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Dynamic capacity allocation control for resource sharing networks (RSN) is studied when the networks are in heavy traffic. The goal is to minimize an ergodic cost with a linear holding cost function. Our main result shows that the optimal cost associated with an associated Brownian control problem provides a lower bound for the asymptotic ergodic cost in the RSN for any sequence of control policies. A similar result for an infinite horizon discounted cost has been previously shown for general resource sharing networks in Budhiraja and Conroy (in Modeling, stochastic control, optimization, and applications, 2019) and for general 'unitary networks' in Budhiraja and Ghosh (Ann Appl Probab 16:1962–2006, 2006). The study of an ergodic cost criterion requires different ideas as bounds on ergodic costs only yield an estimate on the controls in a time-averaged sense which makes the time-rescaling ideas of Budhiraja and Conroy (in Modeling, stochastic control, optimization, and applications, 2019) and Budhiraja and Ghosh (Ann Appl Probab 16:1962–2006, 2006) hard to implement. Proofs rely on working with a weaker topology on the space of controlled processes that is more amenable to an analysis for the ergodic cost. As a corollary of the main result, we show that the explicit policies constructed in Budhiraja and Johnson (Math Oper Res 45:797–832, 2020; Ann Appl Probab 34:851–916, 2024) for general RSN are asymptotically optimal for the ergodic cost when the underlying cost per unit time has certain monotonicity properties. [ABSTRACT FROM AUTHOR]

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 network models have been extensively used for performance evaluation in many modern manufacturing and communication systems. The phenomenon of feedback reflects many practical situations, e.g. reworking in the production systems. However, existing research on open queuing network with feedback mainly concentrates on the models with infinite buffers or the models with finite buffers but exponentially distributed inter-arrival and service times. Research on open queuing networks with finite buffers, feedback and general inter-arrival and service times has not been reported. In this paper, a Rate Iterative Method embedded with the Generalised Expansion Method, is proposed for modelling this type of queuing network. System performance measures include the mean throughput, work-in-process and sojourn time all calculated by the proposed method. The accuracy and the efficiency of the proposed method are tested by comparing the results with other methods or simulation results from the experiments. Finally, a case study of a practical production system used in the manufacturing industry is studied and illustrates the applications of the proposed method. The results in this paper can be used as a basis for system design analysis and resource planning. [ABSTRACT FROM PUBLISHER]

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]

Blocking makes the analytical modelling of open queuing networks with finite buffers intractable because the product-form solutions are unavailable. In this paper, about mould manufacturing, a four-stage flexible flow shop with match processing constraint is first modelled as an open queuing network with finite buffers. According to the characteristics of the matching node, the inter-arrival time distributions of parts arriving at the nodes are assumed to be exponential or general. Next, based on approximation of queuing theory, the Decomposition of State Space Method and the Generalized Expansion Method are developed for system performance evaluation. Then, experiments to assess the accuracy of the proposed methods are reported by comparing the analytical results with simulations. Finally, a case of a real-life production system of mould manufacturing is studied to show the application of the proposed methods. The results of experiments reveal that the proposed methods are feasible and effective for system performance evaluation and they can even solve large-size practical problems in a reasonable time. The results in this paper can provide a basis for system design or resource planning, to solve buffer allocation problems and capacity configuration problems. [ABSTRACT FROM AUTHOR]

Queuing networks have been used with partial success for analytical modelling of manufacturing systems. In this paper, we consider a tandem system with high traffic variability caused by downtime events in the first queue. We propose improved approximation for departure variability in order to predict the waiting duration at the bottleneck queue located last in the line. We demonstrate that existing methods do not properly approximate such systems and provide some reasons and insights. Thus, a new decomposition method which employs the variability function principles is proposed. We differentiate between two components of the departure variability in multi-class systems: the ‘within-class effect’ – the variability caused by the class’ own inter-arrival and service time distributions – and the ‘between-class effect’ – the variability caused by interactions with other classes. Our analysis shows that the first effect can be approximated by existing multi-class decomposition methods, while the second effect requires a new development. Our proposed approximation for between-class effect is based on simulating a proper sub-system. The method enables modelling different policies of downtimes (e.g. FCFS, Priority). Numerical experiments show relative errors much smaller vs. existing procedures. [ABSTRACT FROM PUBLISHER]

