# SIGMA References

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- | {| border=3 cellspacing=0 cellpadding=2 | + | {| border=3 cellspacing=0 cellpadding=2 style="background-color:#EFEFFB;" |

- | ! | + | !align="left"|Allore, H.G. and L.W. Schruben, "Disease Management Research Using Event Graphs," Computers and Biomedical Research, 33, August 1999, 245-259. |

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- | | | + | |Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate ion level; also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. |

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- | ! Schruben, Lee W. "A Graphical Approach to Teaching Simulation". Journal of Computing in Higher Education, v4 n1 p27-37 Fall 1992 | + | {| border=3 cellspacing=0 cellpadding=2 style="background-color:#EFEFFB;" |

+ | !align="left"|Juran, D. C., and L. W. Schruben "Using Worker Personality and Demographic Information to Improve System Performance Prediction", Journal of Operations Management, V.22, Issue 4, August 2004, pp. 355-367. | ||

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+ | |This paper presents an approach to modeling workers where human performance has a significant impact on system productivity. Highly technical industries such as semiconductor manufacturing and service industries like banking are relying on fewer but more skilled workers. In these systems, productivity depends on worker availability and organization; therefore, modeling system performance may require accurate representations of individual worker behavior. This paper examines the tradeoffs in including information about the demographics and personalities of workers in system performance simulation models. A series of actual and simulated experiments in which personality and demographic data are used in different ways to model the performance of a team of workers is reported. Significant differences are found in predicted system performance demonstrating that model validity depends on the methodology used for modeling workers. These results have practical implication for the managerial processes of recruiting and selecting individual workers, as well as organizing teams of workers and assigning them to tasks. | ||

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+ | !align="left"|Potente, H., Bastian, M.. "Design of a Compounding Extruder by means of the SIGMA Simulation Software". Advances in Polymer Technology, V.19, No.2, Apr 1999, pp 147-170.' | ||

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+ | |The simulation program SIGMA, which can be used to assess the compounding process on tightly-intermeshing, co-rotating twin screw extruders, was developed within the framework of a joint project conducted by the Institut für Kunststofftechnik (KTP) of the University of Paderborn and fifteen industrial companies of several fields in the polymer industry. The program presented here permits calculations based on physical mathematical models of the pressure, temperature, local degree of filling, melting, residence time, mixed substance characteristics derived therefrom, power consumption, and degree of dispersion of the machine. These results assist the designing process engineer in the optimization of existing equipment or in the designing of new equipment. | ||

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+ | !align="left"|Savage, Eric L., Lee W. Schruben, Enver Yucesan, "On the Generality of Event Graph Models" INFORMS Journal on Computing, V. 17 , Issue 1 (Winter 2005), pp. 3-9 | ||

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+ | |Event graphs model the dynamics of a discrete-event simulation model. This paper demonstrates the modeling power of event graphs by presenting a model that simulates a Turing machine. Therefore, according to Church's thesis, event-graph models are able to model any system that can be implemented on a modern computer. Theoretical and practical implications of this assertion are also discussed. | ||

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+ | !align="left"|Schruben, Lee W. "A Graphical Approach to Teaching Simulation". Journal of Computing in Higher Education, v4 n1 p27-37 Fall 1992 | ||

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|SIGMA (Simulation Graphical Modeling and Analysis) is a computer graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. It uses symbolic representations (computer animation) to depict the logic of large, complex discrete event systems for easier understanding and has proven itself in courses that both teach and use simulation. (Author/MSE) | |SIGMA (Simulation Graphical Modeling and Analysis) is a computer graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. It uses symbolic representations (computer animation) to depict the logic of large, complex discrete event systems for easier understanding and has proven itself in courses that both teach and use simulation. (Author/MSE) | ||

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- | ! Schruben, L.W., “SIGMA - A Graphical Approach to Teaching Simulation,” Journal of Computing in Higher Education, 4 (1), (Fall 1992), 27-37. | + | |

+ | {| border=3 cellspacing=0 cellpadding=2 style="background-color:#EFEFFB;" | ||

+ | !align="left"|Schruben, L.W., “SIGMA - A Graphical Approach to Teaching Simulation,” Journal of Computing in Higher Education, 4 (1), (Fall 1992), 27-37. | ||

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|SIGMA (Simulation Graphical Modeling and Analysis) is a graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. SIGMA is based on “event graphs,” a concept that utilizes symbolic representations to concisely depict large, complex discrete event systems (like airports, hospitals, and factories) so that they can be understood more easily. SIGMA, the computer animation of event graphs, captures the logic of the computational processes underpinning a simulation. | |SIGMA (Simulation Graphical Modeling and Analysis) is a graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. SIGMA is based on “event graphs,” a concept that utilizes symbolic representations to concisely depict large, complex discrete event systems (like airports, hospitals, and factories) so that they can be understood more easily. SIGMA, the computer animation of event graphs, captures the logic of the computational processes underpinning a simulation. | ||

