Queueing Network Research Articles

Determination of the Optimal Number of Forklifts in the Distribution Center Using the Queuing Network Model

Determination of the Optimal Number of Forklifts in the Distribution Center Using the Queuing Network Model

On the cycle maximum of birth–death processes and networks of queues

This paper considers the cycle maximum in birth–death processes as a stepping stone to characterisation of the asymptotic behaviour of the maximum number of customers in single queues and open Kelly–Whittle networks of queues. For positive recurrent birth–death processes we show that the sequence of sample maxima is stochastically compact. For transient birth–death processes we show that the sequence of sample maxima conditioned on the maximum being finite is stochastically compact.We show that the Markov chain recording the total number of customers in a Kelly–Whittle network is a birth–death process with birth and death rates determined by the normalising constants in a suitably defined sequence of closed networks. Explicit or asymptotic expressions for these normalising constants allow asymptotic evaluation of the birth and death rates, which, in turn, allows characterisation of the cycle maximum in a single busy cycle, and convergence of the sequence of sample maxima for Kelly–Whittle networks of queues.

Scaling Limits of a Tandem Queue with Two Infinite Orbits

This paper considers a tandem queueing network with a Poisson arrival process of incoming calls, two servers, and two infinite orbits by the method of asymptotic analysis. The servers provide services for incoming calls for exponentially distributed random times. Blocked customers at each server join the orbit of that server and retry to enter the server again after an exponentially distributed time. Under the condition of low retrial rates, we prove that the joint stationary distribution of scaled numbers of calls in the orbits weakly converges to a two-variable Normal distribution.

An Evaluation of e-Health Service Performance through the Integration of 5G IoT, Fog, and Cloud Computing.

In recent years, Internet of Things (IoT) advancements have led to the development of vastly improved remote healthcare services. Scalability, high bandwidth, low latency, and low power consumption are all essential features of the applications that make these services possible. An upcoming healthcare system and wireless sensor network that can fulfil these needs is based on fifth-generation network slicing. For better resource management, organizations can implement network slicing, which partitions the physical network into distinct logical slices according to quality of service (QoS) needs. Based on the findings of this research, an IoT-fog-cloud architecture is proposed for use in e-Health services. The framework is made up of three different but interconnected systems: a cloud radio access network, a fog computing system, and a cloud computing system. A queuing network serves as a model for the proposed system. The model's constituent parts are then subjected to analysis. To assess the system's performance, we run a numerical example simulation using Java modelling tools and then analyze the results to identify the key performance parameters. The analytical formulas that were derived ensure the precision of the results. Finally, the results show that the proposed model improves eHealth services' quality of service in an efficient way by selecting the right slice compared to the traditional systems.

Comparing the Efficiency of Two Types of Yard Layout in Container Terminals

Traditional container terminals usually use a horizontal yard layout, while automated container terminals usually use a vertical yard layout. The two types of yard layout perform differently in the vehicle travel routes, the handling interface points of vehicles and yard cranes, and the yard cranes travel routes. These differences result in the different indicators between the two types of yard layout, such as yard utilization, average vehicle travel routes, average yard crane travel distance, and overall terminal efficiency etc. This paper uses an analytic method to quantify these indicators of the two types of yard layout. Based on the analysis results, the terminal efficiency is approximated by a queuing network from the overall operations. In the experiment studies, we first evaluate the indicators of the two types of yard layout, respectively. Then, we change the length and width of the yard to compare the efficiency of the two types of yard layout in various yard sizes. Finally, the overall terminal efficiency is compared. Results show that the overall efficiency is significantly affected by the service rate of yard cranes. The results in this paper may provide references for terminal yard design.

A product-form network for systems with job stealing policies

In this paper, we introduce a new product-form queueing network model where servers are always busy. This is obtained by defining a job movement policy that admits instantaneous migrations of jobs from non-empty waiting buffers to empty ones. Thus, the resulting routing scheme is statedependent. This class of networks tends to maximize the system throughput and can be used to model situations where successive refinements on jobs improve the processes quality but are not strictly required to obtain a result.

