Closed Queueing Network Research Articles

Performance Evaluations of Vehicle Sharing in Closed Queueing Networks System

Performance Evaluations of Vehicle Sharing in Closed Queueing Networks System

A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System

A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System

Analyzing Malware Propagation on Wireless Sensor Networks: A New Approach Using Queueing Theory and HJ-Biplot with a SIRS Model

Most research on malware focuses mainly on its detection, without paying attention to its propagation trends. However, modeling the spread of malware is an important research problem because it allows us to predict how malware will evolve and to take steps to prevent its propagation, hence the interest in analyzing this spread from a statistical point of view. This work proposes a malware propagation prediction methodology based on multivariate statistical techniques such as HJ-Biplot in combination with closed queuing networks. Datasets generated using individual-based SIRS models are used to validate the proposed methodology, although any other model could have been chosen to test its validity. Experimental results show that the proposed model can effectively predict and classify malware and discover the influence of different model parameters on the malware propagation situation.

Blind Dynamic Resource Allocation in Closed Networks via Mirror Backpressure

We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with a finite, fixed number of supply units that circulate in the system. Demand arrives stochastically, and serving a demand unit (customer) causes a supply unit to relocate from the “origin” to the “destination” of the customer. The key challenge is to manage the distribution of supply in the network. We consider general controls including customer entry control, pricing, and assignment. Motivating applications include shared transportation platforms and scrip systems. Inspired by the mirror descent algorithm for optimization and the backpressure policy for network control, we introduce a rich family of mirror backpressure (MBP) control policies. The MBP policies are simple and practical and crucially do not need any statistical knowledge of the demand (customer) arrival rates (these rates are permitted to vary in time). Under mild conditions, we propose MBP policies that are provably near optimal. Specifically, our policies lose at most [Formula: see text] payoff per customer relative to the optimal policy that knows the demand arrival rates, where K is the number of supply units, T is the total number of customers over the time horizon, and η is the demand process’ average rate of change per customer arrival. An adaptation of MBP is found to perform well in numerical experiments based on data from NYC Cab. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Funding: Y. Kanoria was supported by the National Science Foundation’s Division of Civil, Mechanical, and Manufacturing Innovation [Grant CMMI-1653477]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4934 .

Optimisation of Buffer Allocations in Manufacturing Systems: A Study on Intra and Outbound Logistics Systems Using Finite Queueing Networks

Optimal buffer allocations can significantly improve system throughput by managing variability and disruptions in manufacturing or service operations. Organisations can minimise waiting times and bottlenecks by strategically placing buffers along the flow path, leading to a smoother and more efficient production or service delivery process. Determining the optimal size of buffers poses a challenging dilemma, as it involves balancing the cost of buffer allocation, system throughput, and waiting times at each service station. This paper presents a framework that utilises finite queueing networks for performance analysis and optimisation of topologies, specifically focusing on buffer allocations. The proposed framework incorporates a finite closed queuing network to model the intra-logistics material transfer process and a finite open queueing network to model the outbound logistics process within a manufacturing setup. The generalised expansion method (GEM) is employed to calculate network performance measures of the system, considering the blocking phenomenon. Discrete event simulation (DES) models are constructed using simulation software, integrating optimisation configurations to determine optimal buffer allocations to maximise system throughput. The findings of this study have significant implications for decision-making processes and offer opportunities to enhance the efficiency of manufacturing systems. By leveraging the proposed framework, organisations can gain valuable insights into supply chain performance, identify potential bottlenecks, and optimise buffer allocations to achieve improved operational efficiency and overall system throughput.

Fleet sizing and charger allocation in electric vehicle sharing systems

In this paper, we propose a closed queueing network model for performance analysis of electric vehicle sharing systems with a certain number of chargers in each neighborhood. Depending on the demand distribution, we devise algorithms to compute the optimal fleet size and number of chargers required to maximize profit while maintaining a certain quality of service. We show that the profit is concave with respect to the fleet size and the number of chargers at each charging point. If more chargers are installed within the city, we show that it can not only reduce the fleet size, but it also improves the availability of vehicles at all the points within a city. We further show through simulation that two slow chargers may outperform one fast charger when the variance of charging time becomes relatively large in comparison to the mean charging time.