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- | {| border=3 cellspacing=0 cellpadding=2 | + | !align="left"|Schruben, L. W., and T. M. Roeder, “Fast Simulations of Large-Scale Highly-Congested Systems.” Simulation (Transactions of the Society for Modeling and SimulationInternational) (March 2003), 79.3, pp. 1-11. |

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- | | | + | |Focusing on resource cycles, the authors developed a semiconductor wafer factory (fab) simulation that executed more than an order of magnitude faster than a job-tracing simulation previously in use. The authors summarize the methodologies used and conclude that the differences in execution speeds are due to the fundamental differences in using an event graph paradigm to model the discrete event system dynamics instead of the more popular process flow paradigm that is used by almost all commercial simulation packages. However, the execution speed of a resource-driven model is insensitive to system congestion, whereas a job-driven model slows dramatically (or halts) as the system becomes heavily loaded. The authors conclude that a resource-driven approach using event scheduling logic offers the best approach to modeling very large-scale highly congested systems such as those found in communication, transportation, and unit-manufacturing operations. |

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- | ! | + | !align="left"|Schruben, L.W. and E. Yucesan, “Complexity of Simulation Models: A Graph Theoretic Approach,” INFORMS Journal on Computing, V.10, Issue 1 (January 1998) pp. 94 - 106. |

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|In this article, we introduce complexity measures for simulation models. The framework of simulation graphs sets the context. A quantifiable measure of complexity is useful in an a priori evaluation of proposed simulation studies that must be completed within a specified budget. They can also be useful in classifying simulation models to obtain a thorough test bed of models to be used in simulation methodology research. The metrics introduced in this article have a rigorous theoretical, as well as empirical, grounding in software engineering. As such, simulation modeling and analysis represent a new area of application. Some surrogate measures of run time complexity are also developed. In particular, we provide estimates for the size of the future events list (or the pending event set). The proposed metrics are illustrated and compared through a limited set of examples. Limitations of the current approach as well as directions for future research are discussed. | |In this article, we introduce complexity measures for simulation models. The framework of simulation graphs sets the context. A quantifiable measure of complexity is useful in an a priori evaluation of proposed simulation studies that must be completed within a specified budget. They can also be useful in classifying simulation models to obtain a thorough test bed of models to be used in simulation methodology research. The metrics introduced in this article have a rigorous theoretical, as well as empirical, grounding in software engineering. As such, simulation modeling and analysis represent a new area of application. Some surrogate measures of run time complexity are also developed. In particular, we provide estimates for the size of the future events list (or the pending event set). The proposed metrics are illustrated and compared through a limited set of examples. Limitations of the current approach as well as directions for future research are discussed. | ||

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+ | !align="left"|Yucesan, E. and L.W. Schruben, “Complexity of Simulation Models: A Graph Theoretic Approach,” INFORMS Journal on Computing, 10 (1), (Winter 1998), 94-106. Also in Proc. 1993 Winter Simulation Conference, Los Angeles, CA, December 12-15, 1993, 641-649. | ||

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+ | |In this article, we introduce complexity measures for simulation models. The framework of simulation graphs sets the context. A quantifiable measure of complexity is useful in an a priori evaluation of proposed simulation studies that must be completed within a specified budget. They can also be useful in classifying simulation models to obtain a thorough test bed of models to be used in simulation methodology research. The metrics introduced in this article have a rigorous theoretical, as well as empirical, grounding in software engineering. As such, simulation modeling and analysis represent a new area of application. Some surrogate measures of run time complexity are also developed. In particular, we provide estimates for the size of the future events list (or the pending event set). The proposed metrics are illustrated and compared through a limited set of examples. Limitations of the current approach as well as directions for future research are discussed. | ||

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+ | ==Conference Proceedings== | ||

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- | ! | + | !align="left"|Michael Freimer, Lee Schruben "Stochastic optimization using simulation: graphical representation of IPA estimation" Proceedings of the 2001 Winter Simulation Conference 2001: 422-427. |

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- | | | + | |Infinitesimal Perturbation Analysis (IPA) estimators of the response gradient for a discrete event stochastic simulation are typically developed within the framework of Generalized semi-Markov processes (GSMPs). Unfortunately, while mathematically rigorous, GSMPs are not particularly useful for modeling real systems. In this paper we describe a procedure that allows IPA gradient estimation to be easily and automatically implemented in the more general and intuitive modeling context of Event Graphs. The intent is to make IPA gradient estimation more easily understood and more widely accessible. The pictorial nature of Event Graphs also provides insights into the basic IPA calculations and alternative descriptions of conditions under which the IPA estimator is known to be unbiased. |

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- | ! | + | !align="left"|Savage, E. and L.W. Schruben, “Eliminating Event Cancellation in Discrete Event Simulation,” Proc. 1995 Winter Simulation Conference, Alexandria, VA, December 3-6, 1995, 744-750. |

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+ | |The cancellation of previously scheduled events not only results in a model running less efficiently, it precludes the application of some analysis techniques such as infinitesimal perturbation analysis. While same simulation languages (SIMSCRIPT, SIGMA) include an explicit facility for event cancellation, others do not (SLAM, GPSS, SIMAN). From computation theory, it is known that event cancellation is never necessary; but it is sometimes a convenient modeling technique. Unfortunately, there has been no general methodology developed for eliminating event cancellation from a simulation model. We present a simple general approach. Applications to two classical models where event cancellation is typically used serve as illustrations of the method. | ||