Spatial Modeling of Airport Surface Fuel Burn for Environmental Impact Analyses

The assessment of the fuel burn and emissions impact of airport surface operations is a key part of understanding the environmental impacts of aviation. These assessments are needed at two levels: the analysis of inventories (the total amount of fuel burned and emissions discharged over some period of time), and the analysis of spatial distributions (the amount of emissions experienced at a particular location within or near the airport). Although the availability of taxi times for the operations of interest is sufficient for inventory analysis, the analysis of spatial distributions requires estimates of where on the airport surface an aircraft is located as it consumes fuel. In this paper, we show how a data-driven queuing network model can be developed in order to estimate the time that an aircraft spends at different congested locations on the airport surface. These models are useful both in spatial distribution analysis and in accurately predicting taxi times in the absence of measurements (for example, for projected demand sets). We use measurements of ultrafine particles at Los Angeles International Airport to demonstrate that the proposed model can help predict the measured emissions at different monitoring sites located in the vicinity of the airport. In the process, we show how one could develop a machine learning model of the spatial distribution of airport surface emissions given the pollutant measurements, air traffic demand, and prevailing weather conditions. Finally, we develop a clustering-based method to evaluate the generalizability of our surface operations modeling framework.

Design of fork-join networks of First-In-First-Out and infinite-server queues applied to clinical chemistry laboratories

This paper considers optimal design of queueing networks in which each node consists of a single-server FIFO queue and an infinite-server queue, which is referred to as incubation queue. Upon service completion at a FIFO queue, a job splits (forks) into two parts: the first part is routed to the next node on its route, and the second part is placed in the incubation queue. Routing of the jobs of multiple types is governed by a central decision maker that decides on the routes for each job type and aims to minimize the mean turnaround time of the jobs, i.e., the time spent in the system until service completion at the FIFO queue in the last node, and at all incubation queues on the job’s route, which may be viewed as a join operation. We provide explicit results for the turnaround time when all service and inter-arrival time distributions are exponential and invoke the Queueing Network Analyzer when these distributions are general. We then develop a Simulated Annealing approach to find the optimal routing configuration. We apply our approach to determine the optimal routing configuration in a chemistry analyzer line.

Likelihood ratio-based CUSUM charts for real-time monitoring the quality of service in a network of queues

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.

Radio and Computing Resource Allocation in Co-Located Edge Computing: A Generalized Nash Equilibrium Model

Mobile Network Operators (MNO) can reduce their Capital and Operational Expenditure (CAPEX) and (OPEX) with the help of tower sharing approach by utilizing the physical infrastructure equipped by a third party tower provider to expand their network coverage. Moreover, Computing Resource Providers (CRP) are also setting up their micro-datacenters at tower stations to provide the Multi-access Edge Computing (MEC) services by cooperating with tower providers. Since both the communication and computing services contribute to the task offloading in MEC, the resource allocation has become a challenging problem. In this paper, we formulate the joint uplink, downlink, and computing resources allocation problem in which the objectives of both MNOs and CRP are to minimize their OPEX. The task offloading is modeled as a network of queues where the end-to-end latency is calculated based on the performance of the queue network. Then, the formulated problem is transformed into a Generalized Nash Equilibrium Problem (GNEP) to capture the conflicting interests in the resource allocation among MNOs and CRP. To solve the formulated GNEP efficiently, two decentralized algorithms are proposed by introducing the penalty parameters to the coupling constraints. In addition, the convergence and performance of the algorithms on different parameters are analyzed.

Nonparametric Approximate Dynamic Programming via the Kernel Method

This paper presents a novel, non-parametric approximate dynamic programming (ADP) algorithm that enjoys dimension-independent approximation and sample complexity guarantees. We obtain this algorithm by “kernelizing” a recent mathematical program for ADP (the “smoothed approximate linear program”). Loosely, our guarantees show that we can exchange the importance of choosing a good approximation architecture a priori (as required by existing approaches) with sampling effort. We also present a simple active set algorithm for solving the resulting quadratic program, and prove the correctness of this method. Via a computational study on a controlled queueing network, we show that our approach is capable of outperforming parametric linear programming approaches to ADP, as well as non-trivial, tailored heuristics for the same network, even when employing generic, polynomial kernels.

Modelling Analysis of a Four-Way Shuttle-Based Storage and Retrieval System on the Basis of Operation Strategy

In the context of sustainable development, this paper rationalises the outbound process of a four-way shuttle system with a focus on their modelling, performance evaluation and configuration using a parallel operation strategy to reduce resource waste, thus achieving sustainable development. The parallelism of the hoist and shuttle is innovatively incorporated into the four-way shuttle system, so the modelling content is divided into parallel and serial types. In the parallel operation strategy model, a separation–aggregation queueing network model is constructed, and the open-loop queueing network is innovatively solved using the maximum entropy method. In the serial operation strategy model, a semi-open-loop queuing network is constructed and solved using the geometric matrix method. By varying different parameters, the accuracy of the model is verified by Arena simulation with an error range of 10% or less, and the error of the system performance index calculation is reduced by 20% compared with the existing methods. Setting up 18 different sizes of shuttle systems provided a better performance than a single serial-operation strategy through the addition of parallel strategies, with an average reduction of 12.6% in the system response time and a minimum reduction of 1.8%. The conclusions of this paper were verified on the basis of an arithmetic case analysis.

