System modelling and simulation 2018

Charcterisation of an off grid hybrid system: Modelling and simulation Modelling and simulation of a stepped frequency radar system based on LabVIEW
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Published Date:12-07-2017
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SYLLABUS SYSTEM MODELLING AND SIMULATION PART – A UNIT – 1 8 Hours Introduction: When simulation is the appropriate tool and when it is not appropriate; Advantages and disadvantages of Simulation; Areas of application; Systems and system environment; Components of a system; Discrete and continuous systems; Model of a system; Types of Models; Discrete-Event System Simulation; Steps in a Simulation Study. The basics of Spreadsheet simulation, Simulation example: Simulation of queuing systems in a spreadsheet. UNIT – 2 6 Hours General Principles, Simulation Software: Concepts in Discrete-Event Simulation: The Event- Scheduling / Time-Advance Algorithm, World Views, Manual simulation Using Event Scheduling; List processing. Simulation in Java; Simulation in GPSS UNIT – 3 6 Hours Statistical Models in Simulation: Review of terminology and concepts; Useful statistical models; discrete distributions; Continuous distributions; Poisson process; Empirical distributions. UNIT – 4 6 Hours Queuing Models: Characteristics of queuing systems; Queuing notation; Long-run measures of performance of queuing systems; Steady-state behavior of M/G/1 queue; Networks of queues; Rough-cut modeling: An illustration.. PART – B UNIT – 5 8 Hours Random-Number Generation, Random-Variate Generation: Properties of random numbers; Generation of pseudo-random numbers; Techniques for generating random numbers; Tests for Random Numbers Random-Variate Generation: Inverse transform technique; Acceptance- Rejection technique; Special properties. UNIT – 6 6 Hours Input Modeling : Data Collection; Identifying the distribution with data; Parameter estimation; Goodness of Fit Tests; Fitting a non-stationary Poisson process; Selecting input models without data; Multivariate and Time-Series input models. UNIT – 7 6 Hours Estimation of Absolute Performance: Types of simulations with respect to output analysis; Stochastic nature of output data; Absolute measures of performance and their estimation; Output analysis for terminating simulations; Output analysis for steady-state simulations. UNIT – 8 6 Hours Verification, Calibration, and Validation; Optimization: Model building, verification and validation; Verification of simulation models; Calibration and validation of models, optimization via Simulation Text Books: 1. Jerry Banks, John S. Carson II, Barry L. Nelson, David M. Nicol: Discrete-Event System Simulation, 5th Edition, Pearson Education, 2010. (Listed topics only from Chapters1 to 12) Reference Books: 1. Lawrence M. Leemis, Stephen K. Park: Discrete – Event Simulation: A First Course, Pearson Education, 2006. 2. Averill M. Law: Simulation Modeling and Analysis, 4th Edition, Tata McGraw-Hill, 2007. UNIT 1: INTRODUCTION TO SIMULATION Simulation A Simulation is the imitation of the operation of a real-world process or system over time Brief Explanation  The behavior of a system as it evolves over time is studied by developing a simulation model.  This model takes the form of a set of assumptions concerning the operation of the system. The assumptions are expressed in  Mathematical relationships  Logical relationships  Symbolic relationships Between the entities of the system. Measures of performance The model solved by mathematical methods such as differential calculus, probability theory, algebraic methods have the solution usually consists of one or more numerical parameters which are called measures of performance. 1.1When Simulation is the Appropriate Tool  Simulation enables the study of and experimentation with the internal interactions of a complex system, or of a subsystem within a complex system.  Informational, organizational and environmental changes can be simulated and the effect of those alternations on the model‘s behavior can be observer.  The knowledge gained in designing a simulation model can be of great value toward suggesting improvement in the system under investigation.  By changing simulation inputs and observing the resulting outputs, valuable insight may be obtained into which variables are most important and how variables interact.  Simulation can be used as a pedagogical device to reinforce analytic solution methodologies.  Simulation can be used to experiment with new designs or policies prior to implementation, so as to prepare for what may happen.  Simulation can be used to verify analytic solutions.  By simulating different capabilities for a machine, requirements can be determined.  Simulation models designed for training, allow learning without the cost and disruption of on-the-job learning.  Animation shows a system in simulated operation so that the plan can be visualized.  The modern system(factory, water fabrication plant, service organization, etc) is so complex that the interactions can be treated only through simulation. When Simulation is Not Appropriate  Simulation should be used when the problem cannot be solved using common sense.  