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+ | !align="left"|Schruben, L.W., “Simulation Graphical Modeling and Analysis (SIGMA) Tutorial,” Proc. 1990 Winter Simulation Conference, New Orleans, LA, December 9-12, 1990, 158-161. | ||

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+ | |SIGMA (Σ), an interactive graphics approach to teaching discrete event simulation, is described. Σ is specifically designed to make learning the fundamentals of simulation modeling easy. Σ can automatically translate a simulation model into Pascal or C source code that can be compiled and run on a wide variety of computers. It is possible to represent systems in all of the conventional discrete event worldviews with Σ. The viewpoint is the modeler's choice, not a dictate of the language. Σ combines the modeling advantages of using network flow process and logic diagrams with the generality and flexibility of explicit event scheduling. The complete source code for Σ-generated simulation models is available to students. Although Σ is elementary, it is completely general; any discrete event simulation (indeed, any computer program) can be created using Σ. | ||

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+ | !align="left"|Schruben, L.W., “SIGMA Tutorial,” Proc. 1991 Winter Simulation Conference, Phoenix, AZ, December 8-11, 1991, 95-100. | ||

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+ | |SIGMA (simulation graphical modeling and analysis) is an interactive graphics approach to discrete event simulation. The author gives a brief introduction to simulation graph modeling with SIGMA. In addition, some recent advances in the SIGMA software are discussed and an example is presented. Among the recent enhancements to SIGMA are graphs for output analysis, ranked lists, and a facility for creating an English description of the simulation graph | ||

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+ | !align="left"|Schruben, L.W., “Building Reusable Simulators Using Hierarchical Event Graphs,” Proc. 1995 Winter Simulation Conference, Alexandria, VA, December 3-6, 1995, 472-475. | ||

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+ | |Hierarchical event graphs are an easy way to build special purpose simulators. At the lowest level, event graphs are created to represent particular components of the system being simulated; steps in a process flow, or hyper-events. These low-level graphs can then be viewed as different classes of vertices that make up the next higher level graph. A special purpose simulation toolkit is thus developed. Three very different types of hierarchical event-graph simulation toolkits are discussed in this article: a Petri net simulator that is used to teach the activity-scanning approach to simulation modeling; SIMAN and GPSS network simulators that are used to teach process interaction modeling and introduce these languages; and an industrial process simulator called QUALPLAN that is used for planning quality inspection systems. | ||

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+ | !align="left"|Schruben, L.W., “Simulations Optimization Using Simultaneous Replications and Event Time Dilation,” Proc. 1997 Winter Simulation Conference, Atlanta, GA, December 1997, 177-180. | ||

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+ | |A new approach to simulation response optimization is presented that takes advantage of the ability to run simultaneous replications of different experimental factor settings in a single run. It is also possible to use different time scales for the events corresponding to different design points. In this manner, the run can focus on factor settings that are likely to be optimal and feasible. An example is presented using a penalty function to dilate event times to find the cycle-time constrained capacity of a queue. | ||

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+ | !align="left"|Schruben, L.W. and D. Briskman, “Teaching Simulation with Σ,” Proc. 1988 Winter Simulation Conference, San Diego, CA, December 12-14, 1988, 869-874. | ||

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+ | |Σ (pronounced SIGMA denoting Simulation Graphical Modeling and Analysis) is an interactive graphics approach to building, testing, and experimenting with discrete event simulation models on personal computers. Σ is written in C but is self-contained and does not need a compiler or special graphics software. Σ is an extension of the simulation teaching system report in [2]. The version of Σ described here requires an IBM PC compatible computer (AT preferred) with at least 420K of free memory, a floppy disk drive, an EGA or equivalent monitor with the corresponding graphics card, and a mouse. | ||

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+ | !align="left"|Schruben, L.W. and E. Savage, “Visualizing Generalized Semi-Markov Processes,” Proc. 1996 Winter Simulation Conference, San Diego, CA, December 8-11, 1996, 1465-1470. | ||

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+ | |Generalized Semi-Markov Processes (GSMPs) are usually described by sets of variables, events and clock distributions. This kind of representation often lacks intuitive appeal. In this paper we propose a mapping from GSMPs to Event Graph Models. This mapping allows us to use an event graph to visualize a GSMP model as an intermediate step to implemcniation. By examining the event graph model, we can perform logic checking and verification more easily than if we try to interpret the GSMP description. | ||

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+ | !align="left"|Schruben, L.W. and E. Yucesan, “Transforming Petri Nets into Event Graph Models,” Proc. 1994 Winter Simulation Conference, Orlando FL, December 11-14, 1994, 560-565. | ||

