Petri net modeling and performance analysis of cluster tools with chamber revisiting

Timed Petri nets are convenient models of cluster tools as they represent the flow of wafers through the chambers of the tool as well as consecutive actions performed by the robotic transporter. Since the durations of all activities are also represented in such model, performance characteristics can be derived for steady-state as well as for transient behaviors. Steady-state performance of tools with chamber revisiting is investigated in this paper. A general description of cluster tools is proposed for systematic derivation of schedules, and a Petri net model is automatically derived from this description. The performance of the modeled system is derived by using place invariants, without exhaustive reachability analysis

A Petri-Net-Based Scheduling Strategy for Dual-Arm Cluster Tools With Wafer Revisiting

International audienceThere are wafer fabrication processes in cluster tools that require wafer revisiting. The adoption of a swap strategy for such tools forms a 3-wafer cyclic (3-WC) period with three wafers completed in each period. It has been shown that, by such a scheduling strategy, the minimal cycle time cannot be reached for some cases. This raises a question of whether there is a scheduling method such that the performance can be improved. To answer this question, a dual-arm cluster tool with wafer revisiting is modeled by a Petri net. Based on the model, the dynamical behavior of the process is analyzed. Then, a 2-wafer cyclic (2-WC) scheduling strategy is revealed for the first time. Cycle time analysis is conducted for the proposed strategy to evaluate its performance. It shows that, for some cases, the performance obtained by a 2-WC schedule is better than that obtained by any existing 3-WC ones. Thus, they can be used to complement each other in scheduling dual-arm cluster tools with wafer revisiting. Illustrative examples are given

Cluster tools with chamber revisiting-modeling and analysis using timed Petri nets

Timed Petri nets are formal models of discrete concurrent systems. Since the durations of all activities are included in the model descriptions, many performance characteristics can be derived from such models. In the case of cluster tools, net models represent the flow of wafers through the chambers of the tool as well as consecutive actions performed by the robotic transporter. Steady-state performance of cluster tools with chamber revisiting is investigated in this paper. A systematic development of detailed tool schedules, based on a general behavioral description of the tool, is proposed and is used to derive the corresponding Petri net models. Symbolic performance characteristics of the modeled tools are obtained by using place invariants, without exhaustive reachability analysis. Simple examples presented in the paper can be easily extended in many ways

Systematic Construction and Performance Analysis of Cluster Tools Using Timed Petri Net Models

A cluster tool is an integrated, envi- ronmentally isolated manufacturing system consisting of process, transport, and cassette modules, mechan- ically linked together, that is used in manufacturing of semiconductor chips. Because of high throughput requirements, cluster tools perform a number of activ- ities concurrently. Petri nets are formal models devel- oped specifically for representation of concurrent ac- tivities and for their coordination. In timed nets, the durations of modeled activities are represented by oc- currence times associated with transitions, and this allows to study the performance characteristics of the modeled systems. Since cluster tools can be quite complex, a system- atic approach to generating net models is proposed. Net models derived in such a way have modular struc- ture, which is used to determine model’s steady–state performance on the basis of net invariants, without the exhaustive reachability analysis. Performance charac- teristics are obtained in symbolic form, in terms of modeling parameters, so different variants of cluster tools can be evaluated and compared very efficiently, without repetitive model analyses

Timed Petri nets in modeling and analysis of cluster tools

Timed Petri nets are used as models of cluster tools representing the flow of wafers through the chambers of the tool as well as sequences of actions performed by the robotic transporter. Since the durations of all activities are also represented in the model, performance characteristics can be derived from the model for steady-state, as well as transient behaviors. The performance of single-blade tools is compared with that of dual-blade tools. The effects of multiple loadlocks, redundant chambers and multiple robots are discussed and, analyzed. Modeling of wafer routings with chamber revisiting and processing of wafers of multiple types is also briefly discussed

Performance evaluation of serial photolithography clusters: Queueing models, throughput and workload sequencing,” in

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Petri Nets and Timed Petri Nets in Modeling and Analysis of Concurrent Systems – An Overview

Petri nets are formal models of systems which exhibit concurrent activities. Communication networks, multiprocessor systems, manufacturing systems and dis- tributed databases are simple examples of such systems. As formal models, Petri nets are bipartite directed graphs, in which the two types of vertices represent, in a very gen- eral sense, conditions and events. An event can occur only when all conditions associated with it (represented by arcs directed to the event) are satisfied. An occurrence of an event usually satisfies some other conditions, indicated by arcs directed from the event. So, an occurrence of one event causes some other event to occur, and so on. In order to study performance aspects of systems modeled by Petri nets, the durations of modeled activities must also be taken into account. This can be done in different ways, resulting in different types of temporal nets. In timed Petri nets, occurrence times are associated with events, and the events occur in real–time (as opposed to instantaneous oc- currences in other models). For timed nets with constant or exponentially distributed occurrence times, the state graph of a net is a Markov chain, in which the stationary prob- abilities of states can be determined by standard methods. These stationary probabilities are used for the derivation of many performance characteristics of the model. Analysis of net models based on exhaustive generation of all possible states is called reachability analysis; it provides detailed characterization of model’s behavior, but often re- quires generation and analysis of huge state spaces (in some models the number of states increases exponentially with some model parameters, which is known as “state explo- sion”). Structural analysis determines the properties of net models on the basis of connections among model elements; structural analysis is usually much simpler than reachability analysis, but can be applied only to models satisfying certain properties. If neither reachability nor structural analysis is feasible, discrete–event simulation of timed nets can be used to study the properties of net models. This paper overviews basic concepts of Petri nets, intro- duces timed Petri nets, and provides brief summaries of sev- eral case studies of performance analysis which are discussed in greater detail in other publications of the author

