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Abstract

The performance of scheduled business processes is of central importance for services and manufacturing systems. However, current techniques for performance analysis do not take both queueing semantics and the process perspective into account. In this work, we address this gap by developing a novel method for utilizing rich process logs to analyze performance of scheduled processes. The proposed method combines simulation, queueing analytics, and statistical methods. At the heart of our approach is the discovery of an individual-case model from data, based on an extension of the Colored Petri Nets formalism. The resulting model can be simulated to answer performance queries, yet it is computational inefficient. To reduce the computational cost, the discovered model is projected into Queueing Networks, a formalism that enables efficient performance analytics. The projection is facilitated by a sequence of folding operations that alter the structure and dynamics of the Petri Net model. We evaluate the approach with a real-world dataset from Dana-Farber Cancer Institute, a large outpatient cancer hospital in the United States.

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... Unlike existing proposals for model simplification [12], these rules are local (affecting only a subnet of the GSPN), come with formal bounds regarding the introduced estimation error, and their applicability is identified automatically by structural decomposition of the GSPN. Foldings, as a form of simplification, may either use aggregation or model elimination. ...
... Given L, operational models such as GSPNs can automatically be discovered and enriched with performance information [16,17]. To quantify q(Y ), a corresponding query q M (Y ) is evaluated over the model, e.g., with the help of simulation [17] or queueing theory approximations [5,12]. A model-based approach overcomes the aforementioned limitations. ...
... The model-based approach suffers from a major drawback, namely over-fitting of the estimated q(Y ) with respect to L [12]. ML-based methods balance over-fitting ofq to L by means of model selection, which comprises two main approaches, namely regularisation, and aggregation [18]. ...
Article
Operational process models such as generalised stochastic Petri nets (GSPNs) are useful when answering performance questions about business processes (e.g. ‘how long will it take for a case to finish?’). Recently, methods for process mining have been developed to discover and enrich operational models based on a log of recorded executions of processes, which enables evidence-based process analysis. To avoid a bias due to infrequent execution paths, discovery algorithms strive for a balance between over-fitting and under-fitting regarding the originating log. However, state-of-the-art discovery algorithms address this balance solely for the control-flow dimension, neglecting the impact of their design choices in terms of performance measures. In this work, we thus offer a technique for controlled performance-driven model reduction of GSPNs, using structural simplification rules, namely foldings. We propose a set of foldings that aggregate or eliminate performance information. We further prove the soundness of these foldings in terms of stability preservation and provide bounds on the error that they introduce with respect to the original model. Furthermore, we show how to find an optimal sequence of simplification rules, such that their application yields a minimal model under a given error budget for performance estimation. We evaluate the approach with two real-world datasets from the healthcare and telecommunication domains, showing that model simplification indeed enables a controlled reduction of model size, while preserving performance metrics with respect to the original model. Moreover, we show that aggregation dominates elimination when abstracting performance models by preventing under-fitting due to information loss.
... Defining such a model manually would require deep knowledge of the process and high levels of expertise, especially in scenarios where the process is not enacted and traced according to a given well-defined workflow schema. This explains the many effort s that have been spent to extract such a model automatically from historical traces [13][14][15][16][17][18][19][20][21] , based on suitable prediction-oriented inductive learning methods. ...
... R1 : Combining forecasts on ongoing and future process instances, reusing process/time-series prediction methods. The performance outcomes of each ongoing process instance can be forecast by leveraging, as a base prediction technique, one among the many ones that have been developed in the active field of performance-oriented predictive process monitoring [13][14][15][16][17][18][19][20][21] . As there is no consensus on which of these solutions is the best one, for the sake of versatility and extensibility it is convenient to define an A-PPI prediction approach parametrically to its underlying single-instance prediction technique. ...
... In particular, as to the fundamental requirement R1, all the approaches to the prediction of (numerical) performance measures developed in the field of predictive process monitoring [13][14][15][16][17][18][19][20][21] provide forecasts for single process instances, but cannot infer anything on the process instances of the current window starting after the current checkpoint. On the other hand, the approaches that only forecast aggregate performances over future time ranges based on time-series predictors [23,24] , assume that all the past values of the target time series (i.e. the series of aggregate perfor-mance value computed for all windows/slots of the process) are known with a sufficient level of certainty; however, this assumption does not hold in our setting, where the process instances of a window/slot may terminate way after the end of the window/slot. ...
