Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike the right balance between efficiency (operating at a high service rate) and parallelism (preventing small jobs from getting stuck behind large ones). We use the framework of heavy-traffic diffusion analysis to devise near optimal control heuristics for such a queueing system. However, although the literature on diffusion control of state-dependent queueing systems begins with a sequence of systems and an exogenously defined drift function, we begin with a finite discrete PS server and propose an axiomatic recipe to explicitly construct a sequence of state-dependent PS servers that then yields a drift function. We establish diffusion approximations and use them to obtain insightful and closed-form approximations for the original system under a static concurrency limit control policy. We extend our study to control policies that dynamically adjust the concurrency limit. We provide two novel numerical algorithms to solve the associated diffusion control problem. Our algorithms can be viewed as “average cost” iteration: The first algorithm uses binary-search on the average cost, while the second faster algorithm uses Newton-Raphson method for root finding. Numerical experiments demonstrate the accuracy of our approximation for choosing optimal or near-optimal static and dynamic concurrency control heuristics.

Using Facebook Advertisements for Women’s Health Research: Methodology and Outcomes of an Observational Study

Background Recruitment of diverse populations for health research studies remains a challenge. The COVID-19 pandemic has exacerbated these challenges by limiting in-person recruitment efforts and placing additional demands on potential participants. Social media, through the use of Facebook advertisements, has the potential to address recruitment challenges. However, existing reports are inconsistent with regard to the success of this strategy. Additionally, limited information is available about processes that can be used to increase the diversity of study participants. Objective A Qualtrics survey was fielded to ascertain women’s knowledge of and health care experiences related to breast density. This paper describes the process of using Facebook advertisements for recruitment and the effectiveness of various advertisement strategies. Methods Facebook advertisements were placed in 2 rounds between June and July 2020. During round 1, multiple combinations of headlines and interest terms were tested to determine the most cost-effective advertisement. The best performing advertisement was used in round 2 in combination with various strategies to enhance the diversity of the survey sample. Advertisement performance, cost, and survey respondent data were collected and examined. Results In round 1, a total of 45 advertisements with 5 different headlines were placed, and the average cost per link click for each headline ranged from US $0.12 to US $0.79. Of the 164 women recruited in round 1, in total 91.62% were eligible to complete the survey. Advertisements used during recruitment in round 2 resulted in an average cost per link click of US $0.11. During the second round, 478 women attempted the survey, and 87.44% were eligible to participate. The majority of survey respondents were White (80.41%), over the age of 55 years (63.94%), and highly educated (63.71%). Conclusions Facebook advertisements can be used to recruit respondents for health research quickly, but this strategy may yield participants who are less racially diverse, more educated, and older than the general population. Researchers should consider recruiting participants through other methods in addition to creating Facebook advertisements targeting underrepresented populations.

Burden of Chronic Heart Failure in Romania

Chronic heart failure (CHF) affects millions of people across the world, with increasing trends in prevalence, putting ever increasing pressure on the healthcare system. The aim of this study was to assess the financial burden of CHF hospital care on the public healthcare sector in Romania by estimating the number of inpatient episodes and the associated costs. Additionally, societal costs associated with missed work and premature death of CHF patients were also estimated. The national claims database was analyzed to estimate the number of CHF patients. Cost data was extracted from a pool of nine public hospitals in Romania. In 2019, 375,037 CHF patient episodes were identified on specific wards at the national level. The average cost calculated for the selected nine hospitals was EUR 996. The calculated weighted national average cost per patient episode was EUR 1002, resulting in a total cost of EUR 376 million at the national level. The cost of workdays missed summed up to EUR 122 million, while the annual costs associated with the premature death of CHF patients was EUR 230 million. In conclusion, the prevalence of CHF in Romania is high, accounting for a large proportion of hospitalizations, which translates into large costs for the national payer.

On Linear Programming for Constrained and Unconstrained Average-Cost Markov Decision Processes with Countable Action Spaces and Strictly Unbounded Costs

We consider the linear programming approach for constrained and unconstrained Markov decision processes (MDPs) under the long-run average-cost criterion, where the class of MDPs in our study have Borel state spaces and discrete countable action spaces. Under a strict unboundedness condition on the one-stage costs and a recently introduced majorization condition on the state transition stochastic kernel, we study infinite-dimensional linear programs for the average-cost MDPs and prove the absence of a duality gap and other optimality results. Our results do not require a lower-semicontinuous MDP model. Thus, they can be applied to countable action space MDPs where the dynamics and one-stage costs are discontinuous in the state variable. Our proofs make use of the continuity property of Borel measurable functions asserted by Lusin’s theorem.

Dealing With Deadstock: A Case Study of Carnivore Conflict Mitigation From Southwestern Alberta

Livestock deaths are an unfortunate reality for livestock producers and dead livestock (i.e., deadstock) disposal options can have implications beyond the ranch itself. In Alberta, Canada, natural disposal (i.e., disposing of the carcass in a manner that allows for scavenging) has increased since the 2003 detection of bovine spongiform encephalopathy (BSE) in Canadian cattle. Prior to BSE, rendering companies removed deadstock for free. However, rendering companies started charging producers to remove deadstock to offset costs associated with new regulatory requirements enacted by the Canadian Food Inspection Agency, which has resulted in increased on-farm natural disposal of deadstock. This increase has ecological implications because deadstock are a major attractant for large carnivores. Carnivores feeding on deadstock are often near other agricultural attractants such as stored grain and feed, silage, and living livestock, which can exacerbate conflict potential and pose a risk to human safety. To help mitigate conflicts associated with deadstock, the Waterton Biosphere Reserve's (a local non-profit) Carnivores and Communities Program (CACP) supported expansion of community deadstock removal efforts beginning in 2009, including reimbursement of on-farm removal costs, bear-resistant deadstock bins, and a livestock compost facility (operational 2013–2014). Here, we present an evaluative case study describing the development, implementation, and results of the deadstock removal program, including the compost facility. We tracked the number of head of livestock removed each year, the number of participating landowners, the average cost per head, and total program costs. We also used an online survey to assess participants' perspectives of the deadstock removal program and future needs. To date, the CACP has removed >5,400 livestock carcasses, representing between 15.1 and 22.6% of available carcasses in the program area, and 67.3% of livestock owners indicated they currently use the deadstock removal program to dispose of deadstock. Average cost to compost an animal was significantly less than other removal methods ($36.89 composting vs. $79.59 non-composting, one-tailed t-test, unequal sampling variances: t = 4.08, df = 5.87, p = 0.003). We conclude by discussing both ecological and social implications for deadstock removal as a conflict mitigation measure and make suggestions for future management considerations.