We consider a two-dimensional reflected Ornstein–Uhlenbeck (ROU) process that arises as the diffusion approximation for a parallel server network with a randomly split Hawkes arrival process (or a multivariate Hawkes arrival process) in heavy traffic. We study the ergodic properties of the process, including the positive recurrence and rate of convergence in total variation distance and in Wasserstein distance. We also provide a numerical scheme based on a Monte Carlo method to approximate the invariant measure of the process. Funding: G. Pang is partly supported by the National Science Foundation [Grants DMS 2216765 and CMMI 2452829].

Purpose The aim of this study is to gain knowledge about the strengths and limitations of the Canadian service delivery model in meeting the needs of the government assisted refugee (GAR) population during the COVID-19 pandemic. Design/methodology/approach This study used a qualitative case study design. Findings This aggregated case narrative identified several challenges, including an overwhelming sense of disconnection from friends and family, cultural services, access to information and access to health and social services. These complex experiences have been captured under the following themes: 1) “We do not know, yet”: Living in a Void; 2) “Limited choice”: Finding Services in a Virtual World; 3) “Between four walls”: Missing Connections; 4) “Thank you”: Staff Carrying a Burden of Compassion. Research limitations/implications This study follows a case study design that includes local responses from a small number of refugees from the Middle East. Although a small sample, this research offers detailed and rich knowledge about the settlement experience during a global pandemic in a mid-size Canadian city. This in-depth knowledge may be transferable to other contexts such as settlement of refugees in other regions across Canada. Because this study was undertaken at the beginning of the pandemic, some interviews took place online, limiting information sharing due to a lack of in-person interaction. Some settlement staff expressed reservations around sharing their experiences of providing services during the pandemic. Similarly, some newcomer families underscored their gratitude to migrate to Canada and may not have felt comfortable critiquing the system. Practical implications For settlement services going forward, having a hybrid model of services would ease the settlement experience for refugees because a combination of virtual and in-person support was noted by our participants as an effective and preferred approach. For federal and provincial governments, prioritizing internet connectivity immediately upon arrival is a key to mitigate the isolation and bewilderment that families may experience, especially amidst public health restrictions. Social implications Providing a timeline for time-sensitive information as it occurs for GARs, so GAR families and settlement workers are prompted to seek/deliver just-in-time information necessary for participants is essential to making the experience of settlement less daunting. Nation-wide implementation of the Welcome Group program is a practical step to promote a positive integration and reduce social isolation (West London Welcome, 2023). Cultural ambassadors can help with learning the language, getting to know the neighbourhood and mitigating the impact of social isolation better than if refugee families were left on their own with basic support from settlement agencies. Originality/value Recommendations for settlement service providers, and municipal, provincial and federal governments, are discussed to adapt to a mixed in-person and virtual service-delivery environment. In terms of better preparing and supporting refugees through the arrival process, there is potential to review the education and information settlement services provide for newcomers on an organizational level, including a hybrid education model, resources in more languages, attention to key timing and literacy accessibility (i.e. written, audio and video materials).

The efficiency of intelligent urban mobility increasingly depends on adaptive mathematical models that can optimize multimodal transportation resources under stochastic and heterogeneous conditions. This study proposes a Markovian stochastic modeling and metaheuristic optimization framework for the adaptive management of bus lane capacity in mixed connected traffic environments. The heterogeneous vehicle arrivals are modeled using a Markov Arrival Process (MAP) to capture correlated and busty flow characteristics, while the system-level optimization aims to minimize total fuel consumption through discrete lane capacity allocation. To support real-time adaptation, a Hidden Markov Model (HMM) is integrated for queue-length estimation under partial observability. The resulting nonlinear and nonconvex optimization problem is solved using Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), ensuring robustness and convergence across diverse traffic scenarios. Numerical experiments demonstrate that the proposed stochastic–adaptive framework can reduce fuel consumption and vehicle delay by up to 68% and 65%, respectively, under high saturation and connected-vehicle penetration. The findings verify the effectiveness of coupling stochastic modeling with adaptive control, providing a transferable methodology for energy-efficient and data-driven lane management in smart and sustainable cities.

