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This study applied a closed BCMP queueing network to a real-world model, examining the limitations of the theoretical solution and the possibility of replacing theoretical values with those from parallel simulation. Parallel computing was applied to mean value analysis (MVA). We first obtained computational and theoretical values by varying the number of nodes from 33 to 300 and customers from 250 to 1500 in a system with three customer classes. The computation time increased proportionally with the number of nodes but exponentially with the number of customers, reaching 146,798.86 seconds for 33 nodes, 3 customer classes, and 1500 customers. We then considered a system with more customer classes; due to the greater computational burden, we proposed addressing this problem with simulation. By using a large-scale computing environment (a supercomputer), it was possible to obtain the theoretical solutions for up to three customer classes and verify the simulation accuracy. The parallel simulations' performance-evaluation indices, such as the average number of people in the system, converged to the theoretical values within an acceptable error range after 100,000 simulation hours for systems with four or more customer classes. These results demonstrate that the proposed parallel simulation approach can serve as an accurate and computationally efficient alternative to theoretical solutions for large-scale closed BCMP queueing networks. [ABSTRACT FROM AUTHOR]

We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper (Braverman et al. in the BAR approach for multi-class queueing networks with SBP service policies, 2023), we are interested in two problems; when this Markov process inherits the same Markov structure under the Palm distributions, and how the state changes at counting instants of the point processes can be handled to derive stationary equations when there are simultaneous counts and each of them influences the state changes. We affirmatively answer the first problem, and propose a framework for resolving the second problem, which is applicable to a general stationary process, which is not needed to be Markov. We also discuss how those results can be applied in deriving BAR's for the diffusion approximation of queueing models in heavy traffic. In particular, as their new application, the heavy traffic limit of the stationary distribution is derived for a single-server queue with a finite waiting room. [ABSTRACT FROM AUTHOR]

Motivated 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 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. [ABSTRACT FROM AUTHOR]

We investigate the equilibrium strategies for customers arriving at overtaking-free queueing networks and receiving partial information about the system's state. In an overtaking-free network, customers cannot be overtaken by others arriving after them. We assume that customer arrivals follow a Poisson process and that service times at any queue are independent and exponentially distributed. Upon arrival, the received partial information is the total number of customers already in the network; however, the distribution of these among the queues is left unknown. Adding rewards for being served and costs for waiting, we analyze the economic behavior of this system, looking for equilibrium threshold strategies. The overtaking-free characteristic allows for coupling of its dynamics with those of corresponding closed Jackson networks, for which an algorithm to compute the expected sojourn times is known. We exploit this feature to compute the profit function and prove the existence of equilibrium threshold strategies. We also illustrate the results by analyzing and comparing two simple network structures. [ABSTRACT FROM AUTHOR]

We develop an efficient reinforcement learning algorithm that learns the optimal admission control policy in a partially observable queueing network. Specifically, only the arrival and departure times from the network are observable, optimality refers to the average holding/rejection cost in infinite horizon, and efficiency is with respect to regret performance. While reinforcement learning in partially-observable Markov Decision Processes (MDP) is prohibitively expensive in general, we show that the regret at time T induced by our algorithm is O ~ T log (1 / ρ) where ρ ∈ (0 , 1) is connected to the mixing time of the underlying MDP. In contrast with existing regret bounds, ours does not depend on the diameter (D) of the underlying MDP, which in most queueing systems is at least exponential in S, i.e., the maximal number of jobs in the network. Instead, the role of the diameter is played by the log (1 / ρ) term, which may depend on S but we find that such dependence is "minimal". In the case of acyclic or hyperstable queueing networks, we prove that log (1 / ρ) = O (S) , which overall provides a regret bound of the order of O ~ TS . In the general case, numerical simulations support the claim that the term log (1 / ρ) remains extremely small compared to the diameter. The novelty of our approach is to leverage Norton's theorem for queueing networks and an efficient reinforcement learning algorithm for MDPs with the structure of birth-and-death processes. [ABSTRACT FROM AUTHOR]

