Queueing Network Research Articles

Supervised-learning-based approximation method for multi-server queueing networks under different service disciplines with correlated interarrival and service times

ABSTRACT Developing efficient performance evaluation methods is important to design and control complex production systems effectively. We present an approximation method (SLQNA) to predict the performance measures of queueing networks composed of multi-server stations operating under different service disciplines with correlated interarrival and service times with merge, split, and batching blocks separated with infinite capacity buffers. SLQNA yields the mean, coefficient of variation, and first-lag autocorrelation of the inter-departure times and the distribution of the time spent in the block, referred as the cycle time at each block. The method generates the training data by simulating different blocks for different parameters and uses Gaussian Process Regression to predict the inter-departure time and the cycle time distribution characteristics of each block in isolation. The predictions obtained for one block are fed into the next block in the network. The cycle time distributions of the blocks are used to approximate the distribution of the total time spent in the network (total cycle time). This approach eliminates the need to generate new data and train new models for each given network. We present SLQNA as a versatile, accurate, and efficient method to evaluate the cycle time distribution and other performance measures in queueing networks.

Scaling limits for closed product-form queueing networks

We consider a general class of closed product-form queueing networks, consisting of single-server queues and infinite-server queues. Even if a network is of product-form type, performance evaluation tends to be difficult due to the potentially large state space and the dependence between the individual queues. To remedy this, we analyze the model in a Halfin–Whitt inspired scaling regime, where we jointly blow up the traffic loads of all queues and the number of customers in the network. This leads to a closed-form limiting stationary distribution, which provides intuition on the impact of the dependence between the queues on the network’s behavior. We assess the practical applicability of our results through a series of numerical experiments, which illustrate the convergence and show how the scaling parameters can be chosen to obtain accurate approximations.

On the well-posedness of deterministic queuing networks with feedback control

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 robust queueing network analyzer based on indices of dispersion

AbstractWe develop a robust queueing network analyzer algorithm to approximate the steady‐state performance of a single‐class open queueing network of single‐server queues with Markovian routing. The algorithm allows nonrenewal external arrival processes, general service‐time distributions and customer feedback. The algorithm is based on a decomposition approximation, where each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance‐time curve, called the index of dispersion for counts (IDC). The required IDC functions for the external arrival processes can be calculated from the model primitives or estimated from data. Approximations for the IDC functions of the internal flows are calculated by solving a set of linear equations. The theoretical basis is provided by heavy‐traffic limits for the flows established in our previous papers. A robust queueing technique is used to generate approximations of the mean steady‐state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm's effectiveness is supported by extensive simulation studies.

Modelling disease transmission from touchscreen user interfaces.

The extensive use of touchscreens for all manner of human–computer interactions has made them plausible instruments of touch-mediated disease transmission. To that end, we employ stochastic simulations to model human–fomite interaction with a distinct focus on touchscreen interfaces. The timings and frequency of interactions from within a closed population of infectious and susceptible individuals was modelled using a queuing network. A pseudo-reproductive number R was used to compare outcomes under various parameter conditions. We then apply the simulation to a specific real-world scenario; namely that of airport self-check-in and baggage drop. A counterintuitive result was that R decreased with increased touch rates required for touchscreen interaction. Additionally, as one of few parameters to be controlled, the rate of cleaning/disinfecting screens plays an essential role in mitigating R, though alternative technological strategies could prove more effective. The simulation model developed provides a foundation for future advances in more sophisticated fomite disease-transmission modelling.

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.

Complete resource pooling of a load-balancing policy for a network of battery swapping stations

To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a battery swapping infrastructure rather than in-vehicle charging of batteries. In this paper, we study a closed Markovian queueing network that allows for spare batteries under a dynamic arrival policy. We propose a provisioning rule for the capacity levels and show that these lead to near-optimal resource utilization, while guaranteeing good quality-of-service levels for electric vehicle users. Key in the derivations is to prove a state-space collapse result, which in turn implies that performance levels are as good as if there would have been a single station with an aggregated number of resources, thus achieving complete resource pooling.