A comprehensive study of the effect of meteorological conditions on fruit abscission and metamitron thinning efficacy in Malus domestica Borkh

Doutoramento em Engenharia Agronómica / Instituto Superior de Agronomia. Universidade de LisboaMetamitron is an apple (Malus domestica Borkh.) fruit thinner that acts by reducing the photosynthetic capacity of trees. Thinning is a common practice among apple growers however, the effect of meteorological conditions, per si, and after metamitron spraying, is far from elucidated. In order to investigate the triggered physiological and biochemical processes, trials with shading nets (SN) during 5 days and high nighttime temperature (HNT) during 5 nights, along with high humidity (HH) for 3 h prior spraying were set in three locations, within 3 years. Lower irradiance caused a momentaneous photosynthetic decrease that led to reduced levels of leaf sucrose and sorbitol and consequent increases in fruit abscission rates. HNT pathway is a slight increment in the respiratory mechanisms, but mainly in the whole tree metabolic activity, finally resulting in a shortage in sucrose and sorbitol levels, reducing fruit growth and promoting higher abscission rates. Metamitron acts through a photosynthetic inhibition, including reductions in RuBisCO total activity, translating in less CH production. In addition, it stimulates vegetative growth, consuming CH and slowing down fruit growth rate, and finally enhancing of abscission. The combined treatments resulted in the strongest thinning efficacy, through a suppression of the CH production caused by metamitron in combination with low radiation and or through enhanced expenditure cause by HNT, frequently over-thinning. The effect of HH may enhance fruit drop under humid climates and in younger trees, more susceptible to variations in CH content. This work shows meteorological conditions, namely cloudy days, periods of HNT and increased humidity levels, may affect metamitron thinning efficacy and must be considered in order to decide which rate to apply to achieve an optimum crop loadN/

Brainless but smart: Investigating cognitive-like behaviors in the acellular slime mold physarum polycephalum

Evolutionary pressures to improve fitness, have enabled living systems to make adaptive decisions when faced with heterogeneous and changing environmental and physiological conditions. This dissertation investigated the mechanisms of how environmental and physiological factors affect the behaviors of non-neuronal organisms. The acellular slime mold Physarum polycephalum was used as the model organism, which is a macroscopic, unicellular organism, that self-organizes into a network of intersecting tubules. Without using neurons, P. polycephalum can solve labyrinth mazes, build efficient tubule networks, and make adaptive decisions when faced with complicated trade-offs, such as between food quality and risk, speed and accuracy, and exploration and exploitation. However, the understanding of the mechanisms used by P. polycephalum in exhibiting such behaviors is very limited. Therefore, the objective of this dissertation is to understand the mechanisms adopted by non-neuronal organisms to explore and exploit resources in the physical environment, using environmental and physiological information. To this end, the dissertation characterizes the direction and amount of influence between different regions of tubule-shaped P. polycephalum cells in binary food choice experiments. The results show that when the two food sources are identical in quality, the regions near the food source act as the drivers of P. polycephalum tubule behavior. Conversely, when one of the food sources is more enriched with nutrients, the regions near the rejected food source were found to drive the tubule behavior. Secondly, a generalized choice-making criterion was formulated to determine the choice-making behaviors of P. polycephalum, examine whether sufficient experimental time was given to make a choice, and determine the time point at which a choice was made. The criterion was tested on binary food choice experiments using P. polycephalum tubules. The results show that P. polycephalum made a choice for the option for the better food option, except when the differences in food quality were low. Moreover, the criterion was found to not determine the choice-making behaviors when the food sources presented were identical in quality. Thirdly, the dissertation investigated whether P. polycephalum cells modify their future exploratory behavior using their past foraging experience. The results did not find a strong influence of the past foraging experience on the exploratory networks formed by P. polycephalum cells. Finally, P. polycephalum exploratory behaviors were examined and compared when the cells were in high-energy versus low-energy physiological conditions. Interestingly, the study found the P. polycephalum cells in low-energy conditions show an increased tendency to split themselves into multiple autonomous cells. Additionally, the behavior is shown to increase the fitness of the cell by increasing its foraging efficiency