We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers. • A queuing network model with feedback that allows service to empty queues. • Prove existence and uniqueness of solutions when the controller is Lipschitz. • Show how dynamic flow propagation can be incorporated into the model. [ABSTRACT FROM AUTHOR]

Age of Information (AoI) is a critical metric for several Internet of Things (IoT) applications, where sensors keep track of the environment by sending updates that need to be as fresh as possible. The development of edge computing solutions has moved the monitoring process closer to the sensor, reducing the communication delays, but the processing time of the edge node needs to be taken into account. Furthermore, a reliable system design in terms of freshness requires the knowledge of the full distribution of the Peak AoI (PAoI), from which the probability of occurrence of rare, but extremely damaging events can be obtained. In this work, we model the communication and computation delay of such a system as two First Come First Serve (FCFS) queues in tandem, analytically deriving the full distribution of the PAoI for the M/M/1 – M/D/1 and the M/M/1 – M/M/1 tandems, which can represent a wide variety of realistic scenarios. [ABSTRACT FROM AUTHOR]

In the previous works we presented a study for modeling and simulation of vehicular traffic systems based on queuing networks. Specifically, in paper (Pasini and Bianchini, 2019), we studied the urban network located in North Siena, in the city of Siena (Italy), in its actual layout, after the Municipality had introduced some changes for vehicular flow management. This system is based on two roundabouts and a crossroad, as shown in Figure 1. In this work, we are going to conclude our previous study, comparing the actual vehicular flow and the flow derived from an alternative system, foreseen by the PRG of the Municipality of Siena which is composed of three roundabouts and which has not been implemented yet.

In the previous works we presented a study for modeling and simulation of vehicular traffic systems based on queuing networks. Specifically, in paper (Pasini and Bianchini, 2019), we studied the urban network located in North Siena, in the city of Siena (Italy), in its actual layout, after the Municipality had introduced some changes for vehicular flow management. This system is based on two roundabouts and a crossroad, as shown in Figure 1. In this work, we are going to conclude our previous study, comparing the actual vehicular flow and the flow derived from an alternative system, foreseen by the PRG of the Municipality of Siena which is composed of three roundabouts and which has not been implemented yet. [ABSTRACT FROM AUTHOR]

A real-world topological network consists of multiple entrances along its source nodes. Routing appropriate percentages of pedestrians from these entrances to the particular available routes with relevant arrival rates will improve the network's performance. This paper presents a framework for finding the optimal arrival rates of pedestrians from all available entrances and routes to downstream nodes maximising the network's throughput. The calculation of the arrival rates and movement directions is based on M/G/C/C analytical and simulation models and the network flow model and considers the real distances of the entrances along the source nodes. The framework was tested on the Tuanku Syed Putra Hall, Universiti Sains Malaysia, Malaysia. Extensive analyses of the performances of its available nodes especially on the achievable optimal throughputs were documented and discussed. Quantitative results show that the hall's throughput is optimised when pedestrians' arrival rates to all the available entrances and their movement directions are controlled within certain ranges. [ABSTRACT FROM AUTHOR]

