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This paper presents a cooperative, combinatorial search model for a multi-mobile sensor, multi-mobile target scenario in a two dimensional grid space. In the proposed model, sensors and targets act as searchers and hiders of a search game. A search game is a game between searcher and hider, modeled on a graph. In this paper, the identified problem...
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During epidemics, the population is asked to Socially Distance, with pairs of individuals keeping two meters apart. We model this as a new optimization problem by considering a team of agents placed on the nodes of a network. Their common aim is to achieve pairwise graph distances of at least D, a state we call socially distanced. (If D=1, they wan...
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... The past data of the players' action patterns is studied to gain information and learn about the behaviour of actions (Douglas 2007; Hazra et al. 2017). Assume that the strategy M for P 1 at a particular position remains unchanged without taking into consideration the strategy of P 2 in the same position in several cases. ...
Game theory has recently drawn the attention of researchers from various research communities due to its diverse applications, which include modelling of real-world scenarios. The paper presented here introduces a bridge game for two players and analyses their interactions. The proposed work demonstrates that the payoffs of the players and the outcomes of the game are affected by the nature of the opponent. Furthermore, the presented work demonstrates that the outcome of the game is dependent on insufficient prior knowledge about the respective opponents. The paper emphasises and illustrates how the payoffs of the players change as the strategy mixing probabilities change. The paper also redefines the problem by concealing the identity of the opponent and analyses it using the Bayesian game model. The players’ behavioural changes over time are also mathematically analysed. Furthermore, the paper emphasises that strategies can be improved by learning and gaining information based on available data. The bridge game’s applications in real-world scenarios are also demonstrated in the paper. The paper focuses on the game’s applications in dealing with security issues in communication systems and race conditions in operating systems. To the best of our knowledge, no scientific study has ever examined bridge games by examining the behaviour of the players. There is no existing literature that shows how games can be used to model real-world scenarios. This presented work also establishes four theorems.
... This developed model also generates results which are more reliable than comparable models, due to its capability of random walk in transition matrix and memoryless property. This viewpoint is also consisted with the earlier findings of Piccardi et al. [36], Hazra et al. [37], and Tserenjigmid [38]. Collectively, this study outlines a critical role in developing a model that provides a comprehensive yet simple prediction, which can help solve complicated forecasting problems. ...
A Markov chain is commonly used in stock market analysis, manpower planning, and in many other areas because of its efficiency in predicting long run behavior. However, the Air Quality Index (AQI) suffers from not using a Markov chain in its forecasting approach. Therefore, this paper proposes a simple forecasting tool to predict the future air quality with a Markov chain model. The proposed method introduces the Markov chain as an operator to evaluate the distribution of the pollution level in the long term. Initial state vector and state transition probability were used in forecasting the behavior of Air Pollution Index (API) that has been obtained from the observed frequency for one state shift to another. The study explores that regardless of the present status of API, in the long run, the index shows a probability of 0.9231 for a good state, and a moderate and unhealthy state with a probability of 0.0722 and 0.0037, while for very unhealthy and hazardous states a probability of 0.0001 and 0.0009. The outcome of this study reveals that the model development could be used as a forecasting method that able to help government to project a prevention action plan during hazy weather.
... At the same time, the self-propelled particle systems are close to the mobile robot systems that can be equipped with artificial intelligence. To describe the dynamics of the mobile robot systems, the models of differential games [Alspach 2004;Chung et al. 2011;Galceran and Carreras 2013], random graph models [Hazra et al. 2018;2017a;2017b], which underlie many artificial intelligence systems, etc., are used. Within these model frameworks, different problems are solved: determination of the shortest trajectory of a robot or a group of robots which covers the entire field of vision [Alspach 2004; Galceran and Carreras 2013], searching for the minimum number of robots that guarantee the capture [Chung et al. 2011], and many others. ...
... By applying Markov chain, the following set of equations is formulated to compute the state vectors in each time step (Hazra et al., 2017). ...
... Accordingly, T computes searchers' existence probabilities of the neighbour blocks and explores the one which