Sojourn Time Research Articles

Charging scheduling optimisation of battery electric buses with charging setup time

Battery electric buses (BEBs) are recognised as sustainable modes of transportation. Because of its increasing range, efficient and convenient overnight charging has become crucial. The limited number of charging stations and variability in setup times require the optimisation of BEB charging schedules. This study proposes an optimal overnight centralised charging schedule that considers setup time and battery-degradation costs. We model this as a multi-travelling salesman problem with sojourn time to minimise operating costs, including electricity, setup time, and battery wear, while adhering to the bus-schedule constraints. We introduce a local search grouping genetic algorithm with a 2-opt operator local search to address the complexities of public-transport networks. Our extensive numerical analysis, grounded in real-world data, shows a 4.48% reduction in operating costs using our optimised strategy compared with current methods. Moreover, our charging-station allocation analysis provides insights for resource optimisation, advancing sustainable public transport, and charging strategies. This study contributes to the field of sustainable public transportation and charging optimisation.

Embedding and elimination for performance analysis in stochastic process algebra dtsdPBC

ABSTRACT dtsdPBC extends the well-known algebra of parallel processes, Petri box calculus (PBC), by incorporating discrete time stochastic and deterministic delays. To analyze performance in this extended calculus, the underlying semi-Markov chains, and the related (complete) and reduced discrete time Markov chains of the process expressions are built. The semi-Markov chains are extracted using the embedding method, which constructs the embedded discrete time Markov chains and calculates the sojourn time distributions in the states. The reductions of the discrete time Markov chains are obtained through the elimination method, which removes the vanishing states (those with zero sojourn times) and recalculates the transition probabilities among the tangible states (those with positive sojourn times). We prove that the reduced semi-Markov chain coincides with the reduced discrete time Markov chain, by demonstrating that an additional embedding into the reduced semi-Markov chain is needed for the reduced embedded discrete time Markov chain to match the embedded reduced discrete time Markov chain, and by comparing the respective sojourn times.

Design of randomized controlled trials to estimate cancer-mortality reductions from multicancer detection screening.

Determining whether screening with multicancer detection (MCD) tests saves lives requires randomized controlled trials (RCTs). To inform RCT design, we estimated cancer-mortality outcomes from hypothetical MCD RCTs. We used the Hu-Zelen model, previously used to plan the NLST, to estimate mortality reductions, sample-size, and power for 9 cancers for different RCT design parameters and MCD test parameters. Our base-case RCT with 5 yearly screens and 100,000 people ages 60-74 in each arm, who also undergo standard-of-care screens, has 87-89% power to detect an 9-10% mortality reduction (NNS = 578-724) over 7-9 years. The majority of prevented deaths were from lung-cancers (base-case (64-66%) and all sensitivity analyses), 8-10% from colorectal-cancer, and 26% from the other 7-cancers, mostly from stomach/ovary/esophagus (due to excellent stage-1 survival) and less from liver/pancreas (poor stage-1 survival) or head/neck-cancer/lymphoma (excellent stage-4 survival). There was limited power for mortality reductions at most individual cancer sites. Base-case findings were sensitive to test sensitivity, stage-shifts, and mean sojourn times in the preclinical state (especially for lung-cancer), but 90% power could be recovered by recruiting a substantially higher risk population. Large-scale MCD RCTs would have 89% power to detect a ∼10% cancer-mortality reduction over a relatively short 7-9 year timeframe from trial entry. The estimated NNS for MCD RCTs compares favorably to mammographic screening. Most prevented cancer-deaths in a well-powered MCD RCT would likely be from lung-cancer. Non-lung/CRC cancer sites could be a meaningful proportion of prevented cancer-deaths but power is insufficient to isolate non-lung-cancer mortality reductions.

Impact of screening on mortality for patients diagnosed with hepatocellular carcinoma at a safety-net hospital: An opportunity for addressing disparities.

