Queueing Network Research Articles

A Study on Catastrophic Retrial Feedback Queueing Network Model with Three Nodes in Steady State

Queueing networks, which are effectively used for performance analysis of various systems, including computer, communications, transportation networks, and manufacturing, are discussed in this article. Under the catastrophic condition, we evaluate a queueing network with feedback and retrial for single server. In the third node the customer can decide whether feedback or leave the system with probabilities t, u and 1-t-u. Also using Little's formula, we are determining the likelihood of having idle customers and determining n number of customers in the system. We are deriving for the above model. The purpose of the numerical example gives the richness of our result and the feasibility of this concept.

Collaborative train timetabling and passenger flow control in oversaturated metro lines considering state-dependence

Congestion downgrades the moving speed of passengers in trains and platforms. This in turn affects congestion. That is, the moving speed of passengers interacts with congestion. It is state-dependent and obeys the fundamental diagram. This interaction makes the system unstable and can result in substantial passenger delays and heightened security risks in oversaturated metro lines. This study aims to rectify this by developing a more realistic collaborative optimization approach. Firstly, we formulate a deterministic fluid queuing network model to accurately capture the dynamic propagation of congestion in oversaturated metro lines. This model incorporates the fundamental diagram, thereby effectively considering the interaction between passenger movement speeds and congestion. A recursive algorithm is devised to solve the fluid queuing network model. The complexity of the algorithm is independent of the capacities of the stations and trains. This provides the possibility of analyzing large-scale metro networks. Based on the queuing network model, a mixed-integer nonlinear programming model aimed at minimizing the total passenger waiting time is built. To solve the model effectively, we employ an alternating direction method of multipliers framework to decompose the model into nonlinear programming and integer nonlinear programming problems, which are respectively solved by improved simultaneous perturbation stochastic approximation and adaptive large neighborhood search algorithms. Finally, a small-scale case and a real-world case with data from Chengdu metro lines are implemented to demonstrate the performance and effectiveness of the proposed approach. The experimental results provide some interesting insights. (1) Without consideration of state-dependence, the queuing model underestimates the passenger waiting time and overestimates the service levels. (2) As demand increases, excluding extreme oversaturation scenarios, the optimized results of the state-independent model progressively deteriorate compared to our state-dependent model, with the largest percentage decline being 50.23%. This is especially noticeable when the train capacity is limited. (3) The contribution ratio of passenger flow control in mitigating congestion gradually surpasses that of train timetabling with increasing demand. In the small-scale case, the former contribution ratio to optimization rises from negligible to 98.19%.

Unequal area facility layout problem considering transporters interaction– a queuing theory and machine learning approach

ABSTRACT This study presents a novel analytical framework that merges queueing theory with deep neural networks to optimize facility layout and transporter selection in manufacturing systems. It addresses critical factors such as stochastic service times of facilities, random demand, transporter capacity, speed, and transportation batch size. Three objectives are considered: minimizing material handling costs (MHC), work-in-process (WIP), and the interaction probability of transporters (IP). The latter objective focuses on reducing instances where transporters cross paths to prevent accidents or disruptions. WIP is computed using a multi-class open queueing network model, while IP is determined using a deep neural network. The model facilitates the identification of facilities and the assignment of suitable transporters, considering empty transporter travels to minimize MHC and WIP. Results from the model are compared to a simulation model for validation across various scenarios, demonstrating acceptable accuracy. Additionally, a multi-objective meta-heuristic optimization algorithm is employed to solve the model. The effectiveness of the optimization method is evaluated against other approaches, highlighting its applicability in enhancing manufacturing system performance.

Simulation Optimization of Station-Level Control of Large-Scale Passenger Flow Based on Queueing Network and Surrogate Model

Urban rail transit encounters supply–demand contradictions during peak hours, seriously affecting passenger experience. Therefore, it is necessary to explore and optimize passenger-flow control strategies for urban rail transit stations during peak hours. However, current research mostly focuses on passenger-flow control at the network level, and there is insufficient exploration of specific operational strategies at the station level. At the same time, the microscopic simulation model for passenger-flow control at the station level faces the challenge of balancing efficiency and accuracy. This paper presents a simulation optimization approach to optimize the station-level passenger-flow controlling measures, based on a queueing network and surrogate model, aiming to improve throughput, minimize congestion, and enhance passenger experience. The first stage of the method modeled the urban railway station using queueing network theory and multi-agent theory, and then built a mesoscale simulation model that was based on an urban railway station. In the second stage, a passenger flow management and control model for ingress flow was established by combining the Kriging model with a queuing network model, and the particle swarm optimization algorithm was used to solve the model. On this basis, a simulation optimization method for station passenger-flow control was established. Finally, we conducted an example analysis of Zhongguancun Station on the Beijing subway. By comparing the simulation results before and after control, as well as comparing the optimal control scheme obtained by this method with the results of other control schemes, the results showed that the simulation optimization method proposed in this paper can propose an optimal passenger-flow control scheme. By using this method, stations can significantly enhance sustainability. For example, the method not only saves human resources but also effectively avoids or reduces congestion, boosting passenger travel efficiency and safety. By minimizing wait times, these methods lower energy consumption and support the sustainable development of public transportation systems, contributing to more sustainable urban environments.