We revisit the traditional stochastic clearing problem widely applicable in various supply chain and service systems. We consider the case where the stochastic input (order/customer arrival) process is Poisson and service delay (order/customer waiting) associated with clearing frequency (service) is subject to a nonlinear penalty in the context of a continuous-time setting. The penalty is associated with average order squared delay. It is designed to capture the customers’ impatience/disutility related to waiting times caused by service delays (e.g., delay of delivery of orders to customers). We analyze three practical, renewal-type clearing protocols (known as quantity-based, time-based, and hybrid policies) for operating the system. Our goal is to compare and contrast these policies in terms of average order squared delay, as an indicator of service performance, along with long-run average cost, as an indicator of financial performance. Unlike the case of linear delay penalty in the continuous-time setting–investigated previously in the literature–we find that quantity-based policies are not necessarily optimal with respect to service- or financial performance. Further, one can potentially compute a hybrid policy that dominates the cost-optimal quantity-based policy in terms of both dimensions of performance. This new finding regarding bi-criteria dominance potential of hybrid policies validates the value and importance of consideration of this class of clearing protocols in establishing operational guidelines in practice. Our analysis reveals and builds on some new characteristics of truncated Poisson random variables. To the best of our knowledge, the current paper is the first to formally offer and utilize these properties while simultaneously investigating the financial and service performance of stochastic clearing operations.

Average throughput performance of myopic policy in energy harvesting wireless sensor networks under stochastic data arrival processes

This study presents a hybrid stochastic model for evaluating delays and buffering in 5G-IoT ecosystems with programmable P4 switches, where traffic patterns exhibit strong batch-like properties. The proposed approach integrates a batch Markovian arrival process (BMAP) with a phase-type service structure and semi-Markov modelling of control-plane interactions, thereby capturing both the temporal variability of IoT traffic and the hybrid nature of routing logic. Analytical expressions for the expected processing time and queue length were derived using extended G/G/1, H₂/H₂/1, M/G/1, and M/N/1 queueing frameworks. Unlike traditional queueing models, the proposed framework is the first to simultaneously incorporate BMAP-driven bursty arrivals, phase-type service distributions, and semi-Markov representation of control-plane interaction dynamics. This integrated design enables more accurate characterisation of real IoT traffic and significantly improves predictive accuracy. The model was validated on real-world traffic datasets, demonstrating that BMAP more accurately reflects the structure of IoT traffic than classical Poisson or MMPP models. Notably, the BMAP-based approach reduced the modelling error by up to 38% compared to Poisson-based approximations and by 22% compared to MMPP-based ones under bursty traffic conditions. Simulation results confirm that increasing the control-plane involvement probability from 0.2 to 0.7, under a fixed average batch size of 12 requests, leads to a 2.6-fold increase in processing delay. Furthermore, the H₂/H₂/1 model showed the highest alignment with empirical data, accurately reflecting the multi-phase service structure and control flow saturation effects. Additional 3D analyses revealed strong nonlinear dependencies of delay on the batchiness factor, dispersion in processing times, and phase asymmetry parameters.

We consider a two-sided marketplace in which a market operator sells services to clients and buys services from vendors. The market operator determines the prices dynamically for both clients and vendors. Services are transacted in discrete units called jobs, and the jobs are characterized by their types, service deadlines, client prices, and vendor prices. Jobs are submitted by clients to the marketplace, and the market operator then lists the available jobs. Vendors can view the available jobs and choose them based on their preferences. We consider an infinite-horizon long-run average reward Markov decision process (MDP) model of the market operator’s dynamic pricing problem. The MDP consists of the arrival processes on both sides of the marketplace as well as the choice behavior of both clients and vendors. Because solving this MDP directly is impractical for large market sizes, we study a discrete-time fluid approximation of the problem. This approximation results in a simple pricing policy in which each job’s price trajectory depends on the time remaining until the service deadline but does not depend on the other jobs available in the marketplace. We show that this policy is asymptotically optimal with a loss ratio of order [Formula: see text] on the long-run average reward, where [Formula: see text] represents the scale of demand and supply. The performance of the fixed price trajectory policy is compared with other heuristics, including a constant pricing policy and a state-dependent pricing policy. We also extend the model to continuous-time and finite-horizon settings. This paper was accepted by Omar Besbes, revenue management and market analytics. Funding: The work of Y. Cao was partly supported by the National Natural Science Foundation of China [Grant 72201165, 72221001, 72231003, 72331006], and Shanghai Pujiang Program [Grant 22PJC066]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.00832 .