Self-adaptation has emerged as a primary concern in the context of modern software systems, due to the high dynamicity of the environments where they operate, which implies the need for such systems to properly face significant degrees of uncertainty. To this aim, much work has been done, mainly by coupling autonomic managers to the managed subsystem which perceives and affects the environment through its sensors and actuators, respectively. Such coupling often results into MAPE-K feedback loop(s), i.e. a Knowledge (K)-based architectural model that divides the adaptation process into four activities, namely Monitor (M), Analyze (A), Plan (P) and Execute (E). Performance modeling notations, analysis methods and tools, have been exploited and coupled to other kinds of techniques (e.g. control theory, machine learning) for modeling and assessing the performance of autonomic managers, possibly aimed at supporting the identification of more convenient architectural alternatives. Since moving in such a big arena is not trivial and it is easy to be overwhelmed, in this literature survey, we focus on a particular performance modeling paradigm, namely Queuing Networks, with the aim of clarifying the state-of-art in exploiting such a notation to model and assess performance of Self-Adaptive Software Systems. We conclude by bringing out some research opportunities that may be worth exploring in the near future. [ABSTRACT FROM AUTHOR]

We study the flows induced by different rework loops in serial manufacturing systems with inspection stations. Average values of these flows and queuing network formulas are used for performance evaluation and optimisation of production lines. An application is presented for solving jointly the problems of inventory control and inspection station allocation in a CONWIP production line. [ABSTRACT FROM AUTHOR]

In this paper, a simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system (AVS/RS) is presented. The aim of this study is to develop mathematical functions for the rack configuration of an AVS/RS that reflects the relationship between the outputs (responses) and the input variables (factors) of the system under various scenarios. In the regression model, we consider five outputs: the average cycle time of storage and retrieval transactions, the average waiting time for vehicle transactions, the average waiting time of vehicles (transactions) for the lift, the average utilisation of vehicles and the average utilisation of the lifts. The input variables are the number of tiers, aisles and bays that determine the size of the warehouse. Thirty regression models are developed for six warehouse scenarios. The simulation model of the system is developed using ARENA 12.0 commercial software and the statistical analyses are completed using MINITAB statistical software. Two different approaches are used to fit the regression functions-stepwise regression and the best subsets. After obtaining the regression functions, we optimise them using the LINGO software. We apply the approach to a company that uses AVS/RS in France. [ABSTRACT FROM AUTHOR]

In represented article the questions of estimate of accuracy of an average integral characteristics of random process in the course of imitation modeling is considered. For the purposes of analytical treatment of initial stage of modeling a conditionally nonstationary Gaussian process is analyzed as stationary Gaussian process with boundary prehistory. A model of approximant autocorrelation function is recommended. Analytical expression for variance and mathematical expectation of average integral estimation are obtained. Statistical estimation efficiency criterion, the probability of belonging to correct parameter interval is introduced. Dependences of closeness in estimation statistics clearing interval at transient behavior are researched for various types of processes.

This work fits into the context of our studies on traffic simulation for computer and telecommunication networks [1–5]. The technique that we use is based on complex queuing network models that allow us to simulate the functioning of network devices, and the traffic flows between them. In a previous work [2] we defined a library of objects for the modeling of the computer network. This library also models the network traffic induced by the execution of web applications run in a distributed fashion on various network devices. In this work we describe the changes applied to the service procedures of some library objects, and we develop a specific study for the evaluation of the execution times of three types of applications: 1. Navigation 2. Download Manager 3. Mobile Agents

This work is part of the research activities developed in our department on the construction of vehicle traffic system simulators (TASK Quart. 22 (2) 135 [1], 20 (1) 9 [2], 17 (3) 155 [3], 20 (3) 273 [5], 14 (4) 405 [6], 9 (4) 397 [7], Simulation Modelling Practice and Theory 17 (4) 625 [8]). The modeling of the traffic system is implemented through the use of queuing networks. In this case we analyze, through a simulation, the impact on traffic flows of a structural change that the Municipal Administration has implemented on the urban road system. The study refers to some works published by us previously about the procedures applied by us to build a simulator. In this case we have developed software allowing us to analyze the data tracked by the system simulations to display it graphically. This procedure enables us to clearly compare the traffic system behavior in its new configuration with the traffic system behavior in the previous configuration.