Simulation should not be used if the problem can be solved analytically.  Simulation should not be used, if it is easier to perform direct experiments.  Simulation should not be used, if the costs exceeds savings.  Simulation should not be performed, if the resources or time are not available.  If no data is available, not even estimate simulation is not advised.  If there is not enough time or the person are not available, simulation is not appropriate.  If managers have unreasonable expectation say, too much soon – or the power of simulation is over estimated, simulation may not be appropriate.  If system behavior is too complex or cannot be defined, simulation is not appropriate. 1.2Advantages of Simulation  Simulation can also be used to study systems in the design stage.  Simulation models are run rather than solver.  New policies, operating procedures, decision rules, information flow, etc can be explored without disrupting the ongoing operations of the real system.  New hardware designs, physical layouts, transportation systems can be tested without committing resources for their acquisition.  Hypotheses about how or why certain phenomena occur can be tested for feasibility.  Time can be compressed or expanded allowing for a speedup or slowdown of the phenomena under investigation.  Insight can be obtained about the interaction of variables.  Insight can be obtained about the importance of variables to the performance of the system.  Bottleneck analysis can be performed indication where work-inprocess, information materials and so on are being excessively delayed.\  A simulation study can help in understanding how the system operates rather than how individuals think the system operates.  ―what-if‖ questions can be answered. Useful in the design of new systems. Disadvantages of simulation  Model building requires special training.  Simulation results may be difficult to interpret.  Simulation modeling and analysis can be time consuming and expensive.  Simulation is used in some cases when an analytical solution is possible or even preferable. Applications of Simulation Manufacturing Applications 1. Analysis of electronics assembly operations 2. Design and evaluation of a selective assembly station for highprecision scroll compressor shells. 3. Comparison of dispatching rules for semiconductor manufacturing using large facility models. 4. Evaluation of cluster tool throughput for thin-film head production. 5. Determining optimal lot size for a semiconductor backend factory. 6. Optimization of cycle time and utilization in semiconductor test manufacturing. 7. Analysis of storage and retrieval strategies in a warehouse. 8. Investigation of dynamics in a service oriented supply chain. 9. Model for an Army chemical munitions disposal facility. Semiconductor Manufacturing 1. Comparison of dispatching rules using large-facility models. 2. The corrupting influence of variability. 3. A new lot-release rule for wafer fabs. 4. Assessment of potential gains in productivity due to proactive retied management. 5. Comparison of a 200 mm and 300 mm X-ray lithography cell. 6. Capacity planning with time constraints between operations. 7. 300 mm logistic system risk reduction. Construction Engineering 1. Construction of a dam embankment. 2. Trench less renewal of underground urban infrastructures. 3. Activity scheduling in a dynamic, multiproject setting. 4. Investigation of the structural steel erection process. 5. Special purpose template for utility tunnel construction. Military Applications 1. Modeling leadership effects and recruit type in a Army recruiting station. 2. Design and test of an intelligent controller for autonomous underwater vehicles. 3. Modeling military requirements for nonwarfighting operations. 4. Multitrajectory performance for varying scenario sizes. 5. Using adaptive agents in U.S. Air Force retention. Logistics, Transportation and Distribution Applications 1. Evaluating the potential benefits of a rail-traffic planning algorithm. 2. Evaluating strategies to improve railroad performance. 3. Parametric Modeling in rail-capacity planning. 4. Analysis of passenger flows in an airport terminal. 5. Proactive flight-schedule evaluation. 6. Logistic issues in autonomous food production systems for extended duration space exploration. 7. Sizing industrial rail-car fleets. 8. Production distribution in newspaper industry. 9. Design of a toll plaza 10. Choosing between rental-car locations. 11. Quick response replenishment. Business Process Simulation 1. Impact of connection bank redesign on airport gate assignment. 2. Product development program planning. 3. Reconciliation of business and system modeling. 4. Personal forecasting and strategic workforce planning. Human Systems 1. Modeling human performance in complex systems. 2. Studying the human element in out traffic control. 