Queueing Network Model Research Articles

Analysis of Saturation in the Emergency Department: A Data-Driven Queuing Model Using Machine Learning.

Emergency department is a key component of the health system where the management of crowding situations is crucial to the well-being of patients. This study proposes a new machine learning methodology and a queuing network model to measure and optimize crowding through a congestion indicator, which indicates a real-time level saturation.

Average delay estimation for one queueing network model with resource reservation

Introduction: An urgent task of today is to develop new analysis methods for complex information systems that now demand higher standards for maintaining data integrity. One of the important quality characteristics of such systems is average transaction time. However, currently there are almost no mathematical models and speed estimation tools for such systems. Purpose: To develop and analyze a distributed information system model based on queueing networks. Results: A type of information systems that demand higher standards for maintaining data integrity has been described, the corresponding assumptions for such systems are given. A convenient way to represent such systems as transaction paths dependency graphs has been proposed, with each path being represented as one tandem queueing system. The calculation of their functional characteristics have been provided. This method of representation has made it possible to simplify the analysis of complex systems, which resulted in obtaining closed-form expressions for temporal estimation of the system type in question. In addition, two mechanisms of decomposition of the proposed graph are considered with the subsequent calculation of the lower bound for average transaction time. The accuracy of both approaches is analyzed with simulation modeling methods. Practical relevance: The proposed models allow estimating speed limits of an information system during the design phase.

Centralized and Decentralized Signal Control with Short-Term Origin-Destination Demand for Network Traffic

We develop and assess centralized and decentralized signal control systems with short-term origin-destination (OD) demands as inputs. Considering each intersection turning movement as a virtual link, we assign traffic demand to paths based on minimal instantaneous travel time. Then, the optimal control is formulated using a G/G/n/FIFO open queueing network model (QNM). We also solve the issue of optimal control using a three-step naïve method for the centralized system with the new inputs. Because the optimization of large-scale network traffic signals can involve sizeable numbers of decision variables and nonlinear constraints, making it a nondeterministic polynomial time (NP) complete problem, we further decompose the centralized system into a decentralized system where the network is divided into subnetworks. Each subnetwork has a dedicated agent that optimizes signals within it. Furthermore, traffic demand for the entire network is decomposed into demands for subnetworks via path decomposition index (PDI). The proposed control systems are applied to test scenarios constructed using different demand profiles in grid networks. We also investigate the impact of network decomposition strategy on signal control system performance. Results show that network decomposition with smaller subnetworks results in less computational time (CT) but increased average travel time (ATT) and total travel delay (TTD).

Calibrating nonstationary queueing network models

Calibrating nonstationary queueing network models

Stability and Optimization of Speculative Queueing Networks

We provide a queueing-theoretic framework for job replication schemes based on the principle “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">replicate a job as soon as the system detects it as a straggler</i> ”. This is called job <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">speculation</i> . Recent works have analyzed replication on arrival, which we refer to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">replication</i> . Replication is motivated by its implementation in Google’s BigTable. However, systems such as Apache Spark and Hadoop MapReduce implement speculative job execution. The performance and optimization of speculative job execution is not well understood. To this end, we propose a queueing network model for load balancing where each server can speculate on the execution time of a job. Specifically, each job is initially assigned to a single server by a frontend dispatcher. Then, when its execution begins, the server sets a timeout. If the job completes before the timeout, it leaves the network, otherwise the job is terminated and relaunched or resumed at another server where it will complete. We provide a necessary and sufficient condition for the stability of speculative queueing networks with heterogeneous servers, general job sizes and scheduling disciplines. We find that speculation can increase the stability region of the network when compared with standard load balancing models and replication schemes. We provide general conditions under which timeouts increase the size of the stability region and derive a formula for the optimal speculation time, i.e., the timeout that minimizes the load induced through speculation. We compare speculation with redundant- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and redundant-to-idle-queue- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> rules under an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S\&amp; X$ </tex-math></inline-formula> model. For light loaded systems, redundancy schemes provide better response times. However, for moderate to heavy loadings, redundancy schemes can lose capacity and have markedly worse response times when compared with the proposed speculative scheme.

Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

We construct novel exact and approximate solutions for meanvalue analysis and probabilistic evaluation of closed queueing network models with limited load-dependent (LLD) nodes. In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For single-class models, we provide an explicit formula for the normalizing constant that applies to models with arbitrary LLD functions, whilst retaining constant complexity with respect to the total population size. From this result, we then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between a load-independent solution and a limited load-dependent one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks.