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+ | |Stochastic Petri Nets and simulation Event Graph models both have attractive graphical representations and simple rules that govern their dynamic behavior. A mapping of Stochastic Petri Nets into Event Graph models is presented and discussed. This mapping can be used to develop simulations of Petri Nets that exploit the efficiencies of the event-scheduling paradigm. It also permits the application of some of the rich analytical methodologies in the Petri Net literature to the analysis of event-oriented simulation models. Indeed, these two graphical representations of discrete event dynamic systems work in a complementary manner. We first present the structural and behavioral properties of standard Stochastic Petri Nets and Event Graph models and then discuss their relationship. | ||

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+ | !align="left"|Roeder, Theresa M., Seth A.. Fischbein, Mani Janakiram, and Lee W. Schruben. 2002. Resource-Driven and Job-Driven Simulations. Proceedings of the 2002 International Conference on Modeling and Analysis of Semiconductor Manufacturing: 78-83. | ||

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+ | |The typical approach taken to simulating semiconductor wafer fabs is a time- and memory-intensive process that tracks individual wafers as they pass through the fab. This modeling paradigm is known as a job-driven simulation. In this work, we describe research done at UC Berkeley in cooperation with Intel, the Semiconductor Research Consortium, and SEMATECH to develop a resource-driven simulation to modeling fabs. Developing the new model provided interesting insights into modeling assumptions typically made. It also showed that some aspects of the fab can be modeled more accurately in the resource-driven model, while others are more accurately modeled using a job-driven approach. However, the resource-driven model runs considerably faster, making more extensive experimentation possible. | ||

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+ | !align="left"|Yuan-chia Chu, Yu-yin Kuo, Tsuei-rung Chang, Chih-Chuan Chou, Rung-chuang Feng, and Polun Chang. "SIGMA simulation for Health Promotion Management". AMIA Annu Symp Proc. 2005; p. 926. | ||

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+ | |Background: Health promotion is the key task to achieve global health 2010. Periodical physical check-up have been the most basic manifestation for maintaining personal health care and promotion. Sufficient health check facility was provided in a medical center with annual service of 9200~9500. Sixty customers receive around 20 check ups in this physical check up center daily. Smoothness, efficacy and customer satisfaction of the process will be caretakers’ concern and target for promotion. Purpose of the system: The purpose of applying a information system for health promotion management are: 1. to plan personalized process for physical check-up; 2. to cut waiting time for each tests during the check-up period; 3. to promote satisfaction, loyalty, and consumer relationship. Service/project: Following ID confirmation, clients will enter the flow according to personalized sequence including history taking, blood and urine lab tests, electrocardiogram, abdominal sonography, panendoscope, colonfibroscopy, pulmonary functional tests, and Obstetric-Gynecology routines…etc.. Simultaneously, health education will be provided by the multiple media prior to each tests. At the end of each run, all test results will be lodged onto a personal database with hard copies or e-mail provided. Based on the information system, health care provider can give suggestions and schedules for sequent periodical follow-up. Methodology: The project use SIGMA software to simulate and analyze the relationship between input and output. Input data were defined as actual measurements from 2005/3/11 to 2005/3/13, and coded by BestFit 2.0 software. The output data will include physician’s utilization rate, averaged time course and clients’ complaint rate as variables. To conduct tests, output here will be functions obtained during simulation and it will be remained as the foundation for further comparison. Finally, the regeneration model will be conducted based on those relationship, decision-making analysis and sensitivity. Evaluation: Efficacy of this proposed of e-health promotion management system will be evaluated by the run-time, client attendance, satisfaction and complaints, physician and nurse utilization and satisfaction, set up cost for system construction and labor expenditure. Conclusion: This project will be truly promoted client satisfaction by questionnaire survey, and decreased run-time about 30 minutes and increased client attendance about 30%. | ||

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+ | ==Books== | ||

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+ | {| border=3 cellspacing=0 cellpadding=2 style="background-color:#EFEFFB;" | ||

+ | !align="left"|Schruben, L.W., SIGMA: A Graphical Simulation System, Scientific Press, San Francisco, CA, 1991. (Selected as EDUCOM’s 101 All time Computing Success Stories.) | ||

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+ | !align="left"|Schruben, L.W., Graphical Simulation Modeling, Scientific Press, San Francisco, CA, 1992. | ||

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+ | !align="left"|Schruben, L.W., Graphical Simulation Modeling and Analysis using SIGMA for Windows, Boyd and Fraser Publishing Co., Danvers, MA, 1995. | ||

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+ | !align="left"|Schruben, L.W., Graphical Simulation Modeling and Analysis using SIGMA for Windows, Boyd and Fraser Publishing Co., Danvers, MA, 1995. | ||

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+ | ==Book Chapters== | ||

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+ | {| border=3 cellspacing=0 cellpadding=2 style="background-color:#EFEFFB;" | ||

+ | !align="left"|Schruben, L.W., “Designing Correlation Induction Strategies for Simulation Experiments,” in N. Adam and A Dogramaci (Eds.), Current Issues in Simulation, Academic Press, New York, 1979, 235-256. | ||

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+ | !align="left"|Schruben, L.W., “Testing for Initialization Bias in the Main of a Simulation Output Series,” in R. Disney and T. Ott (Eds.), Applied Probability-Computer Science: The Interface, Birkhauser, Boston, 1982, 381-383. | ||