Networks-on-chip (NoCs) have become the standard for interconnect solutions in industrial designs ranging from client CPUs to many-core chip-multiprocessors. Since NoCs play a vital role in system performance and power consumption, pre-silicon evaluation environments include cycle-accurate NoC simulators. Long simulations increase the execution time of evaluation frameworks, which are already notoriously slow, and prohibit design-space exploration. Existing analytical NoC models, which assume fair arbitration, cannot replace these simulations since industrial NoCs typically employ priority schedulers and multiple priority classes. To address this limitation, we propose a systematic approach to construct priority-aware analytical performance models using micro-architecture specifications and input traffic. Our approach decomposes the given NoC into individual queues with modified service time to enable accurate and scalable latency computations. Specifically, we introduce novel transformations along with an algorithm that iteratively applies these transformations to decompose the queuing system. Experimental evaluations using real architectures and applications show high accuracy of 97% and up to 2.5× speedup in full-system simulation. [ABSTRACT FROM AUTHOR]

We study a new multiple-lift compact automated parking system, which is a new technology with a circular structure using carousel equipped with the shuttles for the horizontal movement and multiple lifts equipped with the platforms for the vertical movement. This paper investigates dedicated and random shuttles operating policies. We divided the carousel into areas based on the number of lifts. We propose a dedicated shuttle operating policy under which each area shuttles can only serve one dedicated lift. A random shuttle operating policy under which shuttles can serve any lift. We get expected throughput time models for the two shuttle operating policies under the same system physical configurations based on queuing network models. We compare the analytical models with simulation models, and the results show that the proposed models provide accurate estimates. A numerical experiment is conducted to illustrate the trade-offs between dedicated shuttle and random shuttle operating policies. The results show that the retrieval time in random shuttle operating policy is larger than the retrieval time in dedicated shuttle operating policy. We also get the optimal system structure, including the number of the lifts. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick's law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski's approach. [ABSTRACT FROM AUTHOR]

In this paper we present a queuing network approach to the problem of routing and rebalancing a fleet of self-driving vehicles providing on-demand mobility within a capacitated road network. We refer to such systems as autonomous mobility-on-demand (AMoD) systems. We first cast an AMoD system into a closed, multi-class Baskett–Chandy–Muntz–Palacios (BCMP) queuing network model capable of capturing the passenger arrival process, traffic, the state-of-charge of electric vehicles, and the availability of vehicles at the stations. Second, we propose a scalable method for the synthesis of routing and charging policies, with performance guarantees in the limit of large fleet sizes. Third, we explore the applicability of our theoretical results on a case study of Manhattan. Collectively, this paper provides a unifying framework for the analysis and control of AMoD systems, which provides a large set of modeling options (e.g. the inclusion of road capacities and charging constraints), and subsumes earlier Jackson and network flow models. [ABSTRACT FROM AUTHOR]

This letter presents a solution to the problem of universal representation of graphs exemplifying communication network topologies with the help of neural networks. The proposed approach is based on message-passing neural networks. The approach enables us to represent topologies and operational aspects of networks. The usefulness of the solution is illustrated with a case study of delay prediction in queuing networks. This shows that performance evaluation can be provided without having to apply complex modeling. In consequence, the proposed solution makes it possible to effectively apply the methods elaborated in the field of machine learning in communications. [ABSTRACT FROM AUTHOR]

This paper outlines a study carried out to answer the questions asked by an architect of the Siena Municipality Office during a conference at our Department on the management of traffic flows through the Siena North city road system. The purpose of the study was to ascertain if changes in the road system introduced and included in the new City Development Plan would resolve the current traffic congestion issues. In order to answer this question, we used the technology for the development of vehicle traffic system simulators which was introduced during our previous projects (TASK Quart. 14 (4) 405, 17 (3) 155, 20 (1) 9, 20 (3) 273).