A fair dynamic content store-based congestion control strategy for named data networking

In this paper, the congestion control for named data networking (NDN) is studied. A novel dynamic content store-based congestion control strategy is proposed on account of the characteristic of in-network cache in NDN. A queuing network model is constructed to judge whether congestion occurs. If the network has the tendency of congestion or the congestion happened, the buffer of the output queue is dynamically expanded by borrowing NDN content store (CS), and the forwarding rates of data packets and corresponding interest packets are reduced so as to prevent or alleviate network congestion. In order to reflect fairness, the CS to be borrowed by the data output queue in the port is calculated in terms of the data output queue length and its weight. The simulation results based on ndnSIM show that the given scheme improves the bottleneck link utilization and maintains a low packet loss rate and average flow completion time.

Analysis of Production systems with Variable Transfer Batch Size

In this paper, we propose a new queueing networks decomposition method for the analysis of production systems with variable transfer batch sizes. In many production and manufacturing systems, jobs arrive in batches and they are moved between stations also in batches. Batching decisions have a considerable impact on costs and lead times. Most of the literature assumes that the batch size remains constant throughout the process. However, in many real-life situations, different transfer batch sizes are used between stations due to practicality or different setup times. We consider queueing network models that incorporate this feature. Since exact analysis is possible for only a limited class of queuing networks, the decomposition methodology is used to obtain approximate results.

A Queuing Network Model for Solving Facility Layout Problem in Multifloor Flow Shop

A Queuing Network Model for Solving Facility Layout Problem in Multifloor Flow Shop

Design and Performance Estimation of Mixed-Robotic Fulfillment System

E-commerce retailers face the challenge to assemble a large number of time-critical picking orders. Common parts-to-picker autonomous intelligent warehouses such as automated vehicle storage and retrieval system and robotic mobile fulfillment system are often a little ill-suited for these prerequisites. A mixed-robotic fulfillment system is a hybrid robot picking system based on multi-device collaboration. It is a fusion innovation of traditional automated vehicle storage and retrieval system and robotic mobile fulfillment system. This paper comprehensively considers the characteristics of the system and customer demand, through the construction of a queuing network model to evaluate the performance of the system. A series of problems such as order service time, throughput capacity, and vehicle quantity configuration are analyzed experimentally. The validity of the model is verified by a simulation model.

A comparative study of different pull control strategies in multi-product manufacturing systems using discrete event simulation

Pull production control strategies coordinate manufacturing operations based on actual demand. Up to now, relevant publications mostly examine manufacturing systems that produce a single type of a product. In this research, we examine the CONWIP, Base Stock, and CONWIP/Kanban Hybrid pull strategies in multi-product manufacturing systems. In a multi-product manufacturing system, several types of products are manufactured by utilizing the same resources. We develop queueing network models of multi-stage, multi-product manufacturing systems operating under the three aforementioned pull control strategies. Simulation models of the alternative production systems are implemented using an open-source software. A comparative evaluation of CONWIP, Base Stock and CONWIP/Kanban Hybrid in multi-product manufacturing is carried out in a series of simulation experiments with varying demand arrival rates, setup times and control parameters. The control strategies are compared based on average wait time of backordered demand, average finished products inventories, and average length of backorders queues. The Base Stock strategy excels when the manufacturing system is subjected to high demand arrival rates. The CONWIP strategy produced consistently the highest level of finished goods inventories. The CONWIP/Kanban Hybrid strategy is significantly affected by the workload that is imposed on the system.

User learning can affect software system's response time

A session-based software system provides various services to its end users through graphical user interfaces. A novice user of a service's user interface takes more think time—the average time to comprehend the content and its layout on the interface—in comparison to expert users. The think time gradually decreases as she repeatedly comprehends the same interface over time. This decrease in think time is the user learning phenomenon. Owing to this learning behavior, the proportion of users—at various learning levels for different services—changes dynamically leading to a difference in the workload. Traditionally though, workload specifications (required for system performance evaluation) never accounted for user learning behavior. They generally assumed a global mean think time, instead. In this work, we first report an experimental study that demonstrates the impact of user learning of the graphical user interfaces of session-based systems. We measure the performance data of a real system while it is getting used by synthetic users (who are) at various learning levels. Statistical tests on our measured data reveal that different human learning curves, combined with different amounts of users arriving the system with various learning levels for different services, produce different system performance. Next, we explain a queueing network (QN) performance model called CogQN that accounts for user learning. It is a multi-class QN model where each service and its learning level constitute a class of users for the service. We present the concept of learning-level dependent, class-switching probabilities to model the probabilistic transition of learning levels of users for different services. This novel concept enables us to avoid the exponential explosion of classes that would otherwise be suffered by traditional class-switching theory, had it been used in this work. We solve the model using discrete-event simulation and validate it against the empirical data. Our CogQN model captures the effect of user learning on overall mean response times across different learning conditions within 10% absolute error in comparison to empirical data.