Post-processing Improvements in Multi-objective Optimization of General Single-server Finite Queueing Networks

An alternative mathematical programming formulation is considered for a mixed-integer optimization problem in queueing networks. The sum of the blocking probabilities of a general service time, single server, and the finite, acyclic queueing network is minimized, and so are the total buffer sizes and the overall service rates. A multi-objective genetic algorithm (MOGA) and a particle swarm optimization (MOPSO) algorithm are combined to solve this difficult stochastic problem. The derived algorithm produces a set of efficient solutions for multiple objectives in the objective function. The implementation of the optimization algorithms is dependent on the generalized expansion method (GEM), a classical tool used to evaluate the performance of finite queueing networks. We carried out a set of computational experiments to attest to the efficacy and efficiency of the proposed approach. In addition, we present a comparative analysis of the solutions before and after post-processing. Insights obtained from the study of complex queue networks may assist the planning of these types of queueing networks.

Redundancy Planning for Cost Efficient Resilience to Cyber Attacks

We investigate the extent to which redundancy (including with diversity) can help mitigate the impact of cyber attacks that aim to reduce system performance. Using analytical techniques, we estimate impacts, in terms of monetary costs, of penalties from breaching Service Level Agreements (SLAs), and find optimal resource allocations to minimize the overall costs arising from attacks. Our approach combines attack impact analysis, based on performance modeling using queueing networks, with an attack model based on attack graphs. We evaluate our approach using a case study of a website, and show how resource redundancy and diversity can improve the resilience of a system by reducing the likelihood of a fully disruptive attack. We find that the cost-effectiveness of redundancy depends on the SLA terms, the probability of attack detection, the time to recover, and the cost of maintenance. In our case study, redundancy with diversity achieved a saving of up to around 50 percent in expected attack costs relative to no redundancy. The overall benefit over time depends on how the saving during attacks compares to the added maintenance costs due to redundancy.

Kullback–Leibler Divergence of an Open-Queuing Network of a Cell-Signal-Transduction Cascade

Queuing networks (QNs) are essential models in operations research, with applications in cloud computing and healthcare systems. However, few studies have analyzed the cell's biological signal transduction using QN theory. This study entailed the modeling of signal transduction as an open Jackson's QN (JQN) to theoretically determine cell signal transduction, under the assumption that the signal mediator queues in the cytoplasm, and the mediator is exchanged from one signaling molecule to another through interactions between the signaling molecules. Each signaling molecule was regarded as a network node in the JQN. The JQN Kullback-Leibler divergence (KLD) was defined using the ratio of the queuing time (λ) to the exchange time (μ), λ/μ. The mitogen-activated protein kinase (MAPK) signal-cascade model was applied, and the KLD rate per signal-transduction-period was shown to be conserved when the KLD was maximized. Our experimental study on MAPK cascade supported this conclusion. This result is similar to the entropy-rate conservation of chemical kinetics and entropy coding reported in our previous studies. Thus, JQN can be used as a novel framework to analyze signal transduction.

Tail Prediction for Heterogeneous Data Center Clusters

Service providers need to meet their service level objectives (SLOs) to ensure better client experiences. Predicting tail sojourn times of applications is an essential step to combat long tail latency. Therefore, as an attempt to further unravel the power of our prediction model, new study scenarios for heterogeneous environments will be introduced in this research by using either of two methods: white- or black-box solutions. This research presents several techniques for modeling clusters of inhomogeneous nodes. Those techniques are recognized as heterogeneous fork-join queuing networks (HFJQNs). Moreover, included in the research is a nested-event-based simulation model, borrowing help from multi-core technologies. This model adopts the multiprocessing technique to take part in its design to enable different architectural designs for all computing nodes. This novel implementation of the simulation model is believed to be the next logical step for research studies targeting heterogeneous clusters in addition to the several provided scenarios. Experimental results confirm that even with the existence of such heterogeneous conditions, the tail latency can be predicted at high-load regions with an approximated relative error of less than 15%.

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

A new framework for balancing and performance evaluation in stochastic assembly line using queueing networks

Analysing a queueing network of the emergency department with deteriorating health in post-disaster situations

Analysing a queueing network of the emergency department with deteriorating health in post-disaster situations