Article
Monitoring the performances of a business process is a key issue in many organizations, especially when the process must comply with predefined performance constraints. In such a case, empowering the monitoring system with prediction capabilities would allow us to know in advance a constraint violation, and possibly trigger corrective measures to eventually prevent the violation. Despite the problem of making run-time predictions for a process, based on pre-mortem log data, is an active research topic in Process Mining, current predictive monitoring approaches in this field only support predictions at the level of a single process instance, whereas process performance constraints are often defined in an aggregated form, according to predefined time windows. Moreover, most of these approaches cannot work well on the traces of a lowly-structured business process when these traces do not refer to well-defined process tasks/activities. For such a challenging setting, we define an approach to the problem of predicting whether the process instances of a given (unfinished) time window will violate an aggregate performance requirement. The approach mainly rely on inducing and integrating two complementary predictive models: (1) a clustering-based predictor for estimating the outcome of each ongoing process instance, (2) a time-series predictor for estimating the performance outcome of “future” process instances that will fall in the window after the moment when the prediction is being made (i.e. instances, not started yet, that will start by the end of the window). Both models are expected to benefit from the availability of aggregate context data regarding the environment that surrounds the process. This discovery approach is conceived as the core of an advanced performance monitoring system, for which an event-based conceptual architecture is here proposed. Tests on real-life event data confirmed the validity of our approach, in terms of accuracy, robustness, scalability, and usability.
... It considers resources and various scheduling patterns with setup costs and temporal constraints, but it does not use a process focus and does not provide a solution methodology. Stochastic approaches for modeling temporal durations are discussed in [25,27]. In [25] non-markovian stochastic distributions are used to represent the durations of an activity and run time predictions are made about completion times and risks of missing deadlines. ...
... In [25] non-markovian stochastic distributions are used to represent the durations of an activity and run time predictions are made about completion times and risks of missing deadlines. The method in [27] combines queuing and simulation with statistical methods to analyze the performance of running processes described as colored Petrinets. Compliance issues of temporal processes are discussed from a diagnostic and alignment perspective in [30] by matching actual log traces with a specified model and deviations are highlighted. ...
... Finally, activity durations, path choices, violation types, degrees and frequencies, and temporal patterns can all be statistically characterized. This would allow for a stochastic approach [25,27,28] to managing constraint violations by using the statistical characterization of paths and durations to allow optimal violation management in light of probabilistic inference for the yet-to-be completed part of the process. ...
Article
While there has been much work on modeling and analysis of temporal constraints in workflows in the context of many real-world applications, there has not been much work on managing violations of temporal constraints. In real-time workflows, such as in medical processes and emergency situations, and also in logistics, finance and in other business processes with deadlines some violations are unavoidable. Here we introduce the notion of controlled violations as the ability to monitor a running process and develop an approach based on constraint satisfaction to determine the best schedule for its completion in a way so as to minimize the total penalty from the violations. The violations are evaluated in terms of metrics like number of violations, delay in process completion, and penalty of weighted violations. We also relate our work to the concept of controllability in literature and show how it can be checked using our method. Finally, we analyze the properties of our approach and also offer a proposal for implementation.
... In [27,28], queues are discovered in stochastic process mining using two formalisms, Process Trees [28] and Queue-Enabling Colored Stochastic Petri Nets [27]. The Process Tree approach is informed by statistics theory and uses both Bayesian and Markov-Chain Monte-Carlo fitting. ...
... In [27,28], queues are discovered in stochastic process mining using two formalisms, Process Trees [28] and Queue-Enabling Colored Stochastic Petri Nets [27]. The Process Tree approach is informed by statistics theory and uses both Bayesian and Markov-Chain Monte-Carlo fitting. ...
Conference Paper
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Many algorithms now exist for discovering process models from event logs. These models usually describe a control flow and are intended for use by people in analysing and improving real-world organizational processes. The relative likelihood of choices made while following a process (i.e., its stochastic behaviour) is highly relevant information which few existing algorithms make available in their automatically discovered models. This can be addressed by automatically discovered stochastic process models. We introduce a framework for automatic discovery of stochastic process models, given a control-flow model and an event log. The framework introduces an estimator which takes a Petri net model and an event log as input, and outputs a Generalized Stochastic Petri net. We apply the framework, adding six new weight estimators, and a method for their evaluation. The algorithms have been implemented in the open-source process mining framework ProM. Using stochastic conformance measures, the resulting models have comparable conformance to existing approaches and are shown to be calculated more efficiently.
... This log contains some 150,000 events in over 1100 cases" and it did not take much to create a "spaghetti" model from an activity log. A few years later, Senderovich et al. experimented on another medical dataset, with RTLS data taken from an American hospital, with approximately 240,000 events per year [5]. In 2014, a smart city dataset, which was used in a task that analyzed bus routes as processes contained over 1 million events per day for a period of one month (approximately 30 million events) [6]. ...
... These features can be used to improve the performance of machine learning algorithms." 5 Domain knowledge brings up again the human-in-the-loop. Clearly, the visualization tools that were developed over the years for process discovery can become handy when gathering domain knowledge for additional perspectives. ...