This paper explores a stochastic queuing-inventory system designed to efficiently manage both new and returned items, offering practical solutions for diverse customer needs. The system differentiates services for various customer classes through dedicated channels, encompassing the sale of new and returned items, as well as the purchase of used items from customers. This model incorporates four parallel queues for distinct customer classes, each serviced by a dedicated server. Customer arrivals are modeled using a Markovian Arrival Process (MMAP), with service times being exponentially distributed and independent. An $(s, S)$ policy is implemented for replenishing fresh items. The primary objective is to enhance service accessibility for various customer types within a single facility, promoting operational efficiency and customer satisfaction. Additionally, the system's ability to purchase used items underscores its role in fostering sustainability in an evolving society. By applying the Neuts matrix geometric technique, the paper analyzes the system to derive the long-term probability distribution and significant performance metrics. Numerical methods are utilized to investigate key system parameters and performance measures, and a cost function is introduced and optimized concerning the reorder level. This comprehensive analysis offers valuable insights for optimizing inventory and queuing systems in practical, real-world applications.

Waiting time is the time used by patients to get health services from the registration point to entering the doctor's examination room. The length of patient waiting time is one of the important things in determining the quality of health services. This study aims to analyze the length of waiting time (arrival process, service, human resources. This study uses a qualitative method with a descriptive approach. Data collection with this study was carried out using in-depth interview techniques and collation methods with observation. The registration process is still lacking because the Hospital still uses manual methods and the use of SIMRS has not been fully implemented. The number of human resources is still lacking, the outpatient waiting time is not up to standard because it exceeds 60 minutes, the availability of facilities and infrastructure is still lacking such as computers, signals. Other factors that cause long patient waiting times and examination results are not yet connected to all units so that it takes a long time.

As a key node in port logistics systems, ship anchorage is often faced with congestion caused by ship flow fluctuations, multi-priority scheduling imbalances and the poor adaptability of scheduling models to complex environments. To solve the above problems, this paper constructs a ship scheduling algorithm based on a Markov-modulated fluid priority queue, which describes the stochastic evolution of the anchorage operation state via a continuous-time Markov chain and abstracts the arrival and service processes of ships into a continuous fluid input and output mechanism modulated by the state. The algorithm introduces a multi-priority service strategy to achieve the differentiated scheduling of different types of ships and improves the computational efficiency and scalability based on a matrix analysis method. Simulation results show that the proposed model reduces the average waiting time of ships by more than 90% compared with the M/G/1/1 and RL strategies and improves the utilization of anchorage resources by about 20% through dynamic service rate adjustment, showing significant advantages over traditional scheduling methods in multi-priority scenarios.

An MAP/PH/N-type queuing system functioning within a finite-state Markovian random environment is studied. The random environment’s state impacts the number of available servers, the underlying processes of customer arrivals and service, and the impatience rate of customers. The impact on the state space of the underlying processes of customer arrivals and of the more general, as compared to exponential, service time distribution defines the novelty of the model. The behavior of the system is described by a multidimensional Markov chain that belongs to the classes of theevel-independent quasi-birth-and-death processes or asymptotically quasi-Toeplitz Markov chains, depending on whether or not the customers are absolutely patient in all states of the random environment or are impatient in ateast one state of the random environment. Using the tools of the corresponding processes or chains, a stationary analysis of the system is implemented. In particular, it is shown that the system is always ergodic if customers are impatient in ateast one state of the random environment. Expressions for the computation of the basic performance measures of the system are presented. Examples of their computation for the system with three states of the random environment are presented as 3-D surfaces. The results can be useful for the analysis of a variety of real-world systems with parameters that may randomly change during system operation. In particular, they can be used for optimally matching the number of active servers and the bandwidth used by the transmission channels to the current rate of arrivals, and vice versa.