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+ | !align="left"|Jacobson, S. and L.W. Schruben, “Optimization of Stochastic Dynamical Systems in the Frequency Domain,” in A. Bensoussan and J.L. Lions (Eds.), Analysis and Optimization of Systems, Springer-Verlag Lecture Notes in Control and Information Sciences, 11, (1988), 925-938. | ||

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- | | | + | !align="left"|Schruben, L.W., “Simulation Graphical Modeling and Analysis (SIGMA),” J. Boettcher (Ed.), in 101 Success Stories of Information Technology in Higher Education: The Joe Wyatt Challenge, McGraw Hill, Inc., New York, 1993, 133-138. |

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+ | !align="left"|Duenyas, I., J. Fowler, and L.W. Schruben, “Japan’s Development of Scheduling Methods for Manufacturing Semiconductors,” in J. Liker, J. Ettlie, and J. Campbell (Eds.), Engineered in Japan: Japanese Technology-Management Practices, Oxford University Press, New York, Oxford, 1995, 263-277. | ||

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## Current revision

## Contents |

## Refereed Publications

Allore, H.G. and L.W. Schruben, "Disease Management Research Using Event Graphs," Computers and Biomedical Research, 33, August 1999, 245-259. |
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Event Graphs, conditional representations of stochastic relationships between discrete events, simulate disease dynamics. In this paper, we demonstrate how Event Graphs, at an appropriate ion level; also extend and organize scientific knowledge about diseases. They can identify promising treatment strategies and directions for further research and provide enough detail for testing combinations of new medicines and interventions. Event Graphs can be enriched to incorporate and validate data and test new theories to reflect an expanding dynamic scientific knowledge base and establish performance criteria for the economic viability of new treatments. To illustrate, an Event Graph is developed for mastitis, a costly dairy cattle disease, for which extensive scientific literature exists. With only a modest amount of imagination, the methodology presented here can be seen to apply modeling to any disease, human, plant, or animal. The Event Graph simulation presented here is currently being used in research and in a new veterinary epidemiology course. |

Juran, D. C., and L. W. Schruben "Using Worker Personality and Demographic Information to Improve System Performance Prediction", Journal of Operations Management, V.22, Issue 4, August 2004, pp. 355-367. |
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This paper presents an approach to modeling workers where human performance has a significant impact on system productivity. Highly technical industries such as semiconductor manufacturing and service industries like banking are relying on fewer but more skilled workers. In these systems, productivity depends on worker availability and organization; therefore, modeling system performance may require accurate representations of individual worker behavior. This paper examines the tradeoffs in including information about the demographics and personalities of workers in system performance simulation models. A series of actual and simulated experiments in which personality and demographic data are used in different ways to model the performance of a team of workers is reported. Significant differences are found in predicted system performance demonstrating that model validity depends on the methodology used for modeling workers. These results have practical implication for the managerial processes of recruiting and selecting individual workers, as well as organizing teams of workers and assigning them to tasks. |

Potente, H., Bastian, M.. "Design of a Compounding Extruder by means of the SIGMA Simulation Software". Advances in Polymer Technology, V.19, No.2, Apr 1999, pp 147-170.' |
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The simulation program SIGMA, which can be used to assess the compounding process on tightly-intermeshing, co-rotating twin screw extruders, was developed within the framework of a joint project conducted by the Institut für Kunststofftechnik (KTP) of the University of Paderborn and fifteen industrial companies of several fields in the polymer industry. The program presented here permits calculations based on physical mathematical models of the pressure, temperature, local degree of filling, melting, residence time, mixed substance characteristics derived therefrom, power consumption, and degree of dispersion of the machine. These results assist the designing process engineer in the optimization of existing equipment or in the designing of new equipment. |

Savage, Eric L., Lee W. Schruben, Enver Yucesan, "On the Generality of Event Graph Models" INFORMS Journal on Computing, V. 17 , Issue 1 (Winter 2005), pp. 3-9 |
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Event graphs model the dynamics of a discrete-event simulation model. This paper demonstrates the modeling power of event graphs by presenting a model that simulates a Turing machine. Therefore, according to Church's thesis, event-graph models are able to model any system that can be implemented on a modern computer. Theoretical and practical implications of this assertion are also discussed. |

Schruben, Lee W. "A Graphical Approach to Teaching Simulation". Journal of Computing in Higher Education, v4 n1 p27-37 Fall 1992 |
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SIGMA (Simulation Graphical Modeling and Analysis) is a computer graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. It uses symbolic representations (computer animation) to depict the logic of large, complex discrete event systems for easier understanding and has proven itself in courses that both teach and use simulation. (Author/MSE) |