From aircraft tracking data to network delay model: A data-driven approach considering en-route congestion

En-route congestion causes delays in air traffic networks and will become more prominent as air traffic demand will continue to increase yet airspace volume cannot grow. However, most existing studies on flight delay modeling do not consider en-route congestion explicitly. In this study, we propose a new flight delay model, Multi-layer Air Traffic Network Delay (MATND) model, to capture the impact of en-route congestion on flight delays over an air traffic network. This model is developed by a data-driven approach, taking aircraft tracking data and flight schedules as inputs to characterize a national air traffic network, as well as a system-level model approach, modeling the delay process based on queueing theory. The two approaches combined make the network delay model a close representation of reality and easy-to-implement for what-if scenario analysis. The proposed MATND model includes 1) a data-driven method to learn a network composed of airports, en-route congestion points, and air corridors from aircraft tracking data, 2) a stochastic and dynamic queuing network model to calculate flight delays and track their propagation at both airports and in en-route congestion areas, in which the delays are computed via a space–time decomposition method. Using one month of historical aircraft tracking data over China’s air traffic network, MATND is tested and shows to give an accurate quantification of delays of the national air traffic network. “What-if” scenario analyses are conducted to demonstrate how the proposed model can be used for the evaluation of air traffic network improvement strategies, where the manipulation of reality at such a scale is impossible. Results show that MATND is computationally efficient, well suited for evaluating the impact of policy alternatives on system-wide delay at a macroscopic level.

Mobility service design via joint optimization of transit networks and demand-responsive services

This paper proposes a modeling framework to design an integrated mobility service system that is composed of a local demand-responsive transportation (DRT) component and a fixed-route transit network component. The region is partitioned into disjoint local zones, and a trip is characterized into an intra- or inter-zonal one based on whether its origin and destination belong to the same zone. The transit network provides backbone line-haul service to inter-zonal trips, while the DRT system targets intra-zonal trips as well as the first-mile and last-mile legs of inter-zonal trips. The system components can be broadly defined, and this paper considers, as examples, conventional non-shared taxi or ride-sharing for the DRT service, and regular bus, bus rapid transit (BRT), or metro for the backbone network. For quantitative analysis of the DRT services, new aspatial queuing network models are developed to capture various DRT operations for serving trips with randomly distributed origins and destinations (i.e., intra-zonal trips) and those with origins or destinations concentrated at a set of fixed transit stations (i.e., first- or last-mile trip legs) at the same time. Each queuing model is integrated with the transit network design model, through proper service region partition, to derive closed-form formulas for the agency and passenger costs. Then, we formulate constrained non-linear programs that simultaneously optimize the zone partition, the fleet size and repositioning operation for the local DRT service, as well as the spacing and headway of a grid transit network. We apply the proposed models to a variety of transit technologies and application scenarios, so as to demonstrate applicability of the models, and to show promising performance of the proposed systems.

Effects of Non-Speech Auditory Cues on Control Transition Behaviors in Semi-Automated Vehicles: Empirical Study, Modeling, and Validation

ABSTRACT In semi-automated vehicles, non-speech sounds have been prevalently used as auditory displays for control transitions since these sounds convey urgency well. However, there are no standards of specifications for warning sounds so that diverse non-speech sounds are being employed. To shed light on this, the effects of different non-speech auditory warnings on driver performance were investigated and quantified through the experimental study and human performance modeling approaches. Twenty-four young drivers drove in the driving simulator and experienced both handover and takeover transitions between manual and automated modes while performing a secondary task. The reaction times for handover and takeover, mental workload, and subjective responses were reported. Overall, a traditional warning sound with many repetitions and an indicator sound with decreasing polarity outperformed and were preferred. Additionally, a mathematical model, using the Queuing Network-Model Human Processor (QN-MHP) framework, was applied to quantify the effects of auditory warnings’ acoustic characteristics on drivers’ reaction times in response to takeover request displays. The acoustic characteristics, including the fundamental frequency, the number of repetitions, and the range of dominant frequencies were utilized in modeling. The model was able to explain 99.7% of the experimental data with a root mean square error (RMSE) of 0.148. The present study can contribute to establishing standards and design guidelines for takeover request displays in semi-automated vehicles.

Modelling and analysis for multi-deep compact robotic mobile fulfilment system

With high efficiency and good scalability, Robotic Mobile Fulfilment Systems (RMFS) are increasingly applied in various warehouses, especially the e-commerce warehouses with rigid order completion time. RMFS requires less workers and provide more punctual service for customers. The existing literature on RMFS is based on single-deep non-compact layout. As land supply is limited and expensive in urban area, it’s essential to consider compact storage in RMFS. This paper is the first to model and evaluate the multi-deep compact RMFS. We develop a semi-open queueing network (SOQN) model to characterise the multi-deep compact RMFS and solve it by Approximate Mean Value Analysis (AMVA). The obtained approximate analytic solutions of system throughput, robot utilisation, and queue length were verified and assessed through simulations. The numerical experiments investigated the effects of different configuration of the lane depth, number of picking aisles, arrangement of picking stations and the number of robots on performance. Our research can provide useful guidelines for warehouse planners and managers for designing and operating multi-deep compact RMFS.

