Sojourn Time Research Articles

The Impact of Model Assumptions on Personalized Lung Cancer Screening Recommendations.

Recommendations regarding personalized lung cancer screening are being informed by natural-history modeling. Therefore, understanding how differences in model assumptions affect model-based personalized screening recommendations is essential. Five Cancer Intervention and Surveillance Modeling Network (CISNET) models were evaluated. Lung cancer incidence, mortality, and stage distributions were compared across 4 theoretical scenarios to assess model assumptions regarding 1) sojourn times, 2) stage-specific sensitivities, and 3) screening-induced lung cancer mortality reductions. Analyses were stratified by sex and smoking behavior. Most cancers had sojourn times <5 y (model range [MR]; lowest to highest value across models: 83.5%-98.7% of cancers). However, cancer aggressiveness still varied across models, as demonstrated by differences in proportions of cancers with sojourn times <2 y (MR: 42.5%-64.6%) and 2 to 4 y (MR: 28.8%-43.6%). Stage-specific sensitivity varied, particularly for stage I (MR: 31.3%-91.5%). Screening reduced stage IV incidence in most models for 1 y postscreening; increased sensitivity prolonged this period to 2 to 5 y. Screening-induced lung cancer mortality reductions among lung cancers detected at screening ranged widely (MR: 14.6%-48.9%), demonstrating variations in modeled treatment effectiveness of screen-detected cases. All models assumed longer sojourn times and greater screening-induced lung cancer mortality reductions for women. Models assuming differences in cancer epidemiology by smoking behaviors assumed shorter sojourn times and lower screening-induced lung cancer mortality reductions for heavy smokers. Model-based personalized screening recommendations are primarily driven by assumptions regarding sojourn times (favoring longer intervals for groups more likely to develop less aggressive cancers), sensitivity (higher sensitivities favoring longer intervals), and screening-induced mortality reductions (greater reductions favoring shorter intervals). Models suggest longer screening intervals may be feasible and benefits may be greater for women and light smokers. Natural-history models are increasingly used to inform lung cancer screening, but causes for variations between models are difficult to assess.This is the first evaluation of these causes and their impact on personalized screening recommendations through easily interpretable metrics.Models vary regarding sojourn times, stage-specific sensitivities, and screening-induced lung cancer mortality reductions.Model outcomes were similar in predicting greater screening benefits for women and potentially light smokers. Longer screening intervals may be feasible for women and light smokers.

Incidences of colorectal adenomas and cancers under colonoscopy surveillance suggest an accelerated “Big Bang” pathway to CRC in three of the four Lynch syndromes

BackgroundColorectal cancers (CRCs) in the Lynch syndromes have been assumed to emerge through an accelerated adenoma-carcinoma pathway. In this model adenomas with deficient mismatch repair have an increased probability of acquiring additional cancer driver mutation(s) resulting in more rapid progression to malignancy. If this model was accurate, the success of colonoscopy in preventing CRC would be a function of the intervals between colonoscopies and mean sojourn time of detectable adenomas. Contrary to expectations, colonoscopy did not decrease incidence of CRC in the Lynch syndromes and shorter colonoscopy intervals have not been effective in reducing CRC incidence. The prospective Lynch Syndrome Database (PLSD) was designed to examine these issues in carriers of pathogenic variants of the mis-match repair (path_MMR) genes.Materials and methodsWe examined the CRC and colorectal adenoma incidences in 3,574 path_MLH1, path_MSH2, path_MSH6 and path_PMS2 carriers subjected to regular colonoscopy with polypectomy, and considered the results based on sojourn times and stochastic probability paradigms.ResultsMost of the path_MMR carriers in each genetic group had no adenomas. There was no association between incidences of CRC and the presence of adenomas. There was no CRC observed in path_PMS2 carriers.ConclusionsColonoscopy prevented CRC in path_PMS2 carriers but not in the others. Our findings are consistent with colonoscopy surveillance blocking the adenoma-carcinoma pathway by removing identified adenomas which might otherwise become CRCs. However, in the other carriers most CRCs likely arised from dMMR cells in the crypts that have an increased mutation rate with increased stochastic chaotic probabilities for mutations. Therefore, this mechanism, that may be associated with no or only a short sojourn time of MSI tumours as adenomas, could explain the findings in our previous and current reports.

