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Queuing networks (QNs) are widely used stochastic models for service systems include healthcare systems, transportation systems, and computer networks. While existing literature has extensively focused on modeling and optimizing resource allocation in QNs, very little research has been done on developing systematic statistical monitoring methods for QNs. This paper proposes cumulative sum (CUSUM) control charts that monitor the queuing information collected in real-time from the QN. We compare the proposed methods with existing statistical monitoring methods to demonstrate their ability to quickly detect a change in the service rate of one or more queues at the nodes in the QN. Simulation results show that the proposed CUSUM charts are more effective than existing statistical monitoring methods. The motivation for this research comes from the need to monitor the performance of a hospital emergency department (ED) with the goal of monitoring delays experienced by patients visiting the ED. A case study using the data from the ED of a large academic medical center shows that proposed methods are a promising tool for monitoring the timeliness of care provided to patients visiting the ED. [ABSTRACT FROM AUTHOR]

In this article, we address the online resource allocation problem in service queuing systems under uncertainty. In particular, the optimal control policy is derived by using the real-time data, i.e., without fully knowing information about the system state. We employ the conditional value-at-risk to achieve the minimum long-run average cost subject to the constraints on the risk of instability. Then, we can ensure the service ability of the system at a high level under such on-the-fly uncertainty. We show that the proposed model naturally leads to a minmax saddle point optimization problem. We first present an intuitive offline primal–dual learning method, which can achieve a desirable convergence rate. Then, we further improve the algorithm by learning the optimal Lagrange multiplier concerning the instantaneous system state, i.e., online primal–dual learning algorithm, to achieve the same convergence rate as the offline algorithm. Besides, we demonstrate that the proposed method outperforms classical models in providing the lower average delay under uncertainty, which means it can improve the stability and provide a better quality of service under the ambiguity of uncertainty. A real case of inpatient bed allocation for hospital operations is presented to show the performance in applications. The results show that our model can reduce the average wait with certain total available beds under uncertain arrivals. [ABSTRACT FROM AUTHOR]

Based on comprehensive consideration of stochastic factors and the system performance, we presented an integrated queuing network model (IQNM) to effectively optimize the facility layout of the multi-floor flow shop (MFFS). In this paper, the arrival interval and service times of the workstations are described by the two-moment approximation method, and an iterative algorithm is proposed for estimating the system performance, including the mean throughput, work-in-process (WIP) and sojourn time. In the design process, an optimization model with the throughput and cycle time constraint is established, while the minimize transportation cost is taken as the objective function. After several iterations between system performance and optimization objective, the facility layout problem (FLP) of the MFFS is solved, which takes the maximize throughput and minimize cycle time as the constraint condition. Finally, the effectiveness of the proposed method is verified by a series of numerical experiments. The average error of system throughput is 2.11%. And the sojourn time errors are less than 5% when SCV = 1.5. Therefore, this research can provide relevant theoretical support for the facility layout of the MFFS.

Queuing networks have been widely-used to model congestion in transportation systems. Due to their interconnected nature, delays in a queuing network can propagate as customers traverse through the network; similarly, downstream resources can be underutilized due to poor control policies. This paper considers the regulation of arrivals into a queuing network in order to maintain a desired level of occupancy (queue length) in the system. The dynamics of the queuing network is represented by a fluid-flow model, which is then used to develop a robust controller for tracking the desired queue length. The controller is based on a sliding mode control approach, with predictor-based feedback to account for propagation delays. For a single queue, we determine sufficient conditions for tracking the queue length, and bounds on the tracking error. We also present an analysis of the tracking performance for queues in tandem. We demonstrate our approach for the example of airport surface congestion control. The proposed robust control framework is based on a queuing network model of the airport, and is used to tactically manage aircraft departures in order to reduce congestion on the airport tarmac. [ABSTRACT FROM AUTHOR]