Fork and Join Queueing Networks with Heavy Tails: Scaling Dimension and Throughput Limit

Parallel and distributed computing systems are foundational to the success of cloud computing and big data analytics. These systems process computational workflows in a way that can be mathematically modeled by a fork-and-join queueing network with blocking (FJQN/B). While engineering solutions have long been made to build and scale such systems, it is challenging to rigorously characterize their throughput performance at scale theoretically. What further complicates the study is the presence of heavy-tailed delays that have been widely documented therein. In this article, we utilize an infinite sequence of FJQN/Bs to study the throughput limit and focus on an important class of heavy-tailed service times that are regularly varying with index . The throughput is said to be scalable if the throughput limit infimum of the sequence is strictly positive as the network size grows to infinity. We introduce two novel geometric concepts—scaling dimension and extended metric dimension—and show that an infinite sequence of FJQN/Bs is throughput scalable if the extended metric dimension and only if the scaling dimension . We also show that for the cases where buffer sizes are scaling in an order of , the scalability conditions are relaxed by a factor of . The results provide new insights on the scalability of a rich class of FJQN/Bs with various structures, including tandem, lattice, hexagon, pyramid, tree, and fractals.

Transient queueing analysis for emergency hospital management

Strategic and tactical capacity planning are critical decisions faced by hospitals. While these problems have received significant attention, current queueing-based approaches do not address realistic healthcare constraints such as blocking, transient arrivals, transient capacity assignments, and surge capacities. A queueing methodology is developed to extend the analysis of these constructs. The methodology developed is generic for hospitals responding to demand surges during epidemics and pandemics such as the recent COVID-19, and in other application areas in manufacturing, supply chain management, and logistics. The medical staff and patient chairs in the emergency room, beds in the operating theater, ICU, and medical/surgical care units are used in patient treatment at a hospital. They can be considered as servers in a system, where capacity and operational policies affect performance measures such as patient throughput. The methodology develops the probabilities from which system performance measures can be estimated for a serial queueing network with blocking. Transient analysis is employed, due to the time varying nature of the patient arrival patterns. The methodology has the capability to analyze different interventions such as increasing and decreasing capacities, and ambulance diversion. In order to handle typical hospital sized problems that result in thousands of ordinary differential equations defining the system probabilities, a transient version of Kanban queueing network decomposition is developed along with procedures for dealing with the discontinuities that arise at capacity changes. Verification/validation is presented along with several scenarios that illustrate the potential application of this methodology in emergency hospital management.

On the Flow of Software Security Advisories

In this paper, we report results on a large scale measurement campaign to collect temporal information about events associated with software vulnerabilities. The data is curated so as to extract dates from each of the analyzed security advisories. The resulting time series are our object of study. From our measurements we were able to identify which role was assumed by different platforms (such as websites and forums) in the security landscape, including sources and aggregators of information about vulnerabilities. Then, we propose an analytical model to express the flow of information through security advisories across multiple platforms. The model is based on a queueing network, where each platform corresponds to a queue which adds a delay in the information propagation. Such delays, in turn, have an impact on the visibility of the information at different platforms. Leveraging the proposed model and the collected data, we assess how different system parameters, such as the delays incurred by each platform to propagate its messages, impact the overall flow of information across platforms.

On the Application of Mean Value Analysis Without the Normalization Constant in the Closed Queuing Networks

An example of closed queue network could be view when patients arrive at a doctor’s office to update their medical records, then it’s off to the nurse’s station for various measurements like weight, blood pressure, and so on. The next stop is generally to queue (i.e., wait patiently) for one of the doctors to arrive and begin the consultation and examination. Perhaps it may be necessary to have some X-rays taken, an ultrasound may be called for, and so on. After these procedures have been completed, it may be necessary to talk with the doctor once again. The final center through which the patient must pass is always the billing office. In this work, multiple-node” system in which a customer requires service at more than one node, which may be viewed as a network of nodes, and each node is a service center having storage room for queues to form and perhaps with multiple servers to handle customer requests is investigated in order to provide some insight into the performance measure analysis. Our quest is to exempt the normalization constant in the computation of performance measure in the closed queueing network. The arrival properties and Little’s law are use with the help of some existing equations and formulas in queueing network. Performance measures, such as Mean number of customers, response time, throughput, and marginal probability distribution are obtained for central server and load dependent server closed queuing networks for nodes 4 and 5, and also for k = 3 and k = 10.

Performance evaluation for Robotic Mobile Fulfillment Systems with time-varying arrivals

This paper analyzes the performance of Robotic Mobile Fulfillment Systems with a semi-open queueing network (SOQN) with time-varying arrivals. We use a Markov-modulated Poisson process to characterize the variability in the order arrival rate and offer a matrix-geometric method (MGM)-based approach to solve the SOQN. Simulations are used to validate the analytical model. We verify that assuming time-homogeneous order arrivals will underestimate order throughput time. Numerical experiments are also conducted to explore the effect of peak order arrival rates, peak order arrival durations, and average order arrival rates on system performance. The results show that peak order arrival rates and peak order arrival durations have the most significant impact on order throughput time. Moreover, we compare the order throughput time of various workstation layouts with different width-to-length ratios.