This paper analyzes preemptive priority inventory retrial queueing system with a single vacation, working breakdown, repair, and closedown. We assume that an arrival follows the Marked Markovian arrival process and that the server will provide them with phase-type services. The (s, S) policy to replenish the items and the replenishing duration follow an exponential distribution. In this paper, we consider two types of customers: high-priority(HP) customers and low-priority(LP) customers. Arriving HP customers should get the service if the server is idle and has a positive inventory level; otherwise, they should wait in front of the service station. Arriving LP customers get service only if there is a positive inventory level and there are no high-priority customers in the system; otherwise, go for the finite capacity size of the orbit. After the completion of service, if no one is present in the high-priority queue and orbit, the server will close down the system and then go on a single vacation. The server is idle when the vacation period ends. When the server breaks down, it only serves the present customer and operates in slow mode while it is being repaired. The number of high-priority customers in the system, the number of low-priority customers in the orbit, the inventory level, and server status may all be determined in a steady state. Numerous key performance indicators are defined, and a cost analysis is obtained. To make our mathematical concept clearer, a few numerical examples are provided. [ABSTRACT FROM AUTHOR]

A multi-server queueing system with synchronous differentiated working vacation policy, Bernoulli schedule vacation interruption, and customer impatience (balking and reneging) is studied. The system consists of c servers and a finite capacity N, where customers arrive according to a Poisson process and are served in the chronological order of their arrival. When the system becomes empty, servers wait for a random duration before entering a type-1 working vacation, during which service is provided at a reduced rate. If customers are present in the system at the moment of service achievement during this period, the vacation is interrupted. With a certain probability, servers return to the regular busy period; otherwise, they continue the working vacation. Upon completion of the working vacation, if the system is still empty, servers can take another working vacation of shorter duration, named type-2 working vacation; otherwise, they switch to the regular busy period. Customer impatience is considered during both the normal busy period and working vacations. A recursive analysis method is used to find the steady-state probabilities of the system. Then, some important performance measures are obtained. Furthermore, an optimal operational policy for the model is developed to minimize the total expected cost. The Grey Wolf Optimization (GWO) meta-heuristic approach is employed to determine the optimal service rates for both working vacations and normal busy periods. Finally, several numerical examples are provided to validate and support the theoretical findings. [ABSTRACT FROM AUTHOR]

Several real-life problems are comprised of finite single-server acyclic queueing networks. The performance optimization of these queueing networks has been the subject of several studies. The present study extends the minimization of the total buffer area and overall service rates in the network simultaneously with the maximization of throughput. It is well known that these three objectives are conflicting. This fact leads to a multi-objective approach that the literature in the area has already addressed. Nevertheless, this study aims to demonstrate that there are algorithms with low computational costs that can produce solutions more efficiently than those obtained previously. Furthermore, the provided solutions can enhance throughput by solving a stochastic knapsack problem. The greedy procedure utilizes a technique of redistributing buffers between the queues, ensuring that the overall capacity is less than or equal to the previous overall capacity; thus, one objective is improved (the throughput) without compromising the other objective (total buffer allocation). Several computational experiments attest to the quality of this proposition. In addition, we provide a comparison with previously proposed solutions. [ABSTRACT FROM AUTHOR]

In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/M a , b /c. [ABSTRACT FROM AUTHOR]

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 strive for a steady and adequate supply of volunteer labor. The paper, "A Dynamic Model for Managing Volunteer Engagement", models the volunteer management process. The paper derives a dynamic control policy that judiciously uses the non-profit's resources for volunteer engagement activities depending on explicit congestion thresholds, thereby lowering the overall cost of the non-profit operation. Nonprofit organizations that provide food, shelter, and other services to people in need, rely on volunteers to deliver their services. Unlike paid labor, nonprofit 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 nonprofit organization can manage its volunteer workforce capacity to ensure consistent provision of services. In particular, we formulate a multiclass queueing network model to characterize the optimal engagement activities for the nonprofit organization to minimize the costs of enhancing volunteer engagement, while maximizing productive work done by volunteers. Because this problem appears intractable, we formulate an approximating Brownian 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 nonprofit 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 significantly reduce the food bank's total annual cost of its volunteer operations while still maintaining almost the same level of social impact. 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. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2021.0419. [ABSTRACT FROM AUTHOR]

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 O(KT+1K+ηK) 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. [ABSTRACT FROM AUTHOR]