In the situation of protracted conflicts in the world, there is a tendency for migration flows to grow. Not only countries, but also cities and communities of territorial communities (municipalities) are faced with the challenges of the influx of migrants. Local self-government occupies a special place in the sense that it faces challenges of migration that in developing countries are not reflected in local strategic documents. Local self-government should have its role in the integration of immigrants and work closely with central authorities to implement migration policies. Although the legislation is in force, the rights of local self-government are limited, but in practice there are cases when self-government itself plays a role in the integration of immigrants and their families. Therefore, it is necessary to precisely define the boundaries of the powers of the central government and the role of local self-government for the effective integration of immigrants into territorial communities. Modern Georgia is struggling with many challenges. Among them is the problem of population migration. Modern migration challenges associated with the mass arrival of refugees to the cities of Tbilisi, Kutaisi and Batumi in Georgia, primarily internally displaced persons, date back to the early 1990s. The minimal process of arrival of immigrants and refugees to Georgia took place before February 24, 2022, the date of the start of the large-scale invasion of Russian troops. However, it was not of such a massive nature. Only with the beginning of Russia's armed invasion in 2014 and Russia's support for separatists - primarily in Donetsk and Luhansk - did this phenomenon begin to intensify and continues to this day with varying intensity. Migrants fleeing armed conflict are by no means a new phenomenon for Georgian cities. Large population movements occurred especially during the years of armed conflicts in Abkhazia and the Tskhinvali region. Refugees from conflict-affected regions arrived in Tbilisi, Kutaisi and Batumi to escape the war in 1991-1993 and 2008. To this should be added immigrants who arrived from the Arab countries of Syria and Lebanon, which were engulfed in armed conflicts in 2011-2022, as well as Ukrainian forced immigrants from Crimea, Luhansk and Donetsk regions in 2014-2022. In Georgia, migration issues are the competence of state authorities. Any actions of local governments depend on the policy pursued by the government. Nevertheless, there were grassroots initiatives in local authorities in Tbilisi, Kutaisi and Batumi that implemented certain measures related to the policy towards immigrants from Ukraine after the large-scale invasion of Russian troops on February 24, 2022. One of the challenges that arise when immigrants arrive is the question of how they will be integrated with other members of the community of a given administrative-territorial unit. From the point of view of the interests of a particular city (municipality), it is important whether this process will ultimately lead to the creation of a single whole - a union at different social levels and the adaptation of the behavior of immigrants to the attitudes prevailing in the community. There are many problems that local governments face in relations between immigrants and local residents. To deepen these considerations, we will define the main concepts: local government, immigration and integration. Keywords: local self-government, immigration, immigrant, integration.

In the last decade and recently, a wide range of industries and organizations have been subject to IT-related security threats and cybersecurity breaches of varying degrees of severity at an alarming rate. A common practice adopted by organizations to ensure system and network security is to conduct regular audits and assessments. This paper takes on an organizational strategy perspective to analytically model the cost impact of random breaches in various types of networks subject to different types of audit policy. The analysis focuses on the interplay between the cost associated with a security breach on the one hand, and audit policy on the other. We develop a model for a non-stationary stochastic arrival process of security breaches and analyze the impact on mean and variance of total cost of different network configurations and audit policies. The generality of our modeling of the arrival process and the cost function permits a variety of attack and cost landscapes to be modeled and analyzed, with different breach intensities and costs (as functions of time) leading to different recommendations in terms of effective audit policy. Our analysis highlights the impact of intensity of security breach and cost of breach on the interaction between different network configurations and audit policies. One of our counter-intuitive findings is that under high security threat conditions a centralized network has a lower mean as well as a lower variance of total cost than a decentralized network, in case of cyclic and random audits; this analytically derived proposition is an interesting instance of a dual risk-pooling effect that goes beyond conventional risk-pooling. We extend our analysis to consider an asymmetric network and correlated breaches.