140 Background: Hepatocellular carcinoma (HCC) is a common and deadly cancer with a rising incidence in the US. HCC almost always develops on a background of chronic liver disease, which disproportionately affects individuals of lower socioeconomic status (SES), perpetuating existing disparities. Compounding these disparities, individuals of lower SES are less likely to participate in recommended cancer screening exams. Here, we describe the outcomes of patients diagnosed with HCC at a large urban safety-net hospital primarily serving the underserved. Methods: We identified patients diagnosed with HCC at John Peter Smith Hospital in Fort Worth, Texas from January 1, 2018, to March 31, 2021 to determine the impact of screening on survival. Patients were allocated to the screened cohort if they had undergone liver imaging within one year prior to HCC diagnosis. Kaplan-Meier methods and log-rank test were used to illustrate and compare 3-year survival curves from an index date of diagnosis until death. Cox proportional hazards model were used to calculate unadjusted and adjusted hazards ratios (HR) and 95% confidence intervals (CI). Lead time bias was adjusted in a sensitivity analysis using the Duffy adjustment and a sojourn time of 70 days and 140 days. Results: A total of 158 patients were included (n=53 screened, n=105 unscreened). The mean age was 62 years; 144 (91%) had cirrhosis, 78% were male, 34% were non-Hispanic white, and 8.2% had private insurance. Those in the unscreened cohort had more severe liver dysfunction (as measured by the ALBI grade) and produced higher levels of AFP, but were less likely to have cirrhosis than the screened cohort. The median overall survival (OS) for the screened cohort was 19.0 months (95% CI: 9.9-NA) and 5.4 months (95% CI: 3.7-8.5) in the unscreened cohort (HR death (unscreened v screened) = 2.4, 95% CI: 1.6-3.6; log rank P <0.0001). After adjusting for ALBI grade, AFP, hepatitis C, insurance status and initial treatment, there was a statistical difference in hazard of death in the three years (HR: 2.3; 95% CI: 1.5-3.6), favoring the screened cohort. The benefit for screening remained after adjusting for lead-time bias. With a mean sojourn time of 70 days, the HR death was 2.19 (95% CI 1.4-3.3, P =0.0002) and was 2.09 (1.4-3.2, P =0.0005) with a 140-day sojourn time. Conclusions: In an urban safety-net population, screening for HCC was associated with improved outcomes compared to patients with incidentally-diagnosed HCC. Altogether, this implies that earlier diagnosis and institution of treatment can positively improve survival for patients with newly diagnosed HCC in a population of patients evaluated at a safety-net hospital. Development of screening programs in accordance with accepted guidelines with outreach to high-risk individuals represents an area of high value care for safety-net hospitals.

Prognostic Factors for Recurrence And Survival of Patients with Breast Cancer Using A Multi-state Model

Background: In many medical studies, patients may experience various events. The analysis in such studies is often administrated using multi-state models. The current study aimed to investigate the effect of risk factors and transition probability on recurrence and death in patients with breast cancer. Materials and Methods: This study was a retrospective cohort study on 814 women with breast cancer admitted to Shahid Ramezanzadeh Radiotherapy Center in Yazd province in Iran between the years 2004 -2012 and were followed until 2016. A multi-state model is applied for data analysis in the R 3.4.1 programming language. Results: Of the 814 patients, 40(5%) experienced recovery after initial treatment and 177(20.7%) experienced the death after initial treatment. For the first year, the transition probabilities from the initial treatment to recovery were estimated at 1.4%, to death was 17% and for recovery to death, it was 29%. The mean sojourn times were estimated as 2.93 and 9.8 years for the treatment and recovery, respectively. Conclusion: Multi-state models predict the transition probabilities in different states of disease, in addition, transition probabilities, mean sojourn time, and hazard ratio in each state can help physicians find suitable care for patients with breast cancer.

The Epstein-Barr Virus Nuclear Antigen 1 Variant Associated with Nasopharyngeal Carcinoma Defines the Sequence Criteria for Serologic Risk Prediction.

Antibodies to select Epstein-Barr virus proteins can diagnose early-stage nasopharyngeal carcinoma (NPC). We have previously shown that IgA against Epstein-Barr virus nuclear antigen 1 (EBNA1) can predict incident NPC in high- and intermediate-risk cohorts 4 years before diagnosis. Here, we tested EBNA1 variants, with mutants, to define the sequence requirements for an NPC risk assay. Mammalian-expressed constructs were developed to represent EBNA1 variants 487V and 487A, which can differ by ≥15 amino acids in the N- and C-termini. Denatured lysates were evaluated by a refined IgA and IgG immunoblot assay in a case-control study using prediagnostic NPC sera from two independent cohorts in Singapore and Shanghai, the People's Republic of China. At 95% sensitivity, 487V yielded a 94.9% specificity compared with 86.1% for 487A. EBNA1 deleted for the conserved glycine-alanine repeats (GAr) reduced false positives by 22.8%. NPC sera reacted more strongly to the C-terminus than healthy controls, but the C-terminal construct (a.a. 390-641) showed lower specificity (84.8%) than the EBNA1 GAr-deleted construct (92.4%) at 95% sensitivity. Although EBNA1 IgA was present in healthy sera, most epitopes localized to the immunodominant GAr. We conclude that a refined EBNA1 antigen deleted for the GAr, but with residues consistently detected in Southeast Asian NPC tumors, is optimized for risk prediction with an extended sojourn time of 7.5 years. Furthermore, distinct EBNA1 serologic profiles enhanced the utility of the EBNA1 IgA assay for risk stratification. This illustrates the importance of serologically relevant EBNA1 sequences for NPC risk prediction and early detection.

Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers

Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers

Double‐sided queues and their applications to vaccine inventory management

AbstractWe consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.

Attack-compensated asynchronous output feedback control for stochastic switching systems with sojourn probability

This study addresses the problem of attack-compensated asynchronous output feedback control for stochastic switching systems with sojourn probability. Unlike traditional Markov/semi-Markov models that rely on transition probabilities, a novel switching rule is introduced that focuses on sojourn probability information associated with the target mode and sojourn time, which are easier to obtain than the well-known transition probabilities. Considering the vulnerability of stochastic switching systems to cyber-attacks, where the system state becomes unobservable and difficult to manage, a compensation-based output feedback controller framework is proposed. Using the Lyapunov method and stochastic analysis, sufficient conditions are provided to ensure system stability. Finally, the effectiveness and applicability of the developed approach are demonstrated using an F-404 aircraft engine system model.

Reliability and availability analysis of high-altitude platform stations through semi-Markov modeling

In the development and deployment of both tethered and autonomous High Altitude Platform Station (HAPS), flight modules such as hexacopter and octocopter with 6 or 8 rotors are most often used. The primary focus of this article is to compute the reliability of tethered HAPS by analyzing the effectiveness of their redundant rotor systems. To measure the performance of such systems, it is convenient to consider mathematical models as k-out-of-n models. Although Markov models have extensively been reported to analyze the reliability of repairable k-out-of-n models, this work introduces an alternative and more thorough methodology. In this work, a semi-Markov model (SMM) is proposed to calculate the probability of rotors being operational after the failure of some rotors in order to analyze system reliability. We emphasize that an SMM model is more appropriate as it provides a more accurate assessment of the probability of system failure over time through non-exponential sojourn time. Further, the efficacy of the proposed SMM is studied through the evaluation of steady-state availability, mean time to failure and reliability. Overall, the findings of this study enhance our comprehension of the reliability of repairable systems and extend the existing knowledge base of HAPS reliability analysis.

A comparative study of numerical methods for reliability assessment based on semi-Markov processes

The semi-Markov process, renowned for its versatile applications, has garnered significant attention in recent years. However, deriving closed-form expressions for computing reliability metrics proves challenging when sojourn times deviate from exponential distributions. This paper investigates three numerical techniques for computing the transition function matrix of the semi-Markov process, including the algebraic method, the truncated method, and the iterative method. It delves into their truncation and discretization errors, as well as their computational complexities. Additionally, the Laplace-based method and the semi-Markov-chain-based method are discussed to contrast their effectiveness with the three devised numerical approaches. Building on the linkage between the Markov renewal equation and system reliability metrics, five computational methods are applied to the evaluation of system reliability and availability. A case study on sequential cyber-attacks is presented to illustrate the applicability of these methods, considering sojourn times that follow exponential, gamma, lognormal, and Weibull distributions respectively. The results reveal that the three proposed numerical methods not only achieve high precision and rapid speed but also address scenarios beyond the capability of the Laplace-based method.

Using multistate models with clinical trial data for a deeper understanding of complex disease processes.

A clinical trial represents a large commitment from all individuals involved and a huge financial obligation given its high cost; therefore, it is wise to make the most of all collected data by learning as much as possible. A multistate model is a generalized framework to describe longitudinal events; multistate hazards models can treat multiple intermediate/final clinical endpoints as outcomes and estimate the impact of covariates simultaneously. Proportional hazards models are fitted (one per transition), which can be used to calculate the absolute risks, that is, the probability of being in a state at a given time, the expected number of visits to a state, and the expected amount of time spent in a state. Three publicly available clinical trial datasets, colon, myeloid, and rhDNase, in the survival package in R were used to showcase the utility of multistate hazards models. In the colon dataset, a very well-known and well-used dataset, we found that the levamisole+fluorouracil treatment extended time in the recurrence-free state more than it extended overall survival, which resulted in less time in the recurrence state, an example of the classic "compression of morbidity." In the myeloid dataset, we found that complete response (CR) is durable, patients who received treatment B have longer sojourn time in CR than patients who received treatment A, while the mutation status does not impact the transition rate to CR but is highly influential on the sojourn time in CR. We also found that more patients in treatment A received transplants without CR, and more patients in treatment B received transplants after CR. In addition, the mutation status is highly influential on the CR to transplant transition rate. The observations that we made on these three datasets would not be possible without multistate models. We want to encourage readers to spend more time to look deeper into clinical trial data. It has a lot more to offer than a simple yes/no answer if only we, the statisticians, are willing to look for it.