Efficient performance evaluation methods are needed to design and control production systems. We propose a method to analyse single-server open queueing network models of manufacturing systems composed of delay, batching, merge and split blocks with correlated interarrival and service times. Our method (SLQNA) is based on using a supervised learning approach to determine the mean, the coefficient of variation, and the first-lag autocorrelation of the inter-departure time process as functions of the mean, coefficient of variation and first-lag autocorrelations of the interarrival and service times for each block, and then using the predicted inter-departure time process as the input to the next block in the network. The training data for the supervised learning algorithm is obtained by simulating the systems for a wide range of parameters. Gaussian Process Regression is used as a supervised learning algorithm. The algorithm is trained once for each block. SLQNA does not require generating additional training data for each unique network. The results are compared with simulation and also with the approximations that are based on Markov Arrival Process modelling, robust queueing, and G/G/1 approximations. Our results show that SLQNA is flexible, computationally efficient, and significantly more accurate and faster compared to the other methods. [ABSTRACT FROM AUTHOR]

In this article, a single-server Markovian queueing model with balking is closely considered. Balking refers to a particular behavior of an impatient customer. Upon arrival, if the queue is too long, a customer may join the queue or leave the system without getting served. If he decides not to join the queue and leaves the system without getting served, this phenomenon is called as balking. In this article, balking probability is treated as a function rather than a constant, which depends on the number of customers present in the system. The emphasis of this article will mainly be placed on maximum likelihood and Bayesian estimation of traffic intensity ( ρ), average size of system ( L s ), and average size of queue ( L q ). In addition, a simulation study has also been performed to support our findings. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion approximation of queueing networks has been studied extensively. In the existing results related to this topic, the Hurst parameter of multidimensional fractional Brownian motion is only a constant H (0 < H < 1). However, just as pointed out by many scholars and practitioners, various Hurst parameters may be more appropriate. On the other hand, as a multivariate extension of fractional Brownian motion, operator fractional Brownian motion has operator self-similarity, and the dependence structure across the components of it is determined by the Hurst matrix. Moreover, it has also many potential applications in queueing theory. Inspired by these facts, we consider a queueing network with ON/OFF sources, and show that the workload process can be approximated by a reflected operator fractional Brownian motion under a heavy traffic condition. With this fact, it is important to consider stationarity. However, except for some special cases, there is no literature related to this topic. In our work, we construct an explicit stationary process associated with a two-dimensional reflected operator fractional Brownian motion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This research paper investigates the dynamic behaviour of a heterogeneous three-server queuing model with multiple vacation. The model also accounts for the possibility that a disaster could occur during busy periods or on vacation, in which case the restoration process would begin immediately. The time-dependent probabilities of system size are presented in the work with explicit equations computed in terms of modified Bessel functions, employing generating functions. To support the theoretical conclusions, numerical examples are given. [ABSTRACT FROM AUTHOR]

We consider a single server queueing model with three service types, each with three phases, where customers arrive according to a Poisson process and the service time of each customer follows a Hyper-Erlang distribution. This study aims to analyze the impact of interruptions, such as breakdowns, repairs, and single working vacations, on the performance of the queueing system. The standby server activates whenever the main server experiences a breakdown. Using the matrix geometric method, we examine the steady-state probability vector of the model. Our results demonstrate the impact of these interruptions on system performance measures and provide a cost analysis. Finally, we present numerical examples to illustrate the practical applications of our findings in an image compression system. [ABSTRACT FROM AUTHOR]

The Asynchronous Transfer Mode (ATM) is an efficient technology for call relays, and it transmits information from multiple services including data, video, or voice. This information is conveyed at ATM multiplexers in small fixed-size packets called cells. The acceptable cell loss probability at ATM multiplexers is about 10 − 12 . Important Sampling (IS) is an efficient method for estimating tiny probabilities that cannot be achieved by traditional Monte Carlo (MC) methods. This research presents a novel approach for evaluating the tail probability in the MMPP/D/1 queue system utilizing importance sampling simulation in the ATM network. To generate more rare events, a virtual queue is implemented in the dequeue process by decreasing the processing rate in the queue. In this way, the tail probability can be estimated on a real-time network. [ABSTRACT FROM AUTHOR]

This article studied a queueing-inventory system with batch demands, randomized order policy, and multiple vacations. Customers arrive in this system according to a Poisson process and take away batch items after a service time. The system sends a replenishment order and starts multiple vacations simultaneously once the on-hand inventory level drops to zero. The replenishment is based on a random order size policy. Customers arriving during this period are assumed to be lost. Under the assumption that all the underlying random variables are exponential, the stationary joint probability is obtained in product form. Based on the stationary distribution, the expected sojourn time of a permitted entering customer is derived in recursive form. Several numerical examples are processed to analyze the effect of variant parameters on the performance measures. The numerical results show that the expected total cost function is a convex function with respect to the maximum allowable inventory. The influence of various parameters on the optimal value is also displayed visually. [ABSTRACT FROM AUTHOR]