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.

Matched queues with matching batch pair [formula omitted]

In this paper, we develop the matrix-analytic method to discuss an interesting but challenging bilateral stochastic matching problem: A matched queue with matching batch pair (m,n) and two types of impatient customers, where the two types of customers arrive according to two independent Poisson processes. Once m A-customers and n B-customers are matched as a group, the m+n customers immediately leave the system. We show that this matched queue can be expressed as a novel bidirectional level-dependent quasi-birth-and-death (QBD) process whose analysis has its own interests, and specifically, computing the maximal non-positive inverse matrices of bidirectional infinite sizes by using the RG-factorizations. Based on this, we can provide an effective matrix-analytic method to deal with this matched queue, including the system stability, the average stationary queue lengths, the average sojourn times, and the departure process. We believe that the methodology and results developed in this paper can be applicable to studying more general matched queueing systems, which are widely encountered in many practical areas.

Transition probabilities of diabetic retinopathy and death in an Asian population with diabetes

PurposeTo evaluate the dynamic transitions in diabetic retinopathy (DR) severity over time and associated risk factors in an Asian population with diabetes. DesignLongitudinal cohort study MethodsWe analyzed data from 9481 adults in the Singapore Integrated Diabetic Retinopathy Screening Program (2010–2015) with linkage to death registry. A multistate Markov model adjusted for age, sex, systolic blood pressure (SBP), diabetes duration, HbA1c, and body mass index (BMI) was applied to estimate annual transition probabilities between four DR states (no, mild, moderate, and severe/proliferative) and death, and the mean sojourn time in each state. ResultsThe median assessment interval was 12 months, with most patients having 3 assessments. Annual probabilities for DR progression (no-to-mild, mild-to-moderate and moderate-to-severe/proliferative) were 6.1 %, 7.0 % and 19.3 %, respectively; and for regression (mild-to-no, moderate-to-mild and severe-to-moderate) were 55.4 %, 17.3 % and 4.4 %, respectively. Annual mortality rates from each DR state were 1.2 %, 2.0 %, 18.7 %, and 30.0 %. The sojourn time in each state were 8.2, 0.8, 0.8 and 2.2 years. Higher HbA1c and SBP levels were associated with progression of no-mild and mild-moderate DR, and diabetes duration with no-to-mild and moderate-to-severe/proliferative DR. Lower HbA1c levels were associated with regression from mild-to-no and moderate-to-mild, and higher BMI with mild-to-no DR. ConclusionsOur results suggest a prolonged duration (∼8 years) in developing mild DR, with faster transitions (within a year) from mild or moderate states. Moderate/above DR greatly increases the probability of progression and death as compared to mild DR/below. HbA1c was associated with both progression as well as regression.

The speed of neutral evolution on graphs.

The speed of evolution on structured populations is crucial for biological and social systems. The likelihood of invasion is key for evolutionary stability. But it makes little sense if it takes long. It is far from known what population structure slows down evolution. We investigate the absorption time of a single neutral mutant for all the 112 non-isomorphic undirected graphs of size 6. We find that about three-quarters of the graphs have an absorption time close to that of the complete graph, less than one-third are accelerators, and more than two-thirds are decelerators. Surprisingly, determining whether a graph has a long absorption time is too complicated to be captured by the joint degree distribution. Via the largest sojourn time, we find that echo-chamber-like graphs, which consist of two homogeneous graphs connected by few sparse links, are likely to slow down absorption. These results are robust for large graphs, mutation patterns as well as evolutionary processes. This work serves as a benchmark for timing evolution with complex interactions, and fosters the understanding of polarization in opinion formation.

Almost sure synchronization of stochastic multi-links semi-Markov jump systems via aperiodically intermittent control

This paper concentrates on the almost sure synchronization for a class of stochastic multi-links coupled semi-Markov jump systems through aperiodically intermittent control. For these stochastic switching systems, almost sure synchronization is investigated by employing mode-dependent multiple Lyapunov-like function method and stochastic analysis. Notably, mode-dependent multiple Lyapunov-like function method is designed to provide more flexibility. In addition, when considering the sojourn time distribution of the semi-Markov jump, dependence on both the current state and the next state can effectively reduce unnecessary restrictions compared with previous assumption of the sojourn time distribution function. Ultimately, the Chua’s circuit along with numerical simulations are provided to validate the effectiveness of the theoretical results.

