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Passenger behavior analysis is a key issue in passenger assignment research, in which the path choice is a fundamental component. A highly complex transit network offers multiple paths for each origin–destination (OD) pair and thus resulting in more flexible choices for each passenger. To reflect a passenger’s flexible choice for the transit network, the optimal strategy was proposed by other researchers to determine passenger choice behavior. However, only strategy links have been searched in the optimal strategy algorithm and these links cannot complete the whole path. To determine the paths for each OD pair, this study proposes the depth-first path generation algorithm, in which a strategy node concept is newly defined. The proposed algorithm was applied to the Beijing metro network. The results show that, in comparison to the shortest path and the K-shortest path analysis, the proposed depth-first optimal strategy path generation algorithm better represents the passenger behavior more reliably and flexibly.

We consider positive zero-sum stochastic games with countable state and action spaces. For each player, we provide a characterization of those strategies that are optimal in every subgame. These characterizations are used to prove two simplification results. We show that if player 2 has an optimal strategy then he/she also has a stationary optimal strategy, and prove the same for player 1 under the assumption that the state space and player 2's action space are finite.

The smart grid technology permits the revolution of the electrical system from a conventional power grid to an intelligent power network which has led the improvements in electrical system in terms of energy efficiency and sustainable energy integration. This study presents the energy management/coordination scheme for domestic demand using the key strategy of smart grid energy efficiency modelling. The structure consists of combining renewable energy resources, photovoltaic (PV) and wind power generation connected to the utility grid with energy storage system (ESS) in an optimal control manner to coordinate the power flow of a residential home. Based on the demand response schemes in the framework of real-time electricity pricing, this work designs a closed-loop optimal control strategy that is created by the dynamic model of the ESS to compute the system performance index, which is formulated by the cost of the energy flows. A dynamic distributed energy storage strategy (DDESS) is implemented to optimally coordinate the energy system, which reduces the total energy consumption from the main grid of more than 100% of the load demand. The designed model introduces a payback scheme while robustly optimising the energy flows and minimising the utility grid's energy consumption cost.

In some cases model-based and model-assisted inferences can lead to very different estimators. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz–Thompson estimator. If the heteroscedasticity of the model is ‚fully explainable’ by the auxiliary variables, then this strategy is also optimal in a model-based sense. Moreover, under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model, the best linear unbiased estimator and the Horvitz–Thompson estimator are equal. Finally, it is possible to construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model.

We consider killed Markov decision processes with uncountable sets of states and controls on finite time interval. We provide definitions of killed Markov decision process, assessment of the path, and optimal strategy and prove the fundamental equation for the case where set of states and set of controls are measurable spaces. We propose a method to construct the optimal strategy and prove the existence of uniformly optimal strategy in the case where set of states and set of controls are separable metric spaces.

In this paper, we study a game called \"Mafia,\" in which different players have different types of information, communication and functionality. The players communicate and function in a way that resembles some real-life situations. We consider two types of operations. First, there are operations that follow an open democratic discussion. Second, some subgroups of players who may have different interests make decisions based on their own group interest. A key ingredient here is that the identity of each subgroup is known only to the members of that group. In this paper, we are interested in the best strategies for the different groups in such scenarios and in evaluating their relative power. The main focus of the paper is the question: How large and strong should a subgroup be in order to dominate the game? The concrete model studied here is based on the popular game \"Mafia.\" In this game, there are three groups of players: Mafia, detectives and ordinary citizens. Initially, each player is given only his/her own identity, except the mafia, who are given the identities of all mafia members. At each \"open\" round, a vote is made to determine which player to eliminate. Additionally, there are collective decisions made by the mafia where they decide to eliminate a citizen. Finally, each detective accumulates data on the mafia/citizen status of players. The citizens win if they eliminate all mafia members. Otherwise, the mafia wins. We first find a randomized strategy that is optimal in the absence of detectives. This leads to a stochastic asymptotic analysis where it is shown that the two groups have comparable probabilities of winning exactly when the total population size is R and the mafia size is of order √R. We then show that even a single detective changes the qualitative behavior of the game dramatically. Here, the mafia and citizens have comparable winning probabilities only for a mafia size linear in R. Finally, we provide a summary of simulations complementing the theoretical results obtained in the paper.

Individuals must often choose among discrete actions with imperfect information about their payoffs. Before choosing, they have an opportunity to study the payoffs, but doing so is costly. This creates new choices such as the number of and types of questions to ask. We model these situations using the rational inattention approach to information frictions. We find that the decision maker's optimal strategy results in choosing probabilistically in line with a generalized multinomial logit model, which depends both on the actions' true payoffs as well as on prior beliefs.

Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait t ∈ in environment e ∈ ε is given by some (fixed) distribution ϒ t,e on ℕ. Then, the phenotypes are attributed using a distribution (strategy) π t,e on the trait space . We look for the optimal strategy π t,e , t ∈ , e ∈ ε, maximizing the net growth rate or Lyapounov exponent, and characterize the set of optimal strategies. This is considered for various models of interest in biology: hereditary versus nonhereditary strategies and strategies involving or not involving a sensing mechanism. Our main results are obtained in the setting of nonhereditary strategies: thanks to a reduction to simple branching processes in a random environment, we derive an exact expression for the net growth rate and a characterization of optimal strategies. We also focus on typical genealogies, that is, we consider the problem of finding the typical lineage of a randomly chosen organism.

Populations of invasive species often spread heterogeneously across a landscape, consisting of local populations that cluster in space but are connected by dispersal. A fundamental dilemma for invasive species control is how to optimally allocate limited fiscal resources across local populations. Theoretical work based on perfect knowledge of demographic connectivity suggests that targeting local populations from which migrants originate (sources) can be optimal. However, demographic processes such as abundance and dispersal can be highly uncertain, and the relationship between local population density and damage costs (damage function) is rarely known. We used a metapopulation model to understand how budget and uncertainty in abundance, connectivity, and the damage function, together impact return on investment (ROI) for optimal control strategies. Budget, observational uncertainty, and the damage function had strong effects on the optimal resource allocation strategy. Uncertainty in dispersal probability was the least important determinant of ROI. The damage function determined which resource prioritization strategy was optimal when connectivity was symmetric but not when it was asymmetric. When connectivity was asymmetric, prioritizing source populations had a higher ROI than allocating effort equally across local populations, regardless of the damage function, but uncertainty in connectivity structure and abundance reduced ROI of the optimal prioritization strategy by 57% on average depending on the control budget. With low budgets (monthly removal rate of 6.7% of population), there was little advantage to prioritizing resources, especially when connectivity was high or symmetric, and observational uncertainty had only minor effects on ROI. Allotting funding for improved monitoring appeared to be most important when budgets were moderate (monthly removal of 13–20% of the population). Our result showed that multiple sources of observational uncertainty should be considered concurrently for optimizing ROI. Accurate estimates of connectivity direction and abundance were more important than accurate estimates of dispersal rates. Developing cost-effective surveillance methods to reduce observational uncertainties, and quantitative frameworks for determining how resources should be spatially apportioned to multiple monitoring and control activities are important and challenging future directions for optimizing ROI for invasive species control programs.

Dengue remains a major public health threat in tropical and subtropical regions. We develop a general human–vector SEIR–SEI optimal‐control framework that integrates four time‐dependent interventions: public awareness/behavioral protection, u1(t) ${{u}_1}( t )$ , enhanced clinical management u2(t) ${{u}_2}( t )$ , adulticide spraying u3(t) ${{u}_3}( t )$ , and larval‐source reduction/larvicide u4(t) ${{u}_4}( t )$ . The controls act by reducing effective human–vector contact, increasing human recovery, increasing adult mosquito mortality, and suppressing vector recruitment, respectively. The objective is to minimize a weighted sum of infectious burden in humans and vectors and the quadratic costs of implementation over a finite horizon, subject to epidemiological dynamics and standard control bounds 0 ≤ ui (t) ≤ 1. Using Pontryagin's Maximum Principle, we derive the necessary conditions for optimality and solve the resulting two‐point boundary value problem numerically. Numerical simulations conducted in MATLAB, calibrated with real data from Bangladesh, perform uncertainty and sensitivity analyses around the basic reproduction number and key transmission, and control parameters reveal that Strategy‐4, which includes public awareness, treatment, and insecticide spraying (u1(t)≠0,u2(t)≠0,u3(t)≠0,u4(t)=0 ${{u}_1}( t ) \\ne 0,\\ {{u}_2}( t ) \\ne 0,\\ {{u}_3}( t ) \\ne 0,{{u}_4}( t ) = 0$ ), is the most effective and cost‐efficient approach. This strategy reduces the time to disease elimination from over 100 days to approximately 74.7 days, achieving a 72.66% faster reduction than natural decay. The findings demonstrate that the proposed control strategies can significantly curb the progression of dengue and support targeted public health interventions to manage outbreaks effectively.