Material handling systems (MHSs) are an integral part of logistics functions in manufacturing and service organizations. Material handling equipment (MHE) is considered the pivotal actor of any given MHS. Decisions ranging from the strategic level, such as selecting the proper MHE, capacity, and ownership (in-house or outsourcing) to operational level decisions such as resource allocation, scheduling, and routing of MHEs, are critical to the efficiency of an MHS. Industry practitioners use various methods and tools to evaluate these MHSs to find the best policies for their operations. This study identifies past works related to the performance evaluation and optimisation of MHSs using queueing network models. Moreover, this study provides a comprehensive analysis of identified research questions. The study methodology adopts a systematic literature review, bibliometric, and content analysis techniques proposed in similar research studies. This study provides material logistics scholars and practitioners with a thorough understanding of queueing networks as a modelling tool for analysing MHS applications in various domains. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we consider a joint sequencing and scheduling appointments problem with stochastic service times and no-shows in multi-stage service systems. The objective is to minimise the total expected weighted costs of customers' waiting times and service providers' idle times over multiple stages. For the problem, we first formulate it as a stochastic program and exploit the sample average approximation approach to reformulate it as a mixed-integer program in further. Then we transform the stochastic program into a two-stage optimisation problem and develop a standard Benders decomposition algorithm. To overcome the long running time of Benders decomposition, we simplify the master problem in the algorithm and propose a Benders decomposition-based algorithm to find a near-optimal solution. Finally, we conduct a series of numerical experiments to illustrate the efficiency of our proposed algorithm, examine the impact of the number of stages, stochastic service times and no-shows on the optimal job allowances and performance indicators (i.e. waiting times and idle times) and investigate two easy-to-implement sequence rules. The computational results show that both our proposed Benders decomposition-based algorithm and easy-to-implement sequence rules perform well. [ABSTRACT FROM AUTHOR]

• A chat service with actively involved customers and repeating interactions is studied. • The capacity of parallel chats and the server's response effort are derived. • A queueing game for a dual-channel system of chat service and call center is analyzed. • Customer bounded rationality is considered. Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we examine a buffer with active management that rejects packets basing on the buffer occupancy. Specifically, we derive several metrics characterizing how effectively the algorithm can prevent the queue of packets from becoming too long and how well it assists in flushing the buffer quickly when necessary. First, we compute the probability that the size of the queue is kept below a predefined level L. Second, we calculate the distribution of the amount of time needed to cross level L, the buffer overflow probability, and the average time to buffer overflow. Third, we derive the distribution of the amount of time required to flush the buffer and its average value. A general modeling framework is used in derivations, with a general service time distribution, general rejection function, and a powerful model of the arrival process. The obtained formulas enable, among other things, the solving of many design problems, e.g., those connected with the design of wireless sensor nodes using the N-policy. Several numerical results are provided, including examples of design problems and other calculations. [ABSTRACT FROM AUTHOR]

In this article, a quadratic programming problem is considered to identify all link flows in an arterial network when there are unmeasured link flows. A graphical method is provided to determine the minimum number of measurements and sensor locations required to obtain a fully observable model. It is shown that this method is also valid for the augmented graph with turn ratio measurements. If the minimum measurements required are met, a fully determined network can be obtained. If there is not enough measurement, a bound on the magnitude of the resulting inaccuracy in terms of vehicle kilometers traveled (VKT) can be calculated by the proposed linear programming method. The model is that of a queueing network; the parameters describe network geometry, saturation flow rates, turning ratios, timing plan and link flows. Three case studies are conducted to validate this approach. The first two cases are to calculate all missing flows by using a few numbers of measurements and minimum number of measurements required, respectively. Upper and lower bounds in terms of VKT are also calculated for these cases. Third case is to obtain a fully determined network with the minimum number of flow measurements when turn ratio sensors are included. Real measurements are collected from a network in Mugla including 55 links and 16 intersections. Vissim simulator is used to analyze the accuracy of the link flow calculations obtained from the proposed method. The results show that the proposed programming method can calculate the missing flows with a high accuracy and short computation time. [ABSTRACT FROM AUTHOR]