To enhance the speed control performance of the permanent magnet synchronous motor (PMSM) servo system, an improved sliding mode control method integrating a torque observer is presented. The current loop uses current feedback decoupling PID control, and the speed loop applies sliding mode control. In comparison to previous work in hybrid SMC using fuzzy logic and torque observers, this p proposes a hyperbolic tangent function in replacement of the signum function to solve the conflict between rapidity and chattering in the traditional exponential reaching law, and fuzzy and segmental self-tuning rules adjust relevant switching terms to reduce chattering and improve the sliding mode arrival process. A load torque observer is designed to enhance the system’s anti-interference ability by compensating the observed load torque to the current loop input. Simulation results show that compared with traditional sliding mode control with a load torque observer (SMC + LO), PID control with a load torque observer (PID + LO), and Active Disturbance Rejection Control (ADRC), the proposed strategy can track the desired speed in 0.032 s, has a dynamic deceleration of 2.7 r/min during sudden load increases, and has a recovery time of 0.011 s, while the others have relatively inferior performance. Finally, the model experiment is carried out, and the results of the experiment are basically consistent with the simulation results. Simulation and experimental results confirm the superiority of the proposed control strategy in improving the system’s comprehensive performance.

Queueing theory plays a crucial role in analyzing congestion and optimizing resource utilization in complex systems. Traditional models often assume stationary arrival and service processes, typically modeled using homogeneous Poisson processes. However, in many practical scenarios, such as hospital operations, manufacturing systems, cloud computing, and airport security, service rates are time-dependent and are more accurately captured by NHPP. This study presents a three-node tandem queueing model where each node features a time-dependent service mechanism governed by a NHPP. We derive key performance metrics, including the typical No. of Users in line, the duration Users spend before receiving service at each stage and across the entire system, the overall throughput, and the variation in the No. of Users present. A thorough sensitivity analysis is conducted to explore how different service rate parameters impact these PMs. The results highlight the significant effect of time-dependent service dynamics on system behavior, demonstrating that the proposed model offers a more accurate and flexible framework for studying systems with time-varying service processes. Additionally, this three-node model generalizes and extends earlier two-node configurations, providing deeper insights into multi-stage service environments

Urban traffic congestion has emerged as a global challenge constraining sustainable development. Estimating the traffic congestion probability is crucial since it presents valuable information for formulating congestion mitigation strategies and improving traffic management. The existing studies employ deterministic models to predict congestion; however, they do not consider the dynamic coupling between intrinsic traffic flow randomness (e.g. spatiotemporal heterogeneity in vehicle arrivals) and congestion formation mechanisms, causing prediction biases under high-uncertainty scenarios. In this study, we propose a probability-based congestion estimation framework that employs the stochastic traffic flow theory. The traffic arrival process is described using discrete probability distributions owing to the stochastic nature of traffic flows. To prevent the misclassification of transient traffic surges as congestion, we adopt a spatiotemporal persistence criterion with dual thresholds (vehicle accumulation exceeding a critical level and duration surpassing a minimum time) for congestion identification. Additionally, we perform empirical validation using traffic datasets from Portland, USA, which demonstrates that there is no statistically significant deviation from the measured data at the 95% confidence level in the calculated congestion probabilities. The proposed method facilitates the development of targeted congestion mitigation countermeasures and presents novel insights for future transportation planning.

Abstract We consider a single server queue that has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level GI/G/1 queue. This model is motivated by an energy saving problem for a single server queue whose arrival process and service speed are controlled. To obtain its performance in tractable form, we study the limit of the stationary distribution of the queue length in this two-level queue under scaling in heavy traffic. Except for a special case, this limit corresponds to its diffusion approximation. It is shown that this limiting distribution is truncated exponential (or uniform if the drift is null) below the threshold level and exponential above it under suitably chosen system parameters and generally distributed interarrival times and workloads brought by customers. This result is proved under a mild limitation on arrival parameters using the so-called basic adjoint relationship (BAR) approach studied in Braverman, Dai, and Miyazawa (2017, 2024) and Miyazawa (2017, 2024). We also intuitively discuss about a diffusion process corresponding to the limit of the stationary distribution under scaling.