Experimental Investigation and Queuing Network (QN) Modeling of Speed-Accuracy Tradeoff (SAT) in Human Prediction of Robot’s Target Selection in Human-Robot Collaboration

Experimental Investigation and Queuing Network (QN) Modeling of Speed-Accuracy Tradeoff (SAT) in Human Prediction of Robot’s Target Selection in Human-Robot Collaboration

A Queue-SEIAR model: Revealing the transmission mechanism of epidemics in a metro line from a meso level

The COVID-19 pandemic has affected communities worldwide. The metro, an essential means of public transportation in many cities, is particularly vulnerable to the spread of the virus due to its limited space and complex passenger flow structure. As the basis of quick and effective management decision-making, it is very important but intractable to accurately and quickly capture the transmission mechanism of epidemics in the metro line. This study addresses this challenge by proposing a meso-level Queue-SEIAR model. The Queue-SEIAR model integrates a feedback queuing network model, which captures the nonlinear stochastic effect of the congestion propagation on passenger mobility dynamics in the metro line, with an extended SEIAR (Susceptible, Exposed, Infected, Asymptomatic, and Recovered) epidemic model in multiple-subgroups situations. The risk of infection within a metro line is measured using the Total Number of Newly Exposed Travelers (TNNET). The Euler’s method is used to solve the Queue-SEIAR model, with time complexity that is independent of passenger volumes and station and train capacities, making it suitable for the analysis and decision-making of large-scale metro lines. The Queue-SEIAR model is validated versus the micro-level agent-based simulation. Numerical experiments reveal some interesting findings: (1) The gap between the Queue-SEIAR model and the benchmark Macro-level Epidemic Model (MEM) in terms of TNNET will become larger with congestion; (2) From the Queue-SEIAR model, low-demand and low-risk stations may become high-risk because of the congestion propagation, while MEM does not reveal such a pattern; (3) There exists a moderate allowed entering proportion, train dwell time, and social distance to minimize the TNNET; (4) The optimal social distance increases as the train headway or travel demand increases; and (5) The epidemic prevention effectiveness of side platforms surpasses that of island platforms.

The role of energy consumption in robotic mobile fulfillment systems: Performance evaluation and operating policies with dynamic priority

The robotic mobile fulfillment system (RMFS), with wide application in warehousing and logistics, requires many robots powered by electricity, which significantly impacts energy consumption. This paper investigates the energy consumption in the RMFS under a classic e-business environment, which classifies the orders into regular orders and expedited orders. We evaluate the impact of three dynamic priority policies (the earliest deadline first policy, waiting time-dependent policy, and weighted waiting time first policy) on throughput time and energy consumption. This paper proposes multi-class semi-open queuing network models (SOQN) with dynamic priority policies to investigate energy consumption. We validate the accuracy of the analytical models by simulation models. This paper makes the following contributions: (1) In methodology, we propose new methods to solve the SOQN with dynamic priority policies. (2) In operational planning and control, we are among the earliest to investigate the impact of dynamic priority policies on order throughput time and energy consumption in an RMFS. (3) In design optimization, we propose a decision tool to optimize the robot number for realizing the required throughput time with minimal energy consumption. Our model can also decide the optimal warehouse shape to minimize energy consumption. (4) In system analysis, we estimate the energy consumption per transaction in an RMFS, providing logistics managers insights into energy saving of warehouses.

LN: A Flexible Algorithmic Framework for Layered Queueing Network Analysis

Layered queueing networks (LQNs) are an extension of ordinary queueing networks useful to model simultaneous resource possession and stochastic call graphs in distributed systems. Existing computational algorithms for LQNs have primarily focused on mean-value analysis. However, other solution paradigms, such as normalizing constant analysis and mean-field approximation, can improve the computation of LQN mean and transient performance metrics, state probabilities, and response time distributions. Motivated by this observation, we propose the first LQN meta-solver, called LN, that allows for the dynamic selection of the performance analysis paradigm to be iteratively applied to the submodels arising from layer decomposition. We report experiments where this added flexibility helps us to reduce the LQN solution errors. We also demonstrate that the meta-solver approach eases the integration of LQNs with other formalisms, such as caching models, enabling the analysis of more general classes of layered stochastic networks. Additionally, to support the accurate evaluation of the LQN submodels, we develop novel algorithms for homogeneous queueing networks consisting of an infinite server node and a set of identical queueing stations. In particular, we propose an exact method of moment algorithms, integration techniques for normalizing constants, and a fast non-iterative mean-value analysis technique.