New expectation-based conditions for almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control

This paper studies almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control. New expectation-based sufficient conditions for almost sure exponential stability of the system are derived by employing the coupled Lyapunov function related to the sojourn time and the ergodic property of semi-Markov chains. Compared with known results on almost sure exponential stability of discrete-time semi-Markovian linear systems, the results in this paper are shown to be less conservative. At last, three numerical examples are given to illustrate the results.

Observer-based SMC for discrete semi-Markov switching models

This study focuses on the observer-based sliding mode control (SMC) for discrete stochastic switching models, where the semi-Markov kernel information is incomplete. Because the sensors do not always have direct access to the state vector in a complex environment, an observer-based output measurement is considered to estimate the system state. In contrast to previous works, the observer-based strategy is first investigated in studying the SMC for semi-Markov switching systems under the discrete framework. The sufficient condition for achieving mean-square stability is proposed to solve the desired observer and controller gains by utilizing the upper bound of sojourn time, along with the Lyapunov function that pertains to the system mode and the elapsed time. A mode-dependent SMC law is also constructed to ensure that the system state can reach the specified sliding region. Finally, the efficiency of the proposed method is demonstrated through the single-link robot arm model.

A Cyclic Random Motion in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document} Driven by Geometric Counting Processes

We consider the random motion of a particle that moves with constant velocity in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document}. The particle can move along four different directions that are attained cyclically. It follows that the support of the stochastic process describing the particle’s position at a fixed time is a tetrahedron. We assume that the sequence of sojourn times along each direction follows a Geometric Counting Process (GCP). When the initial condition is fixed, we obtain the explicit form of the probability law of the process, for the particle’s position. We also investigate the limiting behavior of the related probability density when the intensities of the four GCPs tend to infinity. Furthermore, we show that the process does not admit a stationary density. Finally, we introduce the first-passage-time problem for the first component of the process through a constant positive boundary providing the bases for future developments.

Multi-objective optimization of production system with staggered production

In the manufacturing industry, timely order fulfilment from diverse customers is important for operational profitability, given the constraints of limited production capacity. This paper proposes a novel queueing system for a production system, in which order processing times are categorised as regular or rush based on customer preference. The proposed queueing system employs variable service rates and service strategies in conjunction with staggered production to deal with heterogeneous arrivals. We compute the steady-state probability distribution and develop system performance indicators. The lower and upper bounds of the expected sojourn time for rush and regular orders are derived. Numerical results show that an appropriate switching policy can reduce rush orders by approximately 35% while regular orders increase by less than 10%, demonstrating significant improvement in order fulfilment management. We formulate a multi-objective optimisation problem and implement the NSGA-II algorithm to obtain Pareto optimal solutions. Finally, three regression models are proposed to determine the minimum cost and the associated optimal service rates, given the maximum acceptable value of the expected number of rush orders. The established models can explain at least 80% of the dataset of the optimal solutions and thus our numerical findings provide useful guidance for decision-makers and production managers.

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

This paper investigates the joint optimization of condition-based opportunistic maintenance and spare inventory policies for a series-parallel system consisting of software and components. Software failure follows a homogeneous Poisson process. Components are subject to mutually dependent competing failure processes. When the software failure occurs, an opportunistic inspection will be implemented for the components. Besides the maintenance policy, the (s, S) inventory policy is applied for components. The maintenance and order decisions will be made according to the conditions of the components and inventory level at each inspection. The state transition probabilities and expected sojourn times can be obtained by the formulated semi-Markov decision process. The optimal inspection interval, the preventive replacement threshold of the component, and the order point can be derived by minimizing the expected average cost rate. Finally, the effectiveness and superiority of the proposed joint optimization model are verified by an illustrative example.