Evaluation of readiness of the technical system using the semi-Markov model with selected sojourn time distributions

Mechanization of forestry work is crucial in forest management, and the specific nature of the tasks performed requires reliable machines with a high level of technical readiness. Therefore, models describing the exploitation process of multi-operational machines used to obtain wood raw materials, and especially assessing the level of their technical readiness, are extremely important. For multi-tasking objects performing random activities in given time intervals, calculating readiness measures is a complex issue. Forecasting subsequent operational states and their durations allows to predict the behavior of technical objects and schedule work. In addition to identifying the sequence of states, it is also important to identify the sojourn time in these states. This article presents a method for identifying the semi-Markov process and then assessing the technical readiness of a Harvester machine. This allowed for conclusions regarding the timely completion of assigned tasks, and also made it possible to adjust the activities carried out to the requirements of forest management.

Guaranteed cost control for a class of composite hybrid aerial/terrestrial precise manipulator with stochastic switching payloads

AbstractThis article investigates the modeling and attitude control of a class of composite hybrid aerial/terrestrial precise manipulator (Chat‐PM) with stochastic switching payloads when attaching to a vertical surface. The dynamics of the Chat‐PM for aerial locomotion are modeled by transferring the force and moment of the end‐effector to the body based on the recursive Newton–Euler equations. Furthermore, the attitude dynamics of the Chat‐PM under the wall‐attachment condition is obtained by limiting the attitude angle/angular velocity and introducing the friction torque acting on the passive wheels for the first time. Taking into consideration the complexity of the task and the stochastic nature of environmental changes, the payload attached to the end‐effector is modeled as a continuous‐time Markov process with mode‐dependent fixed sojourn time in this study. The proposed guaranteed cost controller results in the Chat‐PM capable of stably attaching to a wall under random switching loads, while guaranteeing the quadratic performance cost with an attainable upper bound. Additionally, a convex‐optimization‐based guaranteed cost controller is proposed to optimize the performance cost in the random switching part. Finally, the effectiveness of the proposed guaranteed cost controllers is demonstrated by illustrative examples.

Estimating sojourn time and sensitivity of screening for ovarian cancer using a Bayesian framework.

Ovarian cancer is among the leading causes of gynecologic cancer-related death. Past ovarian cancer screening trials using combination of cancer antigen 125 testing and transvaginal ultrasound failed to yield statistically significant mortality reduction. Estimates of ovarian cancer sojourn time-that is, the period from when the cancer is first screen detectable until clinical detection-may inform future screening programs. We modeled ovarian cancer progression as a continuous time Markov chain and estimated screening modality-specific sojourn time and sensitivity using a Bayesian approach. Model inputs were derived from the screening arms (multimodal and ultrasound) of the UK Collaborative Trial of Ovarian Cancer Screening and the Prostate, Lung, Colorectal and Ovarian cancer screening trials. We assessed the quality of our estimates by using the posterior predictive P value. We derived histology-specific sojourn times by adjusting the overall sojourn time based on the corresponding histology-specific survival from the Surveillance, Epidemiology, and End Results Program. The overall ovarian cancer sojourn time was 2.1 years (posterior predictive P value = .469) in the Prostate, Lung, Colorectal and Ovarian studies, with 65.7% screening sensitivity. The sojourn time was 2.0 years (posterior predictive P value = .532) in the United Kingdom Collaborative Trial of Ovarian Cancer Screening's multimodal screening arm and 2.4 years (posterior predictive P value = .640) in the ultrasound screening arm, with sensitivities of 93.2% and 64.5%, respectively. Stage-specific screening sensitivities in the Prostate, Lung, Colorectal and Ovarian studies were 39.1% and 82.9% for early-stage and advanced-stage disease, respectively. The histology-specific sojourn times ranged from 0.8 to 1.8 years for type II ovarian cancer and 2.9 to 6.6 years for type I ovarian cancer. Annual screening is not effective for all ovarian cancer subtypes. Screening sensitivity for early-stage ovarian cancers is not sufficient for substantial mortality reduction.