Chapter
The discipline of process mining was inaugurated in the BPM community. It flourished in a world of small(er) data, with roots in the communities of software engineering and databases and applications mainly in organizational and management settings. The introduction of big data, with its volume, velocity, variety, and veracity, and the big strides in data science research and practice pose new challenges to this research field. The paper positions process mining along modern data life cycle, highlighting the challenges and suggesting directions in which data science disciplines (e.g., machine learning) may interact with a renewed process mining agenda.
... Provided with the stochastic F/J network, F A , which corresponds to the underlying process, we target local improvement of service policy, whenever conformance is lacking. We assume that splits and joins have a single layer of resource nodes, a plausible assumption since multiple stages can be aggregated into such a construct [34]. ...
... Serve case σ (s) with S 33: t = max t, r σ(s) + p σ(s) 34: flow time to exceed T S max (INIT) and F S max (INIT), respectively. A case (j) will be pushed forward, ahead of cases (i), . . . ...
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Service processes, for example in transportation, telecommunications or the health sector, are the backbone of today's economies. Conceptual models of service processes enable operational analysis that supports, e.g., resource provisioning or delay prediction. In the presence of event logs containing recorded traces of process execution, such operational models can be mined automatically.In this work, we target the analysis of resource-driven, scheduled processes based on event logs. We focus on processes for which there exists a pre-defined assignment of activity instances to resources that execute activities. Specifically, we approach the questions of conformance checking (how to assess the conformance of the schedule and the actual process execution) and performance improvement (how to improve the operational process performance). The first question is addressed based on a queueing network for both the schedule and the actual process execution. Based on these models, we detect operational deviations and then apply statistical inference and similarity measures to validate the scheduling assumptions, thereby identifying root-causes for these deviations. These results are the starting point for our technique to improve the operational performance. It suggests adaptations of the scheduling policy of the service process to decrease the tardiness (non-punctuality) and lower the flow time. We demonstrate the value of our approach based on a real-world dataset comprising clinical pathways of an outpatient clinic that have been recorded by a real-time location system (RTLS). Our results indicate that the presented technique enables localization of operational bottlenecks along with their root-causes, while our improvement technique yields a decrease in median tardiness and flow time by more than 20%.
... The likelihood of future activities can be predicted using Markovian models [12], but without providing any time predictions. Completion time of the next activity can be predicted by training an LSTM neural network [13], or by learning process models with arbitrary probability density functions for time delays through nonparametric regression from event logs [14] that can also be used for learning simulation models to predict performance [15], [16]. Competing for shared resources can be taken into account through simulation models or with queuing models [17]. ...
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Predictive performance analysis is crucial for supporting operational processes. Prediction is challenging when cases are not isolated but influence each other by competing for resources (spaces, machines, operators). The so-called performance spectrum maps a variety of performance-related measures within and across cases over time. We propose a novel prediction approach that uses the performance spectrum for feature selection and extraction to pose machine learning problems used for performance prediction in non-isolated cases. Although the approach is general, we focus on material handling systems as a primary example. We report on a feasibility study conducted for the material handling systems of a major European airport. The results show that the use of the performance spectrum enables much better predictions than baseline approaches.
... Performance prediction for the remaining time until completion of a given case can be predicted by regression models [5], by annotating transition system states with remaining times [4], by learning a clustering of transition system states [6], by combining models for prediction of the next activity in a case with regression models [12]. Completion time of the next activity can be predicted by training an LSTM neural network [22], or by learning process models with arbitrary probability density functions for time delays through non-parametric regression from event logs [14] that can also be used for learning simulation models to predict performance [17,15]. These models predict performance of a single case based on case-specific features. ...
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Performance is central to processes management and event data provides the most objective source for analyzing and improving performance. Current process mining techniques give only limited insights into performance by aggregating all event data for each process step. In this paper, we investigate process performance of all process behaviors without prior aggregation. We propose the performance spectrum as a simple model that maps all observed flows between two process steps together regarding their performance over time. Visualizing the performance spectrum of event logs reveals a large variety of very distinct patterns of process performance and performance variability that have not been described before. We provide a taxonomy for these patterns and a comprehensive overview of elementary and composite performance patterns observed on several real-life event logs from business processes and logistics. We report on a case study where performance patterns were central to identify systemic, but not globally visible process problems.
... According to the data inclusion the process models, it is crucial to analyse the evolution of the objects [16], and to determine whether there are data dependencies and which these dependencies are [17] in order to define whose model can be aligned in BPMN model [6,18]. ...
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The more challenging case of transient analysis of Markov chains is investigated in Chapter 5. The chapter introduces symbolic solutions in simple cases such as small or very regular state spaces. In general, numerical techniques are more suitable and are therefore covered in detail. Uniformization and some variants thereof are introduced as the method of choice for transient analysis in most cases. Particular emphasis is given to stiffness tolerant uniformization that can be of practical relevance in many modeling scenarios where relatively rare and fast events occur concurrently. As an alternative a method for aggregation/disaggregation of stiff Markov chains is introduced for a computation of approximate transient state probabilities. The method is based on a distinction of fast recurrent and fast transient sets of states that can be aggregated with relatively small error. All steps are illustrated by a detailed example model of server breakdown and repair. In addition to numerical results an error analysis is provided as well.