Robustly exponentially almost sure stabilization of uncertain discrete‐time composite switched systems

AbstractThis paper is concerned with the robustly exponentially almost sure (EAS) stabilization of uncertain discrete‐time composite switched systems (CSSs), in which the dominant signal subjects to a semi‐Markov chain, while the subordinate signals follow a family of different Markov chains. Norm‐bounded uncertainties impacting the state and input matrices of the system are taken into account. Utilizing numerical computation methods, bounds on the transient statistical properties of Markov chain are provided. Based on this, sufficient conditions for robustly EAS stabilization are established by combining an estimate of the sojourn time for modes in a semi‐Markov chain. Our result is the discrete counterpart of prior work concerning continuous‐time dual‐switching systems. Two examples are provided to validate the effectiveness of developed results.

Lead-Time Corrected Effect on Breast Cancer Survival in Germany by Mode of Detection.

(1) Background: Screen-detected breast cancer patients tend to have better survival than patients diagnosed with symptomatic cancer. The main driver of improved survival in screen-detected cancer is detection at earlier stage. An important bias is introduced by lead time, i.e., the time span by which the diagnosis has been advanced by screening. We examine whether there is a remaining survival difference that could be attributable to mode of detection, for example, because of higher quality of care. (2) Methods: Women with a breast cancer (BC) diagnosis in 2000-2022 were included from a population-based cancer registry from Schleswig-Holstein, Germany, which also registers the mode of cancer detection. Mammography screening was available from 2005 onwards. We compared the survival for BC detected by screening with symptomatic BC detection using Kaplan-Meier, unadjusted Cox regressions, and Cox regressions adjusted for age, grading, and UICC stage. Correction for lead time bias was carried out by assuming an exponential distribution of the period during which the tumor is asymptomatic but screen-detectable (sojourn time). We used a common estimate and two recently published estimates of sojourn times. (3) Results: The analysis included 32,169 women. Survival for symptomatic BC was lower than for screen-detected BC (hazard ratio (HR): 0.23, 95% confidence interval (CI): 0.21-0.25). Adjustment for prognostic factors and lead time bias with the commonly used sojourn time resulted in an HR of 0.84 (CI: 0.75-0.94). Using different sojourn times resulted in an HR of 0.73 to 0.90. (4) Conclusions: Survival for symptomatic BC was only one quarter of screen-detected tumors, which is obviously biased. After adjustment for lead-time bias and prognostic variables, including UICC stage, survival was 27% to 10% better for screen-detected BC, which might be attributed to BC screening. Although this result fits quite well with published results for other countries with BC screening, further sources for residual confounding (e.g., self-selection) cannot be ruled out.

Natural History of Type 2 Diabetes in Indians: Time to Progression.

To describe the natural history of diabetes in Indians. Data are from participants older than 20 years in the Centre for Cardiometabolic Risk Reduction in South Asia longitudinal study. Glycemic states were defined per American Diabetes Association criteria. Markov models were used to estimate annual transition probabilities and sojourn time through states. Among 2,714 diabetes-free participants, 641 had isolated impaired fasting glucose (iIFG), and 341 had impaired glucose tolerance (IGT). The annual transition to diabetes for those with IGT was 13.9% (95% CI 12.0, 15.9) versus 8.6% (7.3, 9.8) for iIFG. In the normoglycemia ↔ iIFG → diabetes model, mean sojourn time in normoglycemia was 40.3 (34.6, 48.2) years, and sojourn time in iIFG was 9.7 (8.4, 11.4) years. For the normoglycemia ↔ IGT → diabetes model, mean sojourn time in normoglycemia was 34.5 (29.5, 40.8) years, and sojourn time in IGT was 6.1 (5.3, 7.1) years. Individuals reside in normoglycemia for 35-40 years; however, progression from prediabetes to diabetes is rapid.

Prioritization in the Presence of Self-ordering Opportunities in Omnichannel Services

Motivated by the popularity of mobile-order-and-pay applications, especially in fast-casual food restaurants and coffee shops, we study omnichannel service systems—where customers can employ mobile applications for self-ordering—with respect to sojourn times, throughput, and social welfare. Our models are two-stage queues with two customer classes: Walk-ins and mobiles. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class’s mean sojourn times. We allow customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe partial queue length information. We draw from a wide array of techniques, including steady-state, transient, busy period, hitting-time analyses, and matrix analytic methods. We showcase the significance of prioritization on the system throughput and social welfare. We demonstrate settings where a traditional service system’s (typically beneficial) transformation to an omnichannel reduces throughput. Our analysis highlights the importance of prioritization policy choice for an efficient transition to an omnichannel service system. The throughput-optimal policy choice highly depends on the operational parameters and customer patience levels; implementing a wrong policy can yield a significant loss in throughput and profitability.