1.3 Systems A system is defined as an aggregation or assemblage of objects joined in some regular interaction or interdependence toward the accomplishment of some purpose. Example : Production System In the above system there are certain distinct objects, each of which possesses properties of interest. There are also certain interactions occurring in the system that cause changes in the system. Components of a System Entity : An entity is an object of interest in a system. Ex: In the factory system, departments, orders, parts and products are The entities. Attribute An attribute denotes the property of an entity. Ex: Quantities for each order, type of part, or number of machines in a Department are attributes of factory system. Activity Any process causing changes in a system is called as an activity. Ex: Manufacturing process of the department. State of the System The state of a system is defined as the collection of variables necessary to describe a system at any time, relative to the objective of study. In other words, state of the system mean a description of all the entities, attributes and activities as they exist at one point in time. Event An event is defined as an instaneous occurrence that may change the state of the system. System Environment The external components which interact with the system and produce necessary changes are said to constitute the system environment. In modeling systems, it is necessary to decide on the boundary between the system and its environment. This decision may depend on the purpose of the study. Ex: In a factory system, the factors controlling arrival of orders may be considered to be outside the factory but yet a part of the system environment. When, we consider the demand and supply of goods, there is certainly a relationship between the factory output and arrival of orders. This relationship is considered as an activity of the system. Endogenous System The term endogenous is used to describe activities and events occurring within a system. Ex: Drawing cash in a bank. Exogenous System The term exogenous is used to describe activities and events in the environment that affect the system. Ex: Arrival of customers. Closed System A system for which there is no exogenous activity and event is said to be a closed. Ex: Water in an insulated flask. Open system A system for which there is exogenous activity and event is said to be a open. Ex: Bank system. 1.4Discrete and Continuous Systems Continuous Systems Systems in which the changes are predominantly smooth are called continuous system. Ex: Head of a water behind a dam. Discrete Systems Systems in which the changes are predominantly discontinuous are called discrete systems. Ex: Bank – the number of customer‘s changes only when a customer arrives or when the service provided a customer is completed. 1.5Model of a system A model is defined as a representation of a system for the purpose of studying the system. It is necessary to consider only those aspects of the system that affect the problem under investigation. These aspects are represented in a model, and by definition it is a simplification of the system. Types of Models The various types models are  Mathematical or Physical Model  Static Model  Dynamic Model  Deterministic Model  Stochastic Model  Discrete Model  Continuous Model Mathematical Model Uses symbolic notation and the mathematical equations to represent a system. Static Model Represents a system at a particular point of time and also known as Monte-Carlo simulation. Dynamic Model Represents systems as they change over time. Ex: Simulation of a bank Deterministic Model Contains no random variables. They have a known set of inputs which will result in a unique set of outputs. Ex: Arrival of patients to the Dentist at the scheduled appointment time. Stochastic Model Has one or more random variable as inputs. Random inputs leads to random outputs. Ex: Simulation of a bank involves random interarrival and service times. Discrete and Continuous Model Used in an analogous manner. Simulation models may be mixed both with discrete and continuous. The choice is based on the characteristics of the system and the objective of the study. Discrete-Event System Simulation Modeling of systems in which the state variable changes only at a discrete set of points in time. The simulation models are analyzed by numerical rather than by analytical methods. Analytical methods employ the deductive reasoning of mathematics to solve the model. Eg: Differential calculus can be used to determine the minimum cost policy for some inventory models. Numerical methods use computational procedures and are ‗runs‘, which is generated based on the model assumptions and observations are collected to be analyzed and to estimate the true system performance measures. Real-world simulation is so vast, whose runs are conducted with the help of computer. Much insight can be obtained by simulation manually which is applicable for small systems. 1.6 Steps in a Simulation study 1. Problem formulation Every study begins with a statement of the problem, provided by policy makers. Analyst ensures its clearly understood. If it is developed by analyst policy makers should understand and agree with it. 2.Setting of objectives and overall project plan The objectives indicate the questions to be answered by simulation. At this point a determination should be made concerning whether simulation is the appropriate methodology. Assuming it is appropriate, the overall project plan should include  A statement of the alternative systems  A method for evaluating the effectiveness of these alternatives  Plans for the study in terms of the number of people involved  Cost of the study  The number of days required to accomplish each phase of the work with the anticipated results. 