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The discipline of business process management aims at capturing, understanding, and improving work in organizations by using process models as central artifacts. Since business-oriented tasks require different information from such models to be highlighted, a range of abstraction techniques has been developed over the past years to manipulate overly detailed models. At this point, a clear understanding of what distinguishes these techniques and how they address real world use cases has not yet been established. In this paper we systematically develop, classify, and consolidate the use cases for business process model abstraction and present a case study to illustrate the value of this technique. The catalog of use cases that we present is based on a thorough evaluation of the state of the art, as well as on our cooperation with end users in the health insurance sector. It has been subsequently validated by experts from the consultancy and tool vendor domains. Based on our findings, we evaluate how the existing business process model abstraction approaches support the discovered use cases and reveal which areas are not adequately covered, as such providing an agenda for further research in this area.
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This paper describes the "method of surrogates," an approximate solution technique for queueing network models that include the simultaneous or overlapped possession of resources. Simultaneous resource possession arises in many computer system contexts and can have a significant effect on system performance. It poses difficulties in analytic modeling because it violates certain assumptions that are essential to separable or product form queueing networks. Efficient exact solution techniques are thus inapplicable and approximate solution techniques must be used. The essence of the method of surrogates is to partition queueing delay according to which of the simultaneously held resources is responsible, then to iterate between two models, each of which includes an explicit representation of one of the simultaneously held resources and a "delay server" (with service time but no queueing) acting as a surrogate for queueing delay due to congestion at the other simultaneously held resource. The approach provides a unified, practical treatment of a diverse set of problems.
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In this paper we consider an open queueing network having multiple classes, priorities, and general service time distributions. In the case where there is a single bottleneck station we conjecture that normalized queue length and sojourn time processes converge, in the heavy traffic limit, to one-dimensional reflected Brownian motion, and present expressions for its drift and variance. The conjecture is motivated by known heavy traffic limit theorems for some special cases of the general model, and some conjectured “Heavy Traffic Principles” derived from them. Using the known stationary distribution of one-dimensional reflected Brownian motion, we present expressions for the heavy traffic limit of stationary queue length and sojourn time distributions and moments. For systems with Markov routing we are able to explicitly calculate the limits.
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We present a new net-reduction methodology to facilitate the analysis of real-time systems using Delay Time Petri Nets (DTPNs). Net reduction is one of the most important techniques for reducing the state-explosion problem of Petri nets. However, the application of net reduction to current timed-extensions of Petri nets (such as Merlin's Time PNs) is very limited due to the difficulty faced in the preservation of timing constraints. To overcome this problem, we introduce DTPNs which are inspired by Merlin's (1976) Time PNs, Senac's (1994) Hierarchical Time Stream PNs, and Little's (1991) Timed PNs. We show that DTPNs are much more suitable for net reduction. Then, we present a new set of DTPN reduction rules for the analysis of schedule and deadlock analysis. Our work is distinct from the others since our goal is to analyze real-time systems and the reduction methods we propose preserve both timing properties (schedule) and deadlock. To evaluate our framework, we have implemented an automated analysis tool whose main functions include net reduction and class-graph generation. The experimental results show that our net-reduction methodology leads to a significant contribution to the efficient analysis of real-time systems
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The class of stochastic well-formed colored nets (SWN's) was defined as a syntactic restriction of stochastic high-level nets. The interest of the introduction of restrictions in the model definition is the possibility of exploiting the symbolic reachability graph (SRG) to reduce the complexity of Markovian performance evaluation with respect to classical Petri net techniques. It turns out that SWN's allow the representation of any color function in a structured form, so that any unconstrained high-level net can be transformed into a well-formed net. Moreover, most constructs useful for the modeling of distributed computer systems and architectures directly match the “well-formed” restriction, without any need of transformation. A nontrivial example of the usefulness of the technique in the performance modeling and evaluation of multiprocessor architectures is included
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This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solution methodology. The QMIPS Project: The QMIPS project is a collaborative research project supported by the CEC as ESPRITBRA project no 7269. It is being carried out by the following organisations: CWI (Amsterdam), EHEI (University of Paris V), Imperial College (London), INRIA (Sophia-Antipolis), University of Erlangen, University of Newcastle, University of Torino and University of Zaragoza. 1 Introduction The purpose of this paper is to present a survey of queueing theoretic methods for the quantitative modeling and analysis of parallel and distributed systems. We discuss a number of queueing models that can be viewed as key models for the performance analysis and optimization of parallel ...
A comparison of performance Petri nets and queueing network models
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