Problem Definition: Much of the focus of queueing theory (QT) is on performance evaluation that supports comparative analytics, i.e., comparing performance measures under different intervention. However, analytical results are very sensitive to model assumptions. We develop a data-driven Structured Causal Model adapted to queueing systems (SCQM) that automatically adapts to the data generating process, finds causal relations, and supports comparative analytics. Numerical experiments show that the accuracy of SCQM is competitive with QT even for examples where analytical queueing solutions are available.

‍Methodology: We use structured causal modeling methodology to develop a non-queueing simulator without prior knowledge of the system. We employ Machine Learning (ML) models for identifying the parent sets and causal relations. We then provide intervention analysis using Monte Carlo simulation.

‍Managerial Implications: We develop an accurate self-adapting data-driven performance evaluator for congested systems that requires no prior knowledge of the system dynamics. Using this method, companies can perform comparative analytics of interventions for queueing systems that may not be analytically solvable.

Problem definition: Motivated by technological advances in real-time data collection about customers location in service systems, we study the effect of partial visibility of customers on waiting time prediction. We consider systems where the predictor observes only a subset of the customers interacting with the system while serving all customers indiscriminately.

‍Methodology/results: We formulate a novel model of a partially visible queue and analyze the waiting time prediction problem, deriving a closed-form expression for the optimal prediction. This facilitates quantifying the performance loss of arbitrary prediction methods because of partial visibility and their inherent limitations (i.e., bias and variance). We compare the performance of a wide range of commonly used predictive methods and examine how partial visibility along with other system parameters affects their performance. We further extend these numerical analyses to queueing systems that exhibit characteristics that are common in practice and that were studied in the service operations literature.

‍Managerial implications: Our analysis shows that the phenomenon of invisible customers profoundly impacts the ability to accurately predict waiting times and should, therefore, be considered an important factor in the development of prediction tools. Such tools cannot be effectively deployed if technological barriers or operational limitations prevent a sufficiently high level of data integrity. This work provides specific insights into the effectiveness of various commonly used prediction methods, some of which are shown to be highly sensitive to partial visibility and other queueing systems characteristics. Our findings suggest that machine learning methods that use carefully chosen features offer the most effective generic solution for waiting time prediction in the presence of invisible customers and explain the mechanisms through which partial visibility deteriorates the performance of prediction methods.

Business Process Simulation (BPS) is an approach to analyze the performance of business processes under different scenarios. For example, BPS allows us to estimate the impact of adding one or more resources on the cycle time of a process. The starting point of BPS is a process model annotated with simulation parameters (a BPS model). BPS models may be manually designed, based on information collected from stakeholders and from empirical observations, or automatically discovered from historical execution data. Regardless of its provenance, a key question when using a BPS model is how to assess its quality. In particular, in a setting where we are able to produce multiple alternative BPS models of the same process, this question becomes: How to determine which model is better, to what extent, and in what respect? In this context, this article studies the question of how to measure the quality of a BPS model with respect to its ability to accurately replicate the observed behavior of a process. Rather than pursuing a one-size-fits-all approach, the article recognizes that a process covers multiple perspectives. Accordingly, the article outlines a framework that can be instantiated in different ways to yield quality measures that tackle different process perspectives. The article defines a number of concrete quality measures and evaluates these measures with respect to their ability to discern the impact of controlled perturbations on a BPS model, and their ability to uncover the relative strengths and weaknesses of two approaches for automated discovery of BPS models. The evaluation shows that the proposed measures not only capture how close a BPS model is to the observed behavior, but they also help us to identify the sources of discrepancies.

We apply supervised learning to a general problem in queueing theory: using a neural net, we develop a fast and accurate predictor of the stationary system-length distribution of a GI/GI/1 queue—a fundamental queueing model for which no analytical solutions are available. To this end, we must overcome three main challenges: (i) generating a large library of training instances that cover a wide range of arbitrary interarrival and service time distributions, (ii) labeling the training instances, and (iii) providing continuous arrival and service distributions as inputs to the neural net. To overcome (i), we develop an algorithm to sample phase-type interarrival and service time distributions with complex transition structures. We demonstrate that our distribution-generating algorithm indeed covers a wide range of possible positive-valued distributions. For (ii), we label our training instances via quasi-birth-and-death(QBD) that was used to approximate PH/PH/1 (with phase-type arrival and service process) as labels for the training data. For (iii), we find that using only the first five moments of both the interarrival and service times distribution as inputs is sufficient to train the neural net. Our empirical results show that our neural model can estimate the stationary behavior of the GI/GI/1—far exceeding other available methods in terms of both accuracy and runtimes.

Information systems have been widely adopted to support service processes in various domains, e.g., in the telecommunication, finance, and health sectors. Information recorded by systems during the operation of these processes provides an angle for operational process analysis, commonly referred to as process mining. In this work, we establish a queueing perspective in process mining to address the online delay prediction problem, which refers to the time that the execution of an activity for a running instance of a service process is delayed due to queueing effects. We present predictors that treat queues as first-class citizens and either enhance existing regression-based techniques for process mining or are directly grounded in queueing theory. In particular, our predictors target multi-class service processes, in which requests are classified by a type that influences their processing. Further, we introduce queue mining techniques that derive the predictors from event logs recorded by an information system during process execution. Our evaluation based on large real-world datasets, from the telecommunications and financial sectors, shows that our techniques yield accurate online predictions of case delay and drastically improve over predictors neglecting the queueing perspective.