3.Model conceptualization The construction of a model of a system is probably as much art as science. The art of modeling is enhanced by an ability  To abstract the essential features of a problem  To select and modify basic assumptions that characterize the system  To enrich and elaborate the model until a useful approximation results Thus, it is best to start with a simple model and build toward greater complexity. Model conceptualization enhance the quality of the resulting model and increase the confidence of the model user in the application of the model. 4.Data collection There is a constant interplay between the construction of model and the collection of needed input data. Done in the early stages. Objective kind of data are to be collected. 5.Model translation Real-world systems result in models that require a great deal of information storage and computation. It can be programmed by using simulation languages or special purpose simulation software. Simulation languages are powerful and flexible. Simulation software models development time can be reduced. 6.Verified It pertains to he computer program and checking the performance. If the input parameters and logical structure and correctly represented, verification is completed. 7.Validated It is the determination that a model is an accurate representation of the real system. Achieved through calibration of the model, an iterative process of comparing the model to actual system behavior and the discrepancies between the two. 8.Experimental Design The alternatives that are to be simulated must be determined. Which alternatives to simulate may be a function of runs. For each system design, decisions need to be made concerning  Length of the initialization period  Length of simulation runs  Number of replication to be made of each run 9.Production runs and analysis They are used to estimate measures of performance for the system designs that are being simulated. 10.More runs Based on the analysis of runs that have been completed. The analyst determines if additional runs are needed and what design those additional experiments should follow. 11.Documentation and reporting Two types of documentation. o Program documentation o Process documentation Program documentation Can be used again by the same or different analysts to understand how the program operates. Further modification will be easier. Model users can change the input parameters for better performance. Process documentation Gives the history of a simulation project. The result of all analysis should be reported clearly and concisely in a final report. This enables to review the final formulation and alternatives, results of the experiments and the recommended solution to the problem. The final report provides a vehicle of certification. 12. Implementation Success depends on the previous steps. If the model user has been thoroughly involved and understands the nature of the model and its outputs, likelihood of a vigorous implementation is enhanced. The simulation model building can be broken into 4 phases. I Phase  Consists of steps 1 and 2  It is period of discovery/orientation  The analyst may have to restart the process if it is not fine-tuned  Recalibrations and clarifications may occur in this phase or another phase. II Phase  Consists of steps 3,4,5,6 and 7  A continuing interplay is required among the steps  Exclusion of model user results in implications during implementation III Phase  Consists of steps 8,9 and 10  Conceives a thorough plan for experimenting  Discrete-event stochastic is a statistical experiment  The output variables are estimates that contain random error and therefore proper statistical analysis is required. IV Phase  Consists of steps 11 and 12  Successful implementation depends on the involvement of user and every steps successful completion. 1.7SIMULATION EXAMPLES  Simulation is often used in the analysis of queueing models. In a simple typical queueing model, shown in fig 1, customers arrive from time to time and join a queue or waiting line, are eventually served, and finally leave the system.  The term "customer" refers to any type of entity that can be viewed as requesting "service" from a system. server Calling population Waiting line of customers Simple Queue Model Characteristics of Queueing Systems  The key elements, of a queueing system are the customers and servers. The term "customer" can refer to people, machines, trucks, mechanics, patients—anything that arrives at a facility and requires service.  The term "server" might refer to receptionists, repairpersons, CPUs in a computer, or washing machines….any resource (person, machine, etc. which provides the requested service.  