Asynchronous Sliding-Mode Control for Discrete-Time Networked Hidden Stochastic Jump Systems With Cyber Attacks.

In this study, asynchronous sliding-mode control (SMC) for discrete-time networked hidden stochastic jump systems subjected to the semi-Markov kernel (SMK) and cyber attacks is investigated. Considering the statistical characteristic of the SMK, which is challenging to acquire in engineering, this study recognizes the SMK to be incomplete. Due to the mode mismatch between the original system and the control law in the operating process, a hidden semi-Markov model is proposed to describe the considered asynchronous situation. The main aim of this study is to construct an asynchronous SMC mechanism based on an incomplete SMK framework under the condition of random denial-of-service attacks so that the resulting closed-loop system can realize the mean-square stability. By virtue of the upper bound of the sojourn time in each mode, innovative techniques are developed for mean-square stability analysis under an incomplete SMK. Furthermore, an asynchronous SMC scheme is designed to achieve the reachability of the quasi-sliding mode. Finally, the effectiveness is verified using an electronic throttle model.

Resilient and finite‐time H∞$$ {H}_{\infty } $$ control of semi‐Markov jump systems with both upper and lower thresholds of sojourn time

AbstractThis article discusses the finite‐time control problem for a type of discrete‐time semi‐Markov jump systems (SMJSs) with partial unavailable information. A mode‐dependent resilient state feedback control strategy and the incomplete semi‐Markov kernel (SMK) method are applied to stabilize the obtained closed‐loop systems to protect against additive disturbances that can easily occur in the controller. By considering the upper and lower thresholds of sojourn time for each mode, the number of jumps of SMJSs is effectively estimated and new finite‐time bounded related criteria are established, which cover the general case of some previous studies and are more practical in depicting systems. Besides, the performance is further discussed and optimization problems are presented to achieve better closed‐loop performance. At last, a simulation example and a practical example are exhibited to reveal the validity of our raised control strategies and theoretical results.

Asymptotic analysis of the sojourn time of a batch in a M [X]/M/1 processor sharing queue

. In this article, we exploit recent results for the Laplace transform of the sojourn time Ω of an entire batch in the M [ X ] / M / 1 processor sharing queue in order to derive the asymptotic behavior of the distribution function of Ω, namely the behavior of ℙ(Ω > x) when x tends to infinity. Specifically, we show that, up to a multiplying factor, ℙ(Ω > x) has the same order of magnitude as ℙ(ω > x) for large x, where ω is the sojourn time of an arbitrary job in the system. From a practical point of view, this means that if a system has to be dimensioned to guarantee the processing time for jobs, then the system can also guarantee processing times for entire batches by introducing a marginal amount of processing capacity.

Energy-Efficient BWP Configuration for Multi-Slice Users.

Fifth Generation (5G) mobile networks introduce the concept of slicing to ensure isolation among the various supported heterogeneous services. The User Equipment (UE) can be connected to multiple slices simultaneously. Additionally, the notion of a Bandwidth Part (BWP) was also instigated to reduce power consumption. A BWP is a small chunk of the bandwidth scanned by the UE to retrieve its service data. Therefore, a UE connected to multiple services can be configured with multiple BWPs each associated with a given service. Such UEs find themselves scanning multiple BWPs, which can be time consuming and highly energy intensive. Hence, it is paramount to study the appropriate choice of the BWP configuration from an energy-efficiency perspective for multi-slice users depending on their battery level. In this paper, two energy-efficient BWP selection solutions are proposed for users connected to multiple slices. The first solution is based on a centralized approach where UEs are stirred optimally to the best BWP configuration, while the second solution relies on a user-centric distributed approach using non-cooperative game theory. The proposed schemes take into account the users' battery level and their sojourn time in the network as well as the scanned BWP size. Both solutions are compared with one another and against the legacy solution. Intensive simulation results demonstrate the efficiency of our proposition in terms of users' energy efficiency and quality of service.