Performance Estimation and Design Optimization of a Congested Automated Container Terminal

Container terminal capacity, as an important indicator of container terminal competitiveness, has become a primary concern of port managers, whereas container flows, which are supported by quay cranes, yard cranes, and automated guided vehicles, have a substantial influence on container terminal capacity. Container flows are analyzed in this article to estimate the performance of an automated container terminal considering traffic congestion, unbalanced task assignment, container batch arrival, and different berth and yard layouts. The operating system is formulated as a closed-queuing network with four stations. Theoretical analysis and the solution method are adopted to determine system capacity. The resource allocation and system design, specifically the number of vehicles, berth and yard layouts, and task assignment strategy, are optimized. Numerical experiments are conducted to provide management insights into port capacity planning, resource optimization, and layout design. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The construction of an automated container terminal (ACT) requires a sizable investment. Analyzing the performance of the container terminal with different configurations in the planning stage, which is before the construction of ports, is very important. Thus, planners can select better resource configurations. Generally, simulation is an intuitive way to estimate performance. However, formulating and running the simulation model with different configurations is time consuming. An analytic model for estimating the performance of an ACT is developed to reduce computational time in this article.

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.

Fleet sizing of trucks for an inter-facility material handling system using closed queueing networks

Material handling systems (MHS) are integral to logistics functions by providing various supports such as handling, moving, and storing materials in manufacturing and service organisations. This study considers determining the optimal size of a homogeneous fleet of trucks to be outsourced (or subcontracted) from a third-party logistics provider to be used daily to cyclically transport different types of raw materials from designated storage yards to intermediate buffer locations to be fed as inputs to a production facility for processing. Within this context, the problem is modelled as a closed queueing network (CQN) combined with mixed-integer nonlinear programming (MINLP) to determine the optimal fleet size. This study proposes an analytical method based on sequential quadratic programming (SQP) methodology coupled with a mean value analysis (MVA) algorithm to solve this NP-Hard problem. Furthermore, a discrete event simulation (DES) model is developed to validate the optimisation of non-dominant solutions. The proposed analytical approach, along with the simulation, are implemented in a real case study of a steel manufacturing setup. Analytical model results are validated using the simulation results, which are proved to be very accurate, with deviations ranges within ±7%.

Facilitating load-dependent queueing analysis through factorization

We propose novel exact and approximate solutions for mean-value and probabilistic analysis of closed queueing networks with limited load-dependent nodes. The main result is the derivation of an exact correction factor between the equilibrium solution of a load-dependent model and the one of a related model with fixed-rate queueing stations. This enables the reuse of state-of-the-art methods for fixed-rate stations in the computation of performance metrics for load-dependent systems. As many such algorithms are available, our findings significantly increase the range of techniques available to study load-dependence. We further interpret the correction factor as a load-dependent normalizing constant and propose two novel integral forms, in the real and in the complex domains, which can be used for its efficient computation. These integral forms are also shown to be applicable to evaluate more general limited load-dependent systems, as we illustrate in a sojourn time distribution analysis problem. Lastly, the proposed algorithms are numerically examined through thousands of experiments, which reveal accuracy in the range 1%–6% mean absolute relative error.

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.

Dimensioning On-Demand Vehicle Sharing Systems

We consider the problem of optimal fleet sizing in a vehicle sharing system. Vehicles are available for short-term rental and are accessible from multiple locations. A vehicle rented at one location can be returned to any other location. The size of the fleet must account not only for the nominal load and for the randomness in demand and rental duration but also for the randomness in the number of vehicles that are available at each location because of vehicle roaming (vehicles not returning to the same location from which they were picked up). We model the dynamics of the system using a closed queueing network and obtain explicit and closed form lower and upper bounds on the optimal number of vehicles (the minimum number of vehicles needed to meet a target service level). Specifically, we show that starting with any pair of lower and upper bounds, we can always obtain another pair of lower and upper bounds with gaps between the lower and upper bounds that are independent of demand and bounded by a function that depends only on the prescribed service level. We show that the generated bounds are asymptotically exact under several regimes. We use features of the bounds to construct a simple and closed form approximation that we show to be always within the generated lower and upper bounds and is exact under the asymptotic regimes considered. Extensive numerical experiments show that the approximate and exact values are nearly indistinguishable for a wide range of parameter values. The approximation is highly interpretable with buffer capacity expressed in terms of three explicit terms that can be interpreted as follows: (1) standard buffer capacity that is protection against randomness in demand and rental times, (2) buffer capacity that is protection against vehicle roaming, and (3) a correction term. Our analysis reveals important differences between the optimal sizing of standard queueing systems (where servers always return to the same queue upon service completion) and that of systems where servers, upon service completion, randomly join any one of the queues in the system. We show that the additional capacity needed to buffer against vehicle roaming can be substantial even in systems with vanishingly small demand. This paper was accepted by Baris Ata, stochastic models and simulation.