Table 1 lists a number of different queuing systems. Table 1: Examples of Queueing Systems  The elements of a queuing system are:- The Calling Population:-  The population of potential customers, referred to as the calling population, may beassumed to be finite or infinite.  For example, consider a bank of 5 machines that are curing tires. After an interval of time, a machine automatically opens and must be attended by a worker who removes the tire and puts an uncured tire into the machine. The machines are the "customers", who "arrive" at the instant they automatically open. The worker is the "server", who "serves" an open machine as soon as possible. The calling population is finite, and consists of the five machines.  In systems with a large population of potential customers, the calling population is usually assumed to be finite or infinite. Examples of infinite populations include the potential customers of a restaurant, bank, etc.  The main difference between finite and infinite population models is how the arrival rate is defined. In an infinite-population model, the arrival rate is not affected by the number of customers who have left the calling population and joined the queueing system. On the other hand, for finite calling population models, the arrival rate to the queueing system does depend on the number of customers being served and waiting. System Capacity:-  In many queueing systems there is a limit to the number of customers that may be in the waiting line or system. For example, an automatic car wash may have room for only 10 cars to wait in line to enter the mechanism.  An arriving customer who finds the system full does not enter but returns immediately to the calling population.  Some systems, such as concert ticket sales for students, may be considered as having unlimited capacity. There are no limits on the number of students allowed to wait to purchase tickets.  When a system has limited capacity, a distinction is made between the arrival rate (i.e., the number of arrivals per time unit) and the effective arrival rate (i.e., the number who arrive and enter the system per time unit). The Arrival Process:-  Arrival process for infinite-population models is usually characterized in terms of interarrival times of successive customers. Arrivals may occur at scheduled times or at random times. When at random times, the interarrival times are usually characterized by a probability distribution  The most important model for random arrivals is the Poisson arrival process. If An represents the interarrival time between customer n-1 and customer n (A1 is the actual arrival time of the first customer), then for a Poisson arrival process. An is exponentially distributed with mean I/λ time Units. The arrival rate is λ customers per time unit. The number of arrivals in a time interval of length t, say N( t ) , has the Poisson distribution with mean λt customers.  The Poisson arrival process has been successfully employed as a model of the arrival of people to restaurants, drive-in banks, and other service facilities.  A second important class of arrivals is the scheduled arrivals, such as patients to a physician's office or scheduled airline flight arrivals to an airport. In this case, the interarrival times An , n = 1,2,. . . may be constant, or constant plus or minus a small random amount to represent early or late arrivals.  A third situation occurs when at least one customer is assumed to always be present in the queue, so that the server is never idle because of a lack of customers. For example, the "customers" may represent raw material for a product, and sufficient raw material is assumed to be always available.  For finite-population models, the arrival process is characterized in a completely different fashion. Define a customer as pending when that customer is outside the queueing system and a member of the potential calling population.  Runtime of a given customer is defined as the length of time from departure from the queueing system until that customer‘s next arrival to the queue. 1 2 (i) (i)  Let A ,A , the successive runtimes of customer /, and let S ,S the i 2 (i) (i) (i) corresponding successive system times; that is, S n is the total time spent in the system First arrival of machine 3 Second arrival of machine 3 by customer i during the nth visit. Figure 2 illustrates these concepts for machine 3 in the tire-curing example. The total arrival process is the superposition of the arrival times of all customers. Fig 2 shows the first and second arrival of machine 3. Fig 2: Arrival process for a finite-population model.  One important application of finite population models is the machine repair problem. The machines are the customers and a runtime is also called time to failure. When a machine fails, it "arrives" at the queuing system (the repair facility) and remains there until it is "served" (repaired). Times to failure for a given class of machine have been characterized by the exponential, the Weibull, and the gamma distributions. Models with an exponential runtime are sometimes analytically tractable. Queue Behavior and Queue Discipline:-  Queue behavior refers to customer actions while in a queue waiting for service to begin. In some situations, there is a possibility that incoming customers may balk (leave when they see that the line is too long), renege (leave after being in the line when they see that the line is moving too slowly), or jockey (move from one line to another if they think they have chosen a slow line).  