A greedy post-processing strategy for multi-objective performance optimization of general single-server finite queueing networks

A greedy post-processing strategy for multi-objective performance optimization of general single-server finite queueing networks

An Optimized Model for Service Rates’ Control in M/M/1 Queue Networks with Server Vacations

An Optimized Model for Service Rates’ Control in M/M/1 Queue Networks with Server Vacations

Learning optimal admission control in partially observable queueing networks

Learning optimal admission control in partially observable queueing networks

Transient behaviour of time-varying tandem queueing networks

Transient behaviour of time-varying tandem queueing networks

Performance Analysis of Multi-Tote Storage and Retrieval Autonomous Mobile Robot Systems

Multi-tote storage and retrieval (MTSR) autonomous mobile robots can carry multiple product totes, store and retrieve them from different shelf rack tiers, and transport them to a workstation where the products are picked to fulfill customer orders. In each robot trip, totes retrieved during the previous trip must be stored. This leads to a mixed storage and retrieval route. We analyze this mixed storage and retrieval route problem and derive the optimal travel route for a multiblock warehouse by a layered graph algorithm, based on storage first-retrieval second and mixed storage and retrieval policies. We also propose an effective heuristic routing policy, the closest retrieval (CR) sequence policy, based on a local shortest path. Numerical results show that the CR policy leads to shorter travel times than the well-known S-shape policy, whereas the gap with the optimal mixed storage and retrieval policy in practical scenarios is small. Based on the CR policy, we model the stochastic behavior of the system using a semiopen queuing network (SOQN). This model can accurately estimate average tote throughput time and system throughput capacity as a function of the number of robots in the system. We use the SOQN and corresponding closed queuing network models to optimize the total annual cost as a function of the warehouse shape, the number of robots, and tote buffer positions on the robots for a given average tote throughput time and throughput capacity. Compared with robots that retrieve a single tote per trip, an MTSR system with at least five buffer positions can achieve lower operational costs while meeting given average tote throughput time and tote throughput capacity constraints. Funding: This work was supported by National Natural Science Foundation of China [Grant 72372088] and the Shenzhen Science and Technology Program [Grant GJHZ20220913143003006]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0397 .

A hybrid transmission model for Plasmodium vivax accounting for superinfection, immunity and the hypnozoite reservoir

Malaria is a vector-borne disease that exacts a grave toll in the Global South. The epidemiology of Plasmodium vivax, the most geographically expansive agent of human malaria, is characterised by the accrual of a reservoir of dormant parasites known as hypnozoites. Relapses, arising from hypnozoite activation events, comprise the majority of the blood-stage infection burden, with implications for the acquisition of immunity and the distribution of superinfection. Here, we construct a novel model for the transmission of P. vivax that concurrently accounts for the accrual of the hypnozoite reservoir, (blood-stage) superinfection and the acquisition of immunity. We begin by using an infinite-server queueing network model to characterise the within-host dynamics as a function of mosquito-to-human transmission intensity, extending our previous model to capture a discretised immunity level. To model transmission-blocking and antidisease immunity, we allow for geometric decay in the respective probabilities of successful human-to-mosquito transmission and symptomatic blood-stage infection as a function of this immunity level. Under a hybrid approximation—whereby probabilistic within-host distributions are cast as expected population-level proportions—we couple host and vector dynamics to recover a deterministic compartmental model in line with Ross-Macdonald theory. We then perform a steady-state analysis for this compartmental model, informed by the (analytic) distributions derived at the within-host level. To characterise transient dynamics, we derive a reduced system of integrodifferential equations, likewise informed by our within-host queueing network, allowing us to recover population-level distributions for various quantities of epidemiological interest. In capturing the interplay between hypnozoite accrual, superinfection and acquired immunity—and providing, to the best of our knowledge, the most complete population-level distributions for a range of epidemiological values—our model provides insights into important, but poorly understood, epidemiological features of P. vivax.

Singular control of (reflected) Brownian motion: a computational method suitable for queueing applications

AbstractMotivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we apply a recently developed computational method that is feasible for dimensions up to $$d=30$$ d = 30 or more. To show that nearly optimal solutions are obtainable using this method, we present computational results for a variety of examples, including queueing network examples that have appeared previously in the literature.

