);

CurrentYield = N$SOT_1/N$SOT_2;

mag_Opt_RunYields[mag_Opt_RunIndex,1] = CurrentYield;

mag_Opt_RunMatrix[mag_Opt_RunIndex,1] = S_1;

mag_Opt_RunMatrix[mag_Opt_RunIndex,2] = S_2;

ShowString = PolyCatenate("Run ",String(mag_Opt_NextRunNumber),". ", "");

ShowString = PolyCatenate(ShowString," Yield=",String(CurrentYield),". ");

ShowString = PolyCatenate(ShowString," S_1=",String(S_1), ";");

ShowString = PolyCatenate(ShowString," S_2=",String(S_2), ";");

CommandString = PolyCatenate("SHOW """,ShowString,"""", "");

DoCommand(CommandString);

mag_Opt_RunIndex = mag_Opt_RunIndex + 1;

mag_Opt_NextRunNumber = mag_Opt_NextRunNumber + 1;

RETURN CurrentYield;

END;

*******************************************************

* Run Procedure *

*******************************************************

PROCEDURE mag_Opt_RUN(Run_Number) BEGIN

DoCommand("CLEAR OFF"); /* Must use OFF to preserve results. */

/* EXPAND THIS RMULT IF YOU HAVE MORE RNGs. */

/* All Random Number Streams must have new seeds. */

TEMPORARY CommandString;

/* Evaluate before passing to DoCommand. */

CommandString = Catenate("RMULT ",Run_Number#111);

/* DoCommand compiles the string in Global Context. */

DoCommand(CommandString);

/* SET UP YOUR OWN RUN CONDITIONS. */

DoCommand("START 100,NP"); /* Get past the Startup Period. */

DoCommand("RESET"); /* Begin the Measurement Period. */

DoCommand("START 1000,NP"); /* Run the Simulation. */

END;

*******************************************************