Queue discipline refers to the logical ordering of customers in a queue and determineswhich customer will be chosen for service when a server becomes free.  Common queue disciplines include first-in, first-out (FIFO); last-in firstout (LIFO); service in random order (SIRO); shortest processing time first (SPT) and service according to priority (PR).  In a job shop, queue disciplines are sometimes based on due dates and on expected processing time for a given i type of job. Notice that a FIFO queue discipline implies that services begin in the same order as arrivals, but that customers may leave the system in a different order because of differentlength service times.  Service Times and the Service Mechanism:-  The service times of successive arrivals are denoted by S1, S2, S3…They may be constant or of random duration. The exponential,Weibull, gamma, lognormal, and truncated normal distributions have all been used successfully as models of service times in different situations.  Sometimes services may be identically distributed for all customers of a given type or class or priority, while customers of different types may have completely different service-time distributions. In addition, in some systems, service times depend upon the time of day or the length of the waiting line. For example, servers may work faster than usual when the waiting line is long, thus effectively reducing the service times.  A queueing system consists of a number of service centers and interconnecting queues. Each service center consists of some number of servers, c, working in parallel; that is, upon getting to the head of the line, a customer takes the first available server. Parallel service mechanisms are either single server (c = 1), multiple server (1 c ∞), or unlimited servers (c= ∞). (A self-service facility is usually characterized as having an unlimited number of servers.) Example 1:- Consider a discount warehouse where customers may either serve themselves; or wait of three clerks, and finally leave after paying a single cashier. The system is represented by the flow diagram in figure 1 below: Figure 1: Discount warehouse with three service centers The subsystem, consisting of queue 2 and service center 2, is shown in more detail in figure 2 below. Other variations of service mechanisms include batch service (a server serving several customers simultaneously) or a customer requiring several servers simultaneously. Figure 2: Service center 2, with c = 3 parallel servers.  Example 2:-A candy manufacturer has a production line which consists of three machines separated by inventory-in-process buffers. The first machine makes and wraps the individual pieces of candy, the second packs 50 pieces in a box, and the third seals and wraps the box. The two inventory buffers have capacities of 1000 boxes each. As illustrated by Figure 3, the system is modeled as having three service centers, each center having c = 1 server (a machine), with queue-capacity constraints between machines. It is assumed that a sufficient supply of raw material is always available at the first queue. Because of the queue-capacity constraints, machine 1 shuts down whenever the inventory buffer fills to capacity, while machine 2 shuts down whenever the buffer empties. In brief, the system consists of three single-server queues in series with queue-capacity constraints and a continuous arrival stream at the first queue. Figure 3: Candy production line Queueing Notation:-  Recognizing the diversity of queueing systems, Kendall 1953 proposed a notational system for parallel server systems which has been widely adopted. An abridged version of this convention is based on the format A /B / c / N / K. These letters represent the following system characteristics:  A represents the interarrival time distribution.  B represents the service-time distribution.  Common symbols for A and B include M (exponential or Markov), D (constant or deterministic), Ek (Erlang of order k), PH (phase-type), H (hyperexponential), G (arbitrary or general), and GI (General independent).  c represents the number of parallel servers.  N represents the system capacity.  K represents the size of the calling population  For example, M / M / 1 / ∞ / ∞ indicates a single-server system that has unlimited queue capacity and an infinite population of potential arrivals. The interarrival times and service times are exponentially distributed. When N and K are infinite, they may be dropped from the notation. For example, M / M / 1 / ∞ / ∞ is often shortened to M/M/l.  Additional notation used for parallel server systems is listed in Table 1 given below. The meanings may vary slightly from system to system. All systems will be assumed to have a FIFO queue discipline. Table 1. Queueing Notation for Parallel Server Systems ώ Long-run average time spent in system per customer ώ Long-run average time spent in queue per customer Q

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