Confidence intervals for mean response times of a open queueing network: calibration approach

Response time is a key factor in the analysis of the different queueing network model properties. This study computes a series of response times using a data-based recurrence relation. The true average response time is determined using the sample averages from those response times. Several confidence intervals are created for the open queueing net- work model’s average response times using the calibration approach. Using a numerical simulation analysis, the accuracy of the various confidence intervals is evaluated. Journal of Statistical Research 2023, Vol 57, No.1-2, pp.69-79

Performance estimation and operating policies in a truck-based autonomous mobile robot delivery system

Last-mile delivery is a costly and time-consuming process in e-commerce operations. Piloted by several companies, autonomous mobile robots cooperating with trucks have been implemented for parcel delivery. In this system, a truck departs from the warehouse, carrying robots and parcels, and traverses several drop-off points to release robots for parcel delivery or to deliver parcels by itself. We focus on performance estimation and system configuration, considering the no-zoning policy, where all trucks serve the whole delivery area and the zoning policy, where each truck takes charge of one zone. A queuing network is constructed to estimate the parcel throughput time and a cost minimisation model is developed for the system with a required throughput time. The optimal number of drop-off points and batch size can be numerically found to minimise the order throughput time. The zoning policy is cheaper than no-zoning policy for a small number of drop-off points and a short required throughput time, and it is cheaper in a system with a large number of drop-off points. Moreover, we find that while the truck-based autonomous mobile robot delivery system typically has a larger order throughput time than a delivery system using only robots, it is much less costly.

The battery swapping service network deployment problem: Impact of driver range anxiety and impatience

The burgeoning field of electric vehicles (EVs) presents new challenges for the deployment and operation of urban battery swapping service networks (BSSNs), particularly in terms of driver behavior and dynamic demand, areas that are often overlooked in research. This paper offers a new perspective on BSSN deployment, focusing on customer churn. We develop a dynamic demand model considering driver range anxiety. Subsequently, we create a queue model to describe the battery swap process, factoring in impatient customers. We also examine the impact of customer ‘balking’ and ‘reneging’ on the battery swap process. Furthermore, we develop a queueing network algorithm framework to address this issue. A comparative analysis demonstrates the versatility of this method and its compatibility with heuristic algorithms. We propose two primary strategies to enhance service efficiency and decrease customer churn: increasing battery stocks and adding battery swapping stations (BSSs). Moreover, we investigate the application ranges of these strategies. We further observe that while delayed charging can curtail costs and balance grid loads, it can also cause considerable customer churn. Therefore, cost- and efficiency-oriented service providers should implement different strategies for the optimal deployment and operation of BSSNs.

Inter-Departure Time Correlations in PH/G/1 Queues

In non-Markovian tandem queueing networks the output process of one site, which is the input process to the next site, is not renewal. Consequently, the correlation analysis of that output processes is essential when studying such networks. A correlation analysis in the M/G/1 queue has been studied in the literature via derivation of the joint Laplace-Stieltjes transform (LST) of the sum of two consecutive inter-departure times. That LST is obtained by considering all possible cases at departure epochs. However, those epochs are expressed via dependent variables. In this paper, we first extend the analysis to the more general PH/G/1 queue, and investigate various queues, such as E2/G/1 and C2/C2/1. Then, we consider the lag-n correlation, which requires derivation of the joint LST of sum of n + 1 consecutive inter-departure times. Yet, deriving this LST by the common approach becomes impractical for n + 1 ≥ 3, as the number of all possible cases at departure epochs increases significantly. To overcome this obstacle, we derive a corresponding single-parameter LST, which expresses the sum of n + 1 consecutive inter-departure times via the (n + 1)-st departure epoch only. Consequently, the latter LST is expressed via a much fewer number of possible cases, and not less important, as a function of independent variables only, eliminating the need to derive the corresponding joint density. Considering the M/G/1 and the E2/G/1 queues, we demonstrate that the joint LST can be reconstructed directly via the corresponding single-parameter LST when n + 1 = 2. We further conjecture that the multi-parameter joint LST can be reconstructed from the corresponding single-parameter LST in more general queues and for values of n + 1 > 2. The conjecture is validated for various PH/G/1 queues and proved for n + 1 = 3 in the M/G/1 case. The new approach facilitates the calculation of lag-n correlation of the departure process from PH/G/1 queue for n + 1 ≥ 3. Our analysis illuminates the cases when using renewal approximation of the output process provides a proper approximation when studying non-Markovian stochastic networks.

Performance Evaluations of Vehicle Sharing in Closed Queueing Networks System

Performance Evaluations of Vehicle Sharing in Closed Queueing Networks System