This study conducts a quantitative research survey on the development of queueing networks over years. Development is a process of gradual change that takes place over many years, during which a theory slowly progress and attain a good state. Queueing theory has been through many developments which made its existence inevitable in every field. Queueing networks can be considered as a collection of nodes, where each node stands for a service facility. It has been proved to be a powerful and versatile tool for modelling facilities in manufacturing units and telecommunication networks. This paper presents the development in Queueing networks and its types over years. This paper's main objective is to give all the analysts and researchers the knowledge about the evolution that happened in Queueing networks over years. [ABSTRACT FROM AUTHOR]

This paper considers a Geo/G/1 queueing system within a discrete-time framework. The model seamlessly integrates state-dependent policies, incorporating both single working vacation and multiple vacations, thereby reflecting the dynamic nature of telecommunication environments. The matrix analytic method is utilized to analyze essential system performance indices, such as long-run probabilities of the distinct server states and the expected queue size of the system, offering insights into the nuanced behavior of Geo/G/1 queueing systems within the discrete-time framework. The results are expected to offer valuable insights for enhancing the performance of telecommunication networks. These insights cover various aspects, including single working vacations, multiple vacations, and state-dependent policies. Consequently, they are poised to establish a solid foundation for improving system efficiency and adapting to dynamic operational conditions. [ABSTRACT FROM AUTHOR]

Modeling and decision making for queueing systems have been one of fundamental topics in operations research. For these problems, uncertainty models are established by estimation of key parameters such as expected interarrival and service times. In practice, however, their distributions are unknown, and decision makers are only given historical records of waiting times, which contain relevant but indirect information on the uncertainties. Their complex temporal dependence on the queueing dynamics and the absence of distributional information on the model primitives render estimation of queueing systems remarkably challenging. In the paper "Robust Queue Inference from Waiting Times" by Chaithanya Bandi, Eojin Han, and Alexej Proskynitopoulos, a new inference framework based on robust optimization is proposed to estimate unknown service times from waiting time observations. This new framework allows data-driven, distribution-free estimation on unknown model primitives by solving tractable optimization problems. Observational data from queueing systems are of great practical interest in many application areas because they can be leveraged for better statistical inference of service processes. However, these observations often only provide partial information of the system for various reasons in real-world settings. Moreover, their complex temporal dependence on the queueing dynamics and the absence of distributional information on the model primitives render estimation of queueing systems remarkably challenging. To this end, we consider the problem of inferring service times from waiting time observations. Specifically, we propose an inference framework based on robust optimization, where service times are described via sets that are calibrated by the observed waiting times. We provide conditions under which these data-driven uncertainty sets become asymptotically confident estimators of the service process; that is, they contain unknown service times almost surely as the number of observations grows. We also introduce tractable optimization formulations to compute bounds of various service time characteristics such as moments and risk measures. In this way, our approach is data driven and free of distributional assumptions on unknown model primitives, which is required by existing methods. We also generalize the proposed inference framework to tandem queues and feed-forward networks, offering broader capability in estimation of real-world queueing systems. Our simulation study demonstrates that the proposed approach easily incorporates information of arrival processes such as moments and correlations and performs consistently well on queueing networks under various settings. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0091. [ABSTRACT FROM AUTHOR]

Background: This study addresses optimising fleet size in a system with a heterogeneous truck fleet, aiming to minimise transportation costs in interfacility material transfer operations. Methods: The material transfer process is modelled using a closed queueing network (CQN) that considers heterogeneous nodes and customised service times tailored to the unique characteristics of various truck types and their transported materials. The optimisation problem is formulated as a mixed-integer nonlinear programming (MINLP), falling into the NP-Hard, making exact solution computation challenging. A numerical approximation method, a modified sequential quadratic programming (SQP) method coupled with a mean value analysis (MVA) algorithm, is employed to overcome this challenge. Validation is conducted using a discrete event simulation (DES) model. Results: The proposed analytical model tested within a steel manufacturing plant's material transfer process. The results showed that the analytical model achieved comparable optimisation of the heterogeneous truck fleet size with significantly reduced response times compared to the simulation method. Furthermore, evaluating performance metrics, encompassing response time, utilisation rate, and cycle time, revealed minimal discrepancies between the analytical and the simulation results, approximately ±8%, ±8%, and ±7%, respectively. Conclusions: These findings affirm the presented analytical approach's robustness in optimising interfacility material transfer operations with heterogeneous truck fleets, demonstrating real-world applications. [ABSTRACT FROM AUTHOR]