Schruben, L.W., “SIGMA - A Graphical Approach to Teaching Simulation,” Journal of Computing in Higher Education, 4 (1), (Fall 1992), 27-37. |
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SIGMA (Simulation Graphical Modeling and Analysis) is a graphics environment for building, testing, and experimenting with discrete event simulation models on personal computers. SIGMA is based on “event graphs,” a concept that utilizes symbolic representations to concisely depict large, complex discrete event systems (like airports, hospitals, and factories) so that they can be understood more easily. SIGMA, the computer animation of event graphs, captures the logic of the computational processes underpinning a simulation.
SIGMA was developed to improve the quality of simulation education. Problems addressed during a semester were: how to convey simulation concepts more easily, how to help students understand the many complexities associated with this topic, and how to help students build realistic computer models of large, complicated systems. In SIGMA, stochastic systems are represented as simple, dynamic graphs. Simulation models are easily created by drawing these graphs on a computer with a mouse. Students quickly learn how various events in a system interact by observing SIGMA’s graphics displays. SIGMA has proved itself to be a valuable educational tool, not only for courses that teach simulation, but also for courses that use simulations. Furthermore, SIGMA’s capability to model very large systems has led to successful industrial applications. |

Schruben, L. W., and T. M. Roeder, “Fast Simulations of Large-Scale Highly-Congested Systems.” Simulation (Transactions of the Society for Modeling and SimulationInternational) (March 2003), 79.3, pp. 1-11. |
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Focusing on resource cycles, the authors developed a semiconductor wafer factory (fab) simulation that executed more than an order of magnitude faster than a job-tracing simulation previously in use. The authors summarize the methodologies used and conclude that the differences in execution speeds are due to the fundamental differences in using an event graph paradigm to model the discrete event system dynamics instead of the more popular process flow paradigm that is used by almost all commercial simulation packages. However, the execution speed of a resource-driven model is insensitive to system congestion, whereas a job-driven model slows dramatically (or halts) as the system becomes heavily loaded. The authors conclude that a resource-driven approach using event scheduling logic offers the best approach to modeling very large-scale highly congested systems such as those found in communication, transportation, and unit-manufacturing operations. |

Schruben, L.W. and E. Yucesan, “Complexity of Simulation Models: A Graph Theoretic Approach,” INFORMS Journal on Computing, V.10, Issue 1 (January 1998) pp. 94 - 106. |
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In this article, we introduce complexity measures for simulation models. The framework of simulation graphs sets the context. A quantifiable measure of complexity is useful in an a priori evaluation of proposed simulation studies that must be completed within a specified budget. They can also be useful in classifying simulation models to obtain a thorough test bed of models to be used in simulation methodology research. The metrics introduced in this article have a rigorous theoretical, as well as empirical, grounding in software engineering. As such, simulation modeling and analysis represent a new area of application. Some surrogate measures of run time complexity are also developed. In particular, we provide estimates for the size of the future events list (or the pending event set). The proposed metrics are illustrated and compared through a limited set of examples. Limitations of the current approach as well as directions for future research are discussed. |

Yucesan, E. and L.W. Schruben, “Complexity of Simulation Models: A Graph Theoretic Approach,” INFORMS Journal on Computing, 10 (1), (Winter 1998), 94-106. Also in Proc. 1993 Winter Simulation Conference, Los Angeles, CA, December 12-15, 1993, 641-649. |
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In this article, we introduce complexity measures for simulation models. The framework of simulation graphs sets the context. A quantifiable measure of complexity is useful in an a priori evaluation of proposed simulation studies that must be completed within a specified budget. They can also be useful in classifying simulation models to obtain a thorough test bed of models to be used in simulation methodology research. The metrics introduced in this article have a rigorous theoretical, as well as empirical, grounding in software engineering. As such, simulation modeling and analysis represent a new area of application. Some surrogate measures of run time complexity are also developed. In particular, we provide estimates for the size of the future events list (or the pending event set). The proposed metrics are illustrated and compared through a limited set of examples. Limitations of the current approach as well as directions for future research are discussed. |

## Conference Proceedings

Michael Freimer, Lee Schruben "Stochastic optimization using simulation: graphical representation of IPA estimation" Proceedings of the 2001 Winter Simulation Conference 2001: 422-427. |
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Infinitesimal Perturbation Analysis (IPA) estimators of the response gradient for a discrete event stochastic simulation are typically developed within the framework of Generalized semi-Markov processes (GSMPs). Unfortunately, while mathematically rigorous, GSMPs are not particularly useful for modeling real systems. In this paper we describe a procedure that allows IPA gradient estimation to be easily and automatically implemented in the more general and intuitive modeling context of Event Graphs. The intent is to make IPA gradient estimation more easily understood and more widely accessible. The pictorial nature of Event Graphs also provides insights into the basic IPA calculations and alternative descriptions of conditions under which the IPA estimator is known to be unbiased. |

Savage, E. and L.W. Schruben, “Eliminating Event Cancellation in Discrete Event Simulation,” Proc. 1995 Winter Simulation Conference, Alexandria, VA, December 3-6, 1995, 744-750. |
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The cancellation of previously scheduled events not only results in a model running less efficiently, it precludes the application of some analysis techniques such as infinitesimal perturbation analysis. While same simulation languages (SIMSCRIPT, SIGMA) include an explicit facility for event cancellation, others do not (SLAM, GPSS, SIMAN). From computation theory, it is known that event cancellation is never necessary; but it is sometimes a convenient modeling technique. Unfortunately, there has been no general methodology developed for eliminating event cancellation from a simulation model. We present a simple general approach. Applications to two classical models where event cancellation is typically used serve as illustrations of the method. |