A study on N-policy BMAP/G/1 queueing system

This study presents a simple approach for analyzing the BMAP/G/1 queueing system under N policy. In this policy, the server goes idle at the end of a busy period and the queue length is checked at every arrival moment. The idle server starts serving customers when the queue length reaches or above a predetermined number, namely N, and keeps doing so until the system is completely empty. We first use a simple sequential substitution approach to derive the system length distribution at departure epoch. A comparative study is also conducted to highlight the benefits and strength of our straightforward approach to that of the RG-factorization technique and the roots finding method. We extract the distribution of system length at a random time point by utilizing the remaining service time of a customer who is currently being served as the supplementary variable. The probability density function of the sojourn time distribution for an arbitrary customer of an incoming batch is also computed. We propose an expected linear cost function to estimate the optimal value of N at minimum cost. The validity of our analytic technique has been shown through a variety of numerical examples involving different service time distributions.

Degradation modeling and remaining life prediction of multi-state long-life systems under random environmental influences

Abstract For large-scale systems such as bridges, which have long operating lifetimes, the operating states are usually categorized into multiple levels, and they are also subjected to various random environmental influences during operation. However, due to the significant granularity in the categorization of system states, it is difficult to assess the system state transitions influenced by random environmental factors, which compromises the accuracy of remaining life predictions. In this study, we focus on long-life systems with multiple states and investigate the degradation modeling and remaining life prediction considering the impact of random environmental factors. The system degradation process, based on the semi-Markov process and multi-state modeling, was decomposed into states using the sub-exponential approximation method. A state transition probability model considering exponential environmental influences was constructed. Furthermore, based on the developed model for calculating the distribution of sojourn times in multiple states, a reliability and remaining life prediction model for the system was derived. By taking the bridge deck as a case study, the verification and analysis of remaining life prediction for the bridge deck were conducted under the influences of average daily traffic volume and bridge age. The results indicate that both the average daily traffic volume and bridge age have a significant impact on the degradation of the bridge deck. The relative error of the predicted results considering the above effects falls within the range of 1.77%–12.18%.

Anti‐modal‐asynchrony sliding mode control for semi‐Markov jump systems

AbstractThis article investigates the issue of anti‐modal‐asynchrony sliding mode control (SMC) for discrete semi‐Markov jump systems with bi‐boundary sojourn time. Asynchronous mechanism refers to the mismatch phenomenon between the system mode and the controller mode, in which the modal lag is mode‐dependent to reduce some conservatism compared with traditional mode‐independent lag. In contrast to traditional semi‐Markov jump systems, the sojourn time of each mode in this article is considered to have upper‐and‐lower bounds, representing better characteristics than the upper bound. Based on the semi‐Markov kernel and the Lyapunov function related to the elapsed time of current mode, a sufficient condition is proposed to ensure that the mean‐square stability of the underlying system is achieved under an equivalent SMC mechanism. The conditions for the existence of the designed controller are obtained, which shows that the constructed SMC mechanism is effective against asynchronous mode jumps. An anti‐modal‐asynchrony SMC mechanism is constructed to achieve the reachability of discrete quasi‐sliding mode. Finally, the F‐404 aircraft engine model is given to validate the effectiveness of the control strategy.

Analysis of a Stochastic Model on Human Heart Considering its Failures and Treatments in Different Progression Stages

The goal of the present paper is to analyze the performance of a human heart considering failures of heart in different stages and their treatments. The aim of heart treatments is to progress through the stages or to slow down the progression from one stage to another. The artificial replacement of the heart is also possible these days. Keeping this in view, a stochastic model has been developed and investigated. The analysis of the model in terms of its performance measures is carried out on the basis of Markov process and regenerative point technique. Various conclusions are drawn on the basis of graphical study.. KEYWORDS :Human heart, Mean sojourn time, Mean time to system failure, Survivability, Regenerative point technique.

Strategic Queueing Behavior of Two Groups of Patients in a Healthcare System

Long waiting times and crowded services are the current medical situation in China. Especially in hierarchic healthcare systems, as high-quality medical resources are mainly concentrated in comprehensive hospitals, patients are too concentrated in these hospitals, which leads to overcrowding. This paper constructs a game-theoretical queueing model to analyze the strategic queueing behavior of patients. In such hospitals, patients are divided into first-visit and referred patients, and the hospitals provide patients with two service phases of “diagnosis” and “treatment”. We first obtain the expected sojourn time. By defining the patience level of patients, the queueing behavior of patients in equilibrium is studied. The results suggest that as long as the patients with low patience levels join the queue, the patients with high patience levels also join the queue. As more patients arrive at the hospitals, the queueing behavior of patients with high patience levels may have a negative effect on that of patients with low patience levels. The numerical results also show that the equilibrium behavior deviates from a socially optimal solution; therefore, to reach maximal social welfare, the social planner should adopt some regulatory policies to control the arrival rates of patients.