Robotic compact storage and retrieval systems (RCSRS) have seen many implementations over the last few years. In such a system, the inventory items are stored in bins, organized in a grid. In each cell of the grid, a certain number of bins are stored on top of each other. Robots with transport and lifting capabilities move on the grid roof to transport bins between manual workstations and storage stacks. We estimate performance and evaluate storage policies of RCSRS, considering both dedicated and shared storage policies coupled with random and zoned storage stacks. Semi-open queuing networks (SOQNs) are built to estimate the system performance, which can handle both immediate and delayed reshuffling processes. We approximate the models by reduced SOQNs with two load-dependent service nodes and use the matrix-geometric method to solve them. Both simulations and a real case are used to validate the analytical models. Assuming a given number of stored products, our models can be used to optimize not only the length-to-width ratio of the system but also the stack height, depending on the storage strategy used. For a given inventory and optimal system configuration, we demonstrate that the dedicated storage policy outperforms the shared storage policy when the objective is to minimize dual command throughput time. However, from a cost perspective, with a maximum dual command throughput time as a constraint, we show that shared storage substantially outperforms dedicated storage. The annualized costs of dedicated storage are up to twice as large as those of shared storage, as a result of the larger number of storage positions required by dedicated storage and the relatively lower filling degree of storage stacks. The online appendix is available at https://doi.org/10.1287/trsc.2017.0786. [ABSTRACT FROM AUTHOR]

Consideration was given to the model of a queuing network with resource queuing systems—the multi-server systems with losses where servicing of the accepted customer occupies random volumes of resources with the given distribution function depending on the customer class and the type of required servicing. Customer servicing in a node can be interrupted by a signal arriving at an exponential time from the start of servicing, and during the time of customer sojourn in the network it may be interrupted more than once. Analytical formulas for calculation of the fundamental probability-time model characteristics—including the joint distribution functions of the number of customers in the nodes and the volumes of resources occupied by them—were proposed on the assumption of the Poisson flows incoming to the nodes and arbitrary servicing. [ABSTRACT FROM AUTHOR]

The aim of this work is to define a procedure for the modelling of a computer network for the simulation of the network traffic induced by the execution of web applications. The work consists in describing the objects of a library defined for modelling both the hardware and the software of the system. These are specific objects with an architecture based on complex queuing service structures. The objects of the library are used to both build the computer network model and describe the operation of a web application executed on the network in a distributed fashion.

Wireless Sensor Networks (WSN) utilisation is characterised by its dense deployment in order to fulfil the monitoring tasks. This density of communication leads to interference and congestion. In a previous work, a schedule scheme dubbed REFIACC (Reliable, Efficient, Fair and Interference Aware Congestion Control), that takes into account interferences and different links capacities in order to avoid packet loss due congestion, was proposed. REFIACC idea was validated using comparative simulations. In this study, REFIACC scheduling scheme was modelled using Markov chains. The modelling concerns queue length evolution and global system throughput. Different hypothesis details for queue length monitoring, according to application motivation, have led to many variants of models. The evaluation of the model using MATLAB has shown its effectiveness concerning packet reception ratio and reception overhead. [ABSTRACT FROM AUTHOR]

In a previous work [Pasini L and Sabatini S 2016 TASK Quart. 20 (1) 9], we described a technique that allows a specific system of urban traffic to be associated to a description file system, called Model.dat. This file contains a list of data objects that are defined in the library [Pasini L and Feliziani S 2013 TASK Quart. 17 (3) 155] and that form the architecture model of a vehicular traffic system. This model turns out to be a network of queuing systems. In this work, we illustrate how we adapted the old procedure to study a new urban traffic system. Moreover, through a new tracking procedure, we illustrate how we developed a graphic simulation able to reinterpret the data from the simulation of the queuing networks model, in order to make it easier to check the effectiveness of the simulator and to have a graphical way to analyze the data.

In a previous work [1], we have defined an object library that allows the building of architectural models of urban traffic systems. In this work we illustrate the procedures that enable us to produce a system simulator starting from the architectural model of an urban vehicular traffic system.