On the Throughput Optimization in Large-Scale Batch-Processing Systems

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

Stochastic modeling of multiline orders in integrated storage‐order picking system

AbstractDue to demanding service levels in e‐commerce order fulfillment, modeling and analysis of integrated storage and order picking processes in warehouses deserve special attention. The upstream storage system can have a significant impact on the performance of the downstream order picking process. With a particular focus on multiline e‐commerce orders, we develop an analytical modeling framework for integrated analysis of upstream (shuttle‐based storage and retrieval system) and downstream (pick system) networks. To capture the consolidation delays in fulfilling multiline orders, the downstream pick system is modeled with a closed queuing network that includes synchronization nodes. The configuration of the synchronization station is adapted to model the variety of order profiles handled at the pick station. For the downstream closed queuing network, we propose a decomposition‐based solution methodology that results in good solution accuracy. The resulting semi‐open queuing network (SOQN) of the integrated system is analyzed using the matrix‐geometric method (MGM). To improve the accuracy of analytical estimates of the measures, we propose a hybrid simulation/analytical framework, where the performance measures of complex subnetworks are obtained from simulation. We also develop a detailed simulation model of the physical system for validating the analytical and hybrid estimates of the performance measures. The results from experiments indicate that the hybrid simulation/analytical approach reduces the error in the throughput time estimates to 3% from 18% obtained from the analytical model. Then, we investigate the effect of the upstream network configuration (such as the number of storage aisles) and the downstream network configuration (such as the mixed vs. dedicated picking, CONWIP control for orders, order batching) on the order throughput times. Our analysis provides a threshold on the maximum numbers of allowable orders (CONWIP control) and number of aisles beyond which the improvement in average throughput time of the integrated system is marginal. Numerical experiments with high‐order arrivals also highlight that mixed picking in the downstream network can result in significant throughput time reduction in comparison to dedicated picking.

A priori performance assessment of line-less mobile assembly systems

Present assembly systems are often based on rigid, line-based approaches and are hindered in their reconfiguration capability. Line-less Mobile Assembly Systems (LMAS) are a novel approach for assembly organization. They improve flexibility through mobile resources, permitting spatiotemporal freedom in scheduling and resource assignment. This paper presents a method for a priori assessment of LMAS during the early stages of the assembly system design process. The method applies a modified, extended mean value analysis to a closed queuing network representation of LMAS to estimate performance. The method is validated model analysis and comparison on two use cases indicating plausible model behavior.

A Dynamic Model for Managing Volunteer Engagement

Non-profit organizations that provide food, shelter, and other services to people in need, rely on volunteers to deliver their services. Unlike paid labor, non-profit organizations have less control over unpaid volunteers’ schedules, efforts, and reliability. However, these organizations can invest in volunteer engagement activities to ensure a steady and adequate supply of volunteer labor. We study a key operational question of how a non-profit organization can manage its volunteer workforce capacity to ensure consistent provision of services. In particular, we formulate a multiclass closed queueing network model to characterize the optimal engagement activities for the non-profit organization to minimize the costs of enhancing volunteer engagement and reducing abandonments, while maximizing productive work done by volunteers. Because this problem appears intractable, we formulate an approximating Browning control problem in the heavy traffic limit and study the dynamic control of that system. Our solution is a nested threshold policy with explicit congestion thresholds that indicate when the non-profit should optimally pursue various types of volunteer engagement activities. A numerical example calibrated using data from a large food bank shows that our dynamic policy for deploying engagement activities can reduce the food bank's total annual cost of its volunteer operations by 31%, while lowering its throughput by only 0.01%. This improvement in performance does not require any additional resources -- it only requires that the food bank strategically deploy its engagement activities based on the number of volunteers signed up to work volunteer shifts.