Abstract A pooled study analysis approach has many advantages to that of a single study analysis primarily related to greater sample size to compare treatment outcomes, but also due to the fact that a pooled analysis provides estimated means and the associated standard errors of the means (SEM) with more potential generalizability as they represent data from multiple populations of cattle, study site locations, cattle bio-type, and dietary ingredients. Thus, the objective of this study was to pool data from 4 studies to determine the effects of supplementation of a formulated blend of capsicum oleoresin, clove essential oil, and garlic essential oil (CCG; Fytera® Advance - Selko® USA, Indianapolis IN) on growth performance of steers and cutting-bulls. Randomized complete block design experiments (n = 4 experiments) were used in the pooled analysis. A receiving and finishing study were conducted both in South Dakota (n = 2) and Oklahoma (n = 2). Similar arrival processing was used across experiments where 1701 steers and 341 cutting-bulls [Initial body weight = 320 kg (SEM = 1.3)] were enrolled into 64 pens (32 pens per treatment) with 6 to 80 head per pen. Diets contained monensin (South Dakota only) or monensin and tylosin phosphate (Oklahoma only) and consisted of ingredients common to each region. Within in each study, pens were assigned to 1 of 2 treatments: 1) non-supplemented control (CON); 2) supplemented with 500 mg/steer daily of CCG. Growth performance datawere analyzed with linear mixed models using the GLIMMIX procedure of SAS 9.4 (SAS Institute Inc., Cary, NC, USA). Models were fitted with a Gaussian distribution, Kenward-Roger’s denominator degrees of freedom method, pen as the experimental unit, and treatment as a fixed effect. Additionally, random intercepts for pairs (blocks) within trials were included. Model-adjusted means and standard errors were obtained; means separations included a Tukey-Kramer adjustment for multiple comparisons. Statistical significance was denoted at an α ≤ 0.05 and tendencies were observed at 0.05 < α ≥ 0.10. No statistical differences were noted for DMI and FBW (P ≥ 0.11). However, steers that received CCG had improved G:F by 2.3% (P = 0.02) and ADG tended to be 1.8% greater (P = 0.07). These findings suggest that CCG positively influences growth performance in beef steers and cutting bulls fed diets containing monensin sodium. Furthermore, this response is consistent across multiple phases of growth and management conditions.

Queueing models are vital analytical tools for examining a wide range of real-world scenarios, such as those found in communication networks, transportation systems, machine maintenance, and production lines. These systems often exhibit non-stationary arrival and service processes, reflecting their dynamic nature over time. In this study, we develop and evaluate a queueing model that integrates both sequential and parallel service mechanisms, characterized by non-stationary Poisson arrivals and time-dependent service rates. The model assumes the presence of two parallel queues, each serviced independently, which subsequently converge into a single queue connected to a downstream service station. Such configurations are commonly observed in manufacturing systems and network infrastructures. By employing differential equations, we derive the joint probability generating function for the queue lengths. Additionally, we obtain explicit expressions for key performance indicators, including the average no. of customers in the queue, the average waiting time, and the variation in queue size in response to changes in service station throughput. The results demonstrate that non-stationary arrival and service patterns have a significant effect on overall system performance. This investigation draws inspiration from earlier foundational models while extending their applicability to more complex and realistic scenarios.

In this paper, a model of single server queueing-inventory system (QIS) with Markovian Arrival Process (MAP) and phase-type distribution (PH-distribution) of the service time of consumer customers (c-customers) is considered. After completing the service of c-customer, he (she) can make one of the following decisions: (1) eventually leave the system with probability (w.p.) σℓ; (2) after a random “thinking” time returns the purchased item w.p. σr; (3) after a random “thinking” he (she) feedback to buy a new item w.p. σf . It is assumed that σℓ+σr +σf = 1. If upon arrival of the c-customer the system main warehouse (SMW) is empty, then the incoming customer, according to the Bernoulli scheme, is either joins the infinite queue or leaves the system. A virtual finite orbit can be considered as a waiting room for feedback customers (f-customers). Returned items are considered new and are sent directly to SMW if there is at least one free space; otherwise, this item is sent to a special warehouse for returned items (WRI). After completing the service of each customer, one item is instantly sent from the WRI (if any) to the SMW. In SMW, the (s, S) replenishment policy is used and it is assumed that the lead time follows exponential distribution with finite parameter. When the stock level reaches its maximum value due to items returns, the system immediately cancels the regular order. Along with classical performance measures of QIS new specific measures are defined and numerical method for their calculation as well as maximization of the revenue function are developed. Results of numerical examples to illustrate the effect of different parameters on the system’s performance measures are provided and analyzed. We also provide a detailed analysis of an important special case of the Poisson process/exponential service time model.