Model of series queues networks for passenger at Basra International Airport

Large networks of queue systems represent important systems in the real world such as patients in hospital, calls in call centers, shipping containers in a seaport, and passenger terminals at airports. n this study, we deal with bottlenecks in the series queues networks in the passenger terminal before entering the stage of departure and boarding, and to know the size and absorption that passengers can reach at Basra International Airport. The search was represented statistically by studying the networks of series queues to reduce the waiting time for service performance by using statistical program packages R, as it is one of the latest and most accurate methods ,as well as the lack of calculations. Through the results, it was concluded that there are no bottlenecks at the present time for the lack of travelers due to the Corona pandemic, and it is expected in the near or distant future to increase the number

Model-Predictive Control for Discrete-Time Queueing Networks With Varying Topology

In this article, we equip the conventional discrete-time queueing network with a Markovian input process which, in addition to the usual short-term stochastics, governs the mid- to long-term behavior of the links between the network nodes. This is reminiscent of the so-called Jump–Markov Systems in control theory, allowing the network topology to change over time and, thus, facilitating to model a plethora of useful applications in wireless communication, traffic, or logistics. We argue that the common back-pressure control policy is inadequate to control such network dynamics and propose a novel control policy inspired by the paradigms of Model-Predictive Control . Specifically, by defining a suitable but arbitrary prediction horizon, our policy takes into account future network states and possible control actions. This stands in clear contrast to most other policies which are myopic, i.e., only consider the immediate next state. We show numerically that such an approach can significantly improve the control performance and introduce several variants of the policy, thereby trading off performance versus computational complexity. In addition, we prove so-called throughput optimality of our policy, which guarantees stability for all network flows that can be maintained by the network topology. Interestingly, in contrast to general stability proofs in model-predictive control, our proof does not require the assumption of a terminal set, i.e., the prediction horizon is not required to be large enough as to reach a predetermined set of states with special properties. Finally, we provide several illustrating examples, one of which being a network of assembly-queues. This network, in particular, constitutes an interesting system class for which our policy exerts superiority over general backpressure policies, with the latter ones even losing their throughput optimality.

Stability and Instability of the MaxWeight Policy

Consider a switched queueing network with general routing among its queues. The MaxWeight policy assigns available service by maximizing the objective function [Formula: see text] among the different feasible service options, where [Formula: see text] denotes queue size and [Formula: see text] denotes the amount of service to be executed at queue [Formula: see text]. MaxWeight is a greedy policy that does not depend on knowledge of arrival rates and is straightforward to implement. These properties and its simple formulation suggest MaxWeight as a serious candidate for implementation in the setting of switched queueing networks; MaxWeight has been extensively studied in the context of communication networks. However, a fluid model variant of MaxWeight was previously shown not to be maximally stable. Here, we prove that MaxWeight itself is not in general maximally stable. We also prove MaxWeight is maximally stable in a much more restrictive setting, and that a weighted version of MaxWeight, where the weighting depends on the traffic intensity, is always stable.

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.

Analysing and modeling performances of a long-haul air route network

This paper deals with analyzing and modelling performances of a long-haul air route network operating as the queuing network. The network consists of the routes/tracks with flight levels serving aircraft/flights as the service channels. The main network performances are the ultimate and practical capacity of service channels, the aircraft/flight demand, delays before entering and total time of aircraft/flights spending in the network, and the related generalized costs including those of airlines, air passengers, policy makers and society. The analytical models of the particular network performances and three routing or assignment models/procedures for matching the aircraft/flight demand to capacity are developed and applied to the long-haul air route network in the North Atlantic airspace between Europe and North America.
 The results have indicated that. the network capacity has been strongly dependent on the number of routes/tracks and flight levels, i.e., service channels and their ultimate and/or practical capacity. The ultimate capacity has been mainly influenced by the ATC (Air Traffic Control) separation rules applied between aircraft/flights operating in the same directions. The practical capacity has been strongly influenced by the ultimate capacity and the average delays imposed on aircraft/flights before entering the network. The rather superior and close to optimal model/procedure for matching demand to capacity has been routing or assignment of the aircraft/flights demand in proportion to the ultimate or practical capacity of particular service channels minimizing the total generalized costs of the actors/stakeholders involved.

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.