Optimal design of intermodal mobility networks under uncertainty: Connecting micromobility with mobility-on-demand transit

Mobility-on-Demand Transit (MoDT) is a suitable solution for linking packed urban centers to low-demand suburban areas. Meanwhile, micromobility services, including dockless bikesharing and electric scooters, are growing exponentially worldwide, providing a low-cost, low-emission travel mode for short home-based trips. We propose an intermodal network in which travelers use micromobility for the first-/last-mile connections to MoDT. The optimal design of the intermodal network is formulated as a two-stage stochastic program with a revenue-maximization objective. The first stage solves the near-optimal transfer hub locations, and the second stage considers the integrated operations of the micromobility and MoDT vehicle fleet. This work contributes to the MoD literature by addressing how to coordinate the intermodal transfers and improve the utilization of vehicles with uncertain demand. The movements of these vehicles are modeled as an interconnected closed queueing network with time lags. A new starter-follower model captures the rearranged ride-pooling behavior at these selected transfer hubs. We implement this network design method to evaluate the benefit of combining a bikesharing and a MoDT network in New York City. This paper provides a systematic method for designing intermodal mobility networks, laying the foundation for multimodal mobility applications.

Performance analysis of batching decisions in waveless order release environments for e‐commerce stock‐to‐picker order fulfillment

AbstractWarehouse automation is increasingly adopted to manage throughput fluctuations in e‐commerce order fulfillment. This work develops queuing network models and solution methodologies for performance analysis of a stock‐to‐picker system that connects an upstream automated storage system to a downstream pick station. We focus on the pick station process, quantifying the throughput differences between a pick station that employs a static versus dynamic batching strategy. We consider a waveless order release environment where the item totes are requested from the storage system only when an order arrives. We capture throughput performance in this environment for single as well as multi‐line orders with/without item commonality by developing closed‐queuing network models. The consolidation of multiple product‐lines for a multi‐line order is modeled using fork–join synchronization stations within the closed queuing network. For analyzing such queuing networks, we develop a network‐decomposition based solution methodology. We validate the models using a simulation model of the upstream storage and downstream order‐picking system. We find that in waveless order release environment, dynamic batching always outperforms static batching in terms of system throughput. However, for single‐line orders, the percentage gain in the throughput (by implementing dynamic batching) decreases for smaller item tote inter‐arrival times. For multi‐line orders, dynamic batching increases the system throughput by 37–43%. We also analyze the effect of batch size on the throughput performance. The results indicate that the system throughput increases with an increase in the batch size under both batching policies. But, the marginal benefit reduces as we increase the batch size.

On the Throughput Optimization in Large-scale Batch-processing Systems

We analyse a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function. In practice, throughput optimization relies on numerical searches for the optimal batch size, a process that can take up to multiple days in existing commercial systems. In this paper, we model the system in terms of a closed queueing network; a standard Markovian analysis yields the optimal throughput in ωn4 time. Our main contribution is a mean-field model of the system for the regime where the system size is large. We show that the mean-field model has a unique, globally attractive stationary point which can be found in closed form and which characterizes the asymptotic throughput of the system as a function of the batch size. Using this expression we find the asymptotically optimal throughput in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

Stochastic modeling of parallel process flows in intra-logistics systems: Applications in container terminals and compact storage systems

Many intra-logistics systems, such as automated container terminals, distribution warehouses, and cross-docks, observe parallel process flows, which involve simultaneous (parallel) operations of independent resources while processing a job. When independent resources work simultaneously to process a common job, the effective service requirement of the job is difficult to estimate. For modeling simplicity, researchers tend to assume sequential operations of the resources. In this paper, we propose an efficient modeling approach for parallel process flows using two-phase servers. We develop a closed queuing network model to estimate system performance measures. Existing solution methods can evaluate the performance of closed queuing networks that consist of two-phase servers with exponential service times only. To solve closed queuing networks with general two-phase servers, we propose new solution methods: an approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods from numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation dis-aggregation approach consistently performs best. We illustrate the proposed modeling approach for two intra-logistic systems: a container terminal with automated guided vehicles and a shuttle-based compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and at maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in an underestimation of the throughput capacity up to 9%.