Likelihood-Free Parameter Estimation for Dynamic Queueing Networks: Case Study of Passenger Flow in an International Airport Terminal

Abstract Dynamic queueing networks (DQN) model queueing systems where demand varies strongly with time, such as airport terminals. With rapidly rising global air passenger traffic placing increasing pressure on airport terminals, efficient allocation of resources is more important than ever. Parameter inference and quantification of uncertainty are key challenges for developing decision support tools. The DQN likelihood function is, in general, intractable and current approaches to simulation make likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), infeasible since simulating from these models is computationally expensive. By leveraging a recent advance in computationally efficient queueing simulation, we develop the first parameter inference approach for DQNs. We demonstrate our approach with data of passenger flows in a real airport terminal, and we show that our model accurately recreates the behaviour of the system and is useful for decision support. Special care must be taken in developing the distance for ABC since any useful output must vary with time. We use maximum mean discrepancy, a metric on probability measures, as the distance function for ABC. Prediction intervals of performance measures for decision support tools are easily constructed using draws from posterior samples, which we demonstrate with a scenario of a delayed flight.

Quadric Lyapunov Algorithm for Stochastic Networks Optimization with Q-learning Perspective

In this article, we investigate stochastic networks optimization using Quadric Lyapunov Algorithm (QLA) with Q-learning perspective. We proposed firstly a model of stochastic queueing networks with power constraints. QLA is then proposed aiming at minimizing an expression containing Lyapunov drift. Based on the analysed similarity between QLA and Q-learning, we show the possibility and feasibility of Q-learning. Simulation of a simple queue network model is carried out, and results using both QLA and Q-learning are compared.

GIS aided sustainable urban road management with a unifying queueing and neural network model

With the tide of electrifying urban transportation systems by introducing electric vehicles, the differences between fuel vehicles and electric vehicles in driving styles and strategies to achieve eco-driving have become a burden for efficient operations of urban transportation systems. Most of the previous energy management strategies have sought to achieve system optimisation at a single-vehicle or multi-vehicles level, and failed to consider the vehicle-to-vehicle and vehicle-to-infrastructure effects in a global optimisation manner. Furthermore, as a typical human-in-the-loop cyber–physical system, the mobility behaviours of road users undoubtedly play a vital role in the cooperative and green operations of urban transportation systems. Yet little research has dedicated to develop means to incentivise energy-saving behaviours in transportation systems. Hence, in this paper, we propose a unifying queueing and neural network model to calculate the time and energy efficient course of actions and routes for different types of road users within an urban road network in a real time manner. The lower-level queueing model captures the interactive dynamics of road users and solves the optimal flow ratio at each intersection while the upper-level neural network model further customises desired routes for different types of road users. In addition, an incentive mechanism is proposed to encourage road users to follow the optimal actions via publishing various types of reward-gaining tasks. A case study in a designated area of Beijing shows that the use of the bi-level optimisation algorithm can reduce the average travel time by approximately 20% and decrease the energy consumption by 10% in comparison with the realistic trip data.

Modeling and analysis for an automated container terminal considering battery management

With the development of information technology, automation and intelligence techniques have gradually taken place of the manpower in container terminals. The automation of container terminals can improve the operation efficiency and decrease the labor cost, while the construction of this kind of container terminals always requires a large investment. Thus, it is very important to analyze the performance of the container terminal in the planning stage. In such a system, battery management can seriously affect system performance. This paper develops a nested semi-open queueing network model for estimating the performance of an automated container terminal with consideration of battery management. Since the model is difficult to solve, we employ an approximation approach. We first reduce the network into a semi-open queueing network with two load-dependent service nodes. The matrix-geometric method is applied to solve the reduced semi-open queuing networks and evaluate system performance. Based on the approximation solution, we further optimize resource allocation and layout design of the system, specifically, the optimal number of AGVs, the length-to-width ratio of the yard, optimal task assignment strategy, and battery recovery strategy. Extensive numerical experiments are conducted: (i) we validate the performance of models by comparing them with simulation models and the results show that the proposed analytical models perform very well; (ii) we also conduct numerical experiments for system design optimization and some design insights are concluded; (iii) we investigate which strategy is better by comparing annual cost and the results show that the battery swapping strategy performs better than the plug-in charging strategy unless the price of a spare battery is very high.