Space–air–ground integrated network (SAGIN) is considered an enabler for sixth-generation (6G) networks. By integrating terrestrial and non-terrestrial (satellite, aerial) networks, SAGIN seems to be a quite promising solution to provide reliable connectivity everywhere and all the time. Its availability can be further enhanced if hybrid free space optical (FSO)/radio frequency (RF) links are adopted. In this paper, the performance of a hybrid FSO/RF communication system operating in SAGIN has been analytically evaluated. In the considered system, a high-altitude platform station (HAPS) is used to forward the satellite signal to the ground station. Moreover, the FSO channel model assumed takes into account the turbulence, pointing errors, and path losses, while for the RF links, a relatively new composite fading model has been considered. In this context, a new link selection scheme has been proposed that is designed to reduced the signaling overhead required for the switching operations between the RF and FSO links. The analytical framework that has been developed is based on the Markov chain theory. Capitalizing on this framework, the performance of the system has been investigated using the criteria of outage probability and the average number of link estimations. The numerical results presented reveal that the new selection scheme offers a good compromise between performance and complexity. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]

Batch service queueing systems are basically classified into two types: a time-based system in which the service facilities depart according to inter-departure times that follows a given distribution, such as the conventional bus system, and a demand-responsive system in which the vehicles start traveling provided that a certain number of customers gather at the waiting space, such as ride-sharing and on-demand bus. Motivated by the recent spreading of demand-responsive transportation, this study examines the M/M X / ∞ queue. In this model, whenever the number of waiting customers reaches a capacity set by a discrete random variable X , customers are served by a group. We formulate the M/M X / ∞ queue as a three-dimensional Markov chain whose dimensions are all unbounded and depict a book-type transition diagram. The joint stationary distribution for the number of busy servers, number of waiting customers, and batch size is derived by applying the method of factorial moment generating function. The central limit theorem is proved for the case that X has finite support under heavy traffic using the exact expressions of the first two moments of the number of busy servers. Moreover, we show that the M/M X / ∞ queue encompasses the time-based infinite server batch service queue (M/M G (x) / ∞ queue), which corresponds to the conventional bus system, under a specific heavy traffic regime. In this model, the transportation facility departs periodically according to a given distribution, G (x) , and collects all the waiting customers for a batch service for an exponentially distributed time corresponding to the traveling time on the road. We show a random variable version of Little's law for the number of waiting customers for the M/M G (x) / ∞ queue. Furthermore, we present a moment approach to obtain the distribution and moments of the number of busy servers in a GI/M/ ∞ queue by utilizing the M/M G (x) / ∞ queue. Finally, we provide some numerical results and discuss their possible applications on transportation systems. [ABSTRACT FROM AUTHOR]

A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the exact analysis of the problem intractable. Therefore, we study this problem in the heavy traffic regime. Under the assumptions of complete resource pooling and common travel time and routing distributions, we solve the problem in closed form by analyzing the corresponding Bellman equation. Using this solution, we propose a policy for the queueing system and illustrate its effectiveness in a simulation study. [ABSTRACT FROM AUTHOR]

In densely populated Asian countries, e-bikes have become a new supernova in daily urban transportation. To facilitate the operations of e-bike-based mobility, the present paper studies the management of the battery deployment for the e-bike battery-swapping system, where the unique features of e-bike riding are considered. Given the pedal-assisted mode, e-bike users could abandon waiting and return to the station later on without too much range anxiety. However, because of the time-varying nature of the customer arrival and the complicated user behaviors, the battery quantity at each station is altered to guarantee the designated service level. However, little research has been done on the operations management of the e-bike battery-swapping system. To bridge the gap, we propose a nonstationary queueing network model to characterize the customer behaviors during the battery-swapping service. Then we develop a closed-form delayed infinite-server fluid approximation for the battery deployment of the one-time-loop scenario under various quality-of-service targets. In addition, we handle the infinite-time-loop scenario with the simulation-based iterative staffing algorithm. In the simulation study, we observe that the proposed battery deployment algorithms can help stabilize the system performance in terms of abandonment probability and expected delay in the face of time-varying demand and complex customer behaviors. Moreover, we reveal that the number of return loops correlates with the service level targets on the battery deployment decision. Furthermore, a time gap exists between the demand and the optimal battery deployment, making proactive battery management in the system possible. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72271222, 71871203, 71872093, 72271137, L1924063], and the National Social Science Fund of China [Grant 21&ZD128]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0132. [ABSTRACT FROM AUTHOR]

