Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Conformance checking and performance improvement in scheduled processes: A queueing-network perspective

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%

Analysis of Aircraft Sortie Generation with Concurrent Maintenance and General Service Times

The primary objective of this study was to develop an analytical methodology for evaluating an aircraft sortie generation process. The process is modeled as a closed network of general service queues with a fork join node to model concurrent servicing. The model uses the Mean Value Analysis (MVA) algorithm and general queueing network analysis by decomposition to approximate network performance measures including resource utilization and the overall sortie generation rate. The results of the study show that the analytical approximation\u27s accuracy decreases as server utilization increases. However, when server utilization is kept in realistic ranges, the approximation is very accurate. When applied to a closed system of single server queues and delay stations, the approximation performs significantly better than a pure MVA-based approach. For closed or capacitated open systems with multiserver queues, the approximation can still be applied to provide upper and lower bounds on system performance

Development of a parametric-decomposition methodology for solving queueing networks with simultaneous resource possession under capacity restrictions

Motivated by applications in health care systems, this study focused on queueing network models with instances of simultaneous resource possession under capacity restrictions in different stages. Customers during service at certain nodes in the first-level or primary system may simultaneously need service from a second-level server. In this simultaneous resource possession situation, the time the customer spends waiting for the second-level server will impact the overall service time at first-level server and consequently the performance of the entire system. Closed queueing networks and fork/join approximations for one and two-stage systems were used to capture the capacity restriction effects in different sections of the primary system. An iterative algorithm was developed to incorporate the effect of the second-level server on the performance of the entire system. This study used a modular approach rooted in the parametric-decomposition method and two-moment approximations. Different systems showing the proposed building blocks and their combinations to solve more complex systems illustrated the application of the proposed modeling approach.To evaluate the performance prediction accuracy of the solution algorithms, the analytical results were compared to simulation estimates for several configurations with single and multi-server nodes, a wide range of service time variability, and different levels of capacity constraints. The analytical results tracked the simulation estimates well with errors less than 10% in more than 80% of the configurations simulated. Higher errors in the 15% to 20% range were observed for system with low capacity limits, high service time variability (SCV=2), and high demand (p=0.75) for the second-level server

Hierarchical Analyses Applied to Computer System Performance: Review and Call for Further Studies

We review studies based on analytic and simulation methods for hierarchical performance analysis of Queueing Network - QN models, which result in an order of magnitude reduction in performance evaluation cost with respect to simulation. The computational cost at the lower level is reduced when the computer system is modeled as a product-form QN. A Continuous Time Markov Chain - CTMC or discrete-event simulation can then be used at the higher level. We first consider a multiprogrammed transaction - txn processing system with Poisson arrivals and predeclared locks requests. Txn throughputs obtained by the analysis of multiprogrammed computer systems serve as the transition rates in a higher level CTMC to determine txn response times. We next analyze a task system where task precedence relationships are specified by a directed acyclic graph to determine its makespan. Task service demands are specified on the devices of a computer system. The composition of tasks in execution determines txn throughputs, which serve as transition rates among the states of the higher level CTMC model. As a third example we consider the hierarchical simulation of a timesharing system with two user classes. Txn throughputs in processing various combinations of requests are obtained by analyzing a closed product-form QN model. A discrete event simulator is provided. More detailed QN modeling parameters, such as the distribution of the number of cycles in central server model - CSM affects the performance of a fork/join queueing system. This detail can be taken into account in Schwetman's hybrid simulation method, which counts remaining cycles in CSM. We propose an extension to hybrid simulation to adjust job service demands according to elapsed time, rather than counting cycles. An example where Equilibrium Point Analysis to reduce computaional cost is privided