Schruben, L.W., “Simulation Graphical Modeling and Analysis (SIGMA) Tutorial,” Proc. 1990 Winter Simulation Conference, New Orleans, LA, December 9-12, 1990, 158-161. |
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SIGMA (Σ), an interactive graphics approach to teaching discrete event simulation, is described. Σ is specifically designed to make learning the fundamentals of simulation modeling easy. Σ can automatically translate a simulation model into Pascal or C source code that can be compiled and run on a wide variety of computers. It is possible to represent systems in all of the conventional discrete event worldviews with Σ. The viewpoint is the modeler's choice, not a dictate of the language. Σ combines the modeling advantages of using network flow process and logic diagrams with the generality and flexibility of explicit event scheduling. The complete source code for Σ-generated simulation models is available to students. Although Σ is elementary, it is completely general; any discrete event simulation (indeed, any computer program) can be created using Σ. |

Schruben, L.W., “SIGMA Tutorial,” Proc. 1991 Winter Simulation Conference, Phoenix, AZ, December 8-11, 1991, 95-100. |
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SIGMA (simulation graphical modeling and analysis) is an interactive graphics approach to discrete event simulation. The author gives a brief introduction to simulation graph modeling with SIGMA. In addition, some recent advances in the SIGMA software are discussed and an example is presented. Among the recent enhancements to SIGMA are graphs for output analysis, ranked lists, and a facility for creating an English description of the simulation graph |

Schruben, L.W., “Building Reusable Simulators Using Hierarchical Event Graphs,” Proc. 1995 Winter Simulation Conference, Alexandria, VA, December 3-6, 1995, 472-475. |
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Hierarchical event graphs are an easy way to build special purpose simulators. At the lowest level, event graphs are created to represent particular components of the system being simulated; steps in a process flow, or hyper-events. These low-level graphs can then be viewed as different classes of vertices that make up the next higher level graph. A special purpose simulation toolkit is thus developed. Three very different types of hierarchical event-graph simulation toolkits are discussed in this article: a Petri net simulator that is used to teach the activity-scanning approach to simulation modeling; SIMAN and GPSS network simulators that are used to teach process interaction modeling and introduce these languages; and an industrial process simulator called QUALPLAN that is used for planning quality inspection systems. |

Schruben, L.W., “Simulations Optimization Using Simultaneous Replications and Event Time Dilation,” Proc. 1997 Winter Simulation Conference, Atlanta, GA, December 1997, 177-180. |
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A new approach to simulation response optimization is presented that takes advantage of the ability to run simultaneous replications of different experimental factor settings in a single run. It is also possible to use different time scales for the events corresponding to different design points. In this manner, the run can focus on factor settings that are likely to be optimal and feasible. An example is presented using a penalty function to dilate event times to find the cycle-time constrained capacity of a queue. |

Schruben, L.W. and D. Briskman, “Teaching Simulation with Σ,” Proc. 1988 Winter Simulation Conference, San Diego, CA, December 12-14, 1988, 869-874. |
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Σ (pronounced SIGMA denoting Simulation Graphical Modeling and Analysis) is an interactive graphics approach to building, testing, and experimenting with discrete event simulation models on personal computers. Σ is written in C but is self-contained and does not need a compiler or special graphics software. Σ is an extension of the simulation teaching system report in [2]. The version of Σ described here requires an IBM PC compatible computer (AT preferred) with at least 420K of free memory, a floppy disk drive, an EGA or equivalent monitor with the corresponding graphics card, and a mouse. |

Schruben, L.W. and E. Savage, “Visualizing Generalized Semi-Markov Processes,” Proc. 1996 Winter Simulation Conference, San Diego, CA, December 8-11, 1996, 1465-1470. |
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Generalized Semi-Markov Processes (GSMPs) are usually described by sets of variables, events and clock distributions. This kind of representation often lacks intuitive appeal. In this paper we propose a mapping from GSMPs to Event Graph Models. This mapping allows us to use an event graph to visualize a GSMP model as an intermediate step to implemcniation. By examining the event graph model, we can perform logic checking and verification more easily than if we try to interpret the GSMP description. |

Schruben, L.W. and E. Yucesan, “Transforming Petri Nets into Event Graph Models,” Proc. 1994 Winter Simulation Conference, Orlando FL, December 11-14, 1994, 560-565. |
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Stochastic Petri Nets and simulation Event Graph models both have attractive graphical representations and simple rules that govern their dynamic behavior. A mapping of Stochastic Petri Nets into Event Graph models is presented and discussed. This mapping can be used to develop simulations of Petri Nets that exploit the efficiencies of the event-scheduling paradigm. It also permits the application of some of the rich analytical methodologies in the Petri Net literature to the analysis of event-oriented simulation models. Indeed, these two graphical representations of discrete event dynamic systems work in a complementary manner. We first present the structural and behavioral properties of standard Stochastic Petri Nets and Event Graph models and then discuss their relationship. |

Roeder, Theresa M., Seth A.. Fischbein, Mani Janakiram, and Lee W. Schruben. 2002. Resource-Driven and Job-Driven Simulations. Proceedings of the 2002 International Conference on Modeling and Analysis of Semiconductor Manufacturing: 78-83. |
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The typical approach taken to simulating semiconductor wafer fabs is a time- and memory-intensive process that tracks individual wafers as they pass through the fab. This modeling paradigm is known as a job-driven simulation. In this work, we describe research done at UC Berkeley in cooperation with Intel, the Semiconductor Research Consortium, and SEMATECH to develop a resource-driven simulation to modeling fabs. Developing the new model provided interesting insights into modeling assumptions typically made. It also showed that some aspects of the fab can be modeled more accurately in the resource-driven model, while others are more accurately modeled using a job-driven approach. However, the resource-driven model runs considerably faster, making more extensive experimentation possible. |

Yuan-chia Chu, Yu-yin Kuo, Tsuei-rung Chang, Chih-Chuan Chou, Rung-chuang Feng, and Polun Chang. "SIGMA simulation for Health Promotion Management". AMIA Annu Symp Proc. 2005; p. 926. |
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Background: Health promotion is the key task to achieve global health 2010. Periodical physical check-up have been the most basic manifestation for maintaining personal health care and promotion. Sufficient health check facility was provided in a medical center with annual service of 9200~9500. Sixty customers receive around 20 check ups in this physical check up center daily. Smoothness, efficacy and customer satisfaction of the process will be caretakers’ concern and target for promotion. Purpose of the system: The purpose of applying a information system for health promotion management are: 1. to plan personalized process for physical check-up; 2. to cut waiting time for each tests during the check-up period; 3. to promote satisfaction, loyalty, and consumer relationship. Service/project: Following ID confirmation, clients will enter the flow according to personalized sequence including history taking, blood and urine lab tests, electrocardiogram, abdominal sonography, panendoscope, colonfibroscopy, pulmonary functional tests, and Obstetric-Gynecology routines…etc.. Simultaneously, health education will be provided by the multiple media prior to each tests. At the end of each run, all test results will be lodged onto a personal database with hard copies or e-mail provided. Based on the information system, health care provider can give suggestions and schedules for sequent periodical follow-up. Methodology: The project use SIGMA software to simulate and analyze the relationship between input and output. Input data were defined as actual measurements from 2005/3/11 to 2005/3/13, and coded by BestFit 2.0 software. The output data will include physician’s utilization rate, averaged time course and clients’ complaint rate as variables. To conduct tests, output here will be functions obtained during simulation and it will be remained as the foundation for further comparison. Finally, the regeneration model will be conducted based on those relationship, decision-making analysis and sensitivity. Evaluation: Efficacy of this proposed of e-health promotion management system will be evaluated by the run-time, client attendance, satisfaction and complaints, physician and nurse utilization and satisfaction, set up cost for system construction and labor expenditure. Conclusion: This project will be truly promoted client satisfaction by questionnaire survey, and decreased run-time about 30 minutes and increased client attendance about 30%. |

## Books

Schruben, L.W., SIGMA: A Graphical Simulation System, Scientific Press, San Francisco, CA, 1991. (Selected as EDUCOM’s 101 All time Computing Success Stories.) |
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Schruben, L.W., Graphical Simulation Modeling, Scientific Press, San Francisco, CA, 1992. |

Schruben, L.W., Graphical Simulation Modeling and Analysis using SIGMA for Windows, Boyd and Fraser Publishing Co., Danvers, MA, 1995. |

Schruben, L.W., Graphical Simulation Modeling and Analysis using SIGMA for Windows, Boyd and Fraser Publishing Co., Danvers, MA, 1995. |

## Book Chapters

Schruben, L.W., “Designing Correlation Induction Strategies for Simulation Experiments,” in N. Adam and A Dogramaci (Eds.), Current Issues in Simulation, Academic Press, New York, 1979, 235-256. |
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Schruben, L.W., “Testing for Initialization Bias in the Main of a Simulation Output Series,” in R. Disney and T. Ott (Eds.), Applied Probability-Computer Science: The Interface, Birkhauser, Boston, 1982, 381-383. |

Jacobson, S. and L.W. Schruben, “Optimization of Stochastic Dynamical Systems in the Frequency Domain,” in A. Bensoussan and J.L. Lions (Eds.), Analysis and Optimization of Systems, Springer-Verlag Lecture Notes in Control and Information Sciences, 11, (1988), 925-938. |

Schruben, L.W., “Simulation Graphical Modeling and Analysis (SIGMA),” J. Boettcher (Ed.), in 101 Success Stories of Information Technology in Higher Education: The Joe Wyatt Challenge, McGraw Hill, Inc., New York, 1993, 133-138. |

Duenyas, I., J. Fowler, and L.W. Schruben, “Japan’s Development of Scheduling Methods for Manufacturing Semiconductors,” in J. Liker, J. Ettlie, and J. Campbell (Eds.), Engineered in Japan: Japanese Technology-Management Practices, Oxford University Press, New York, Oxford, 1995, 263-277. |