We analyze the affect of server breakdowns and negative customers on queueing systems. Using the quasi-brithand-death (QBD) process and matrix geometry solution method, the M/M/1 repairable queueing system with two types of server breakdowns and negative customers was studied. In the model, arriving at a negative customer will offset one positive customer, simultaneously, it may reduce the service rate or stop working of the system. The stationary conditions are given, the steadystate probability vectors are obtained, and some steady-state queueing and reliable measures are calculated. The results suggest that the system's mean queue length decreases as the increase of the negative customers arrival rate. Finally, the affect of parameter changes on the system performance measures are shown by graphs, which can provide an actual reference for practical applications. [ABSTRACT FROM AUTHOR]

We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well. [ABSTRACT FROM AUTHOR]

We consider a single-item production–inventory system under a base stock policy for inventory control. We model the system as a closed Gordon–Newell network. The population size of the network is equal to the base stock level, which is the sum of the finished goods and work-in-process inventory. Each exogenous demand, which follows a Poisson process, releases a production order for a new unit and increases the amount of the work-in-process inventory. When there are no items in the finished goods inventory available, arriving demand is lost. The replenishment network operates with state dependent service rates, which we assume to be increasing and concave. First, we analyze the queue length behavior of a two node system and provide conditions under which the mean queue length at the production server is convex in the number of customers in the system. We prove that this leads to convexity of a standard cost function. Using Norton's theorem, we are able to generalize our results for arbitrarily large production–inventory systems. [ABSTRACT FROM AUTHOR]

We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted ("lost sales"). To satisfy a customer's demand a server at the production system needs raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. The routing of items depends on the on-hand inventory at the locations with the aim to obtain "load balancing". We show that the stationary distribution has a product form of the marginal distributions of the production subsystem and the inventory-replenishment subsystem. For the marginal distribution of the production subsystem we derive an explicit solution and for the marginal distribution of the inventory-replenishment subsystem we deduce an explicit solution or a recursive algorithm for some special cases. [ABSTRACT FROM AUTHOR]

A network of queueing-inventory systems is considered where the inventories are replenished by a common central server. Travel times for transport of the items send out from the center and an adaptive dispatching regime to direct transportation towards the locations with queueing-inventory systems are incorporated in the model. The stationary distribution of the system is of product form and is explicitly given. An optimization procedure is developed to find for given locations of the queueing-inventory systems an optimal location for the replenishment center. Optimization is with respect to overall utilization of the resources measured in total throughput of the queueing-inventory systems. [ABSTRACT FROM AUTHOR]

Non-functional properties of collective adaptive systems (CAS) are of paramount relevance practically in any application. This paper compares two recently proposed approaches to quantitative modelling that exploit different system abstractions: the first is based on generalised stochastic Petri nets, and the second is based on queueing networks. Through a case study involving autonomous robots, we analyse and discuss the relative merits of the approaches. This is done by considering three scenarios which differ on the architecture used to coordinate the distributed components. Our experimental results assess a high accuracy when comparing model-based performance analysis results derived from two different quantitative abstractions for CAS. [ABSTRACT FROM AUTHOR]

We consider the following network model motivated, in particular, by blockchains and peer-to-peer live streaming. Data packet flows arrive at the network nodes and need to be disseminated to all other nodes. Packets are relayed through the network via links of finite capacity. A packet leaves the network when it is disseminated to all nodes. Our focus is on two communication disciplines, which determine the order in which packets are transmitted over each link, namely Random-Useful (RU) and Oldest-Useful (OU). We show that RU has the maximum stability region in a general network. For the OU we demonstrate that, somewhat surprisingly, it does not in general have the maximum stability region. We prove that OU does achieve maximum stability in the important special case of a symmetric network, given by the full graph with equal capacities on all links and equal arrival rates at all nodes. We also give other stability results, and compare different disciplines' performances in a symmetric system via simulation. Finally, we study the cumulative delays experienced by a packet as it propagates through the symmetric system, specifically the delay asymptotic behavior as N → ∞ . We put forward some conjectures about this behavior, supported by heuristic arguments and simulation experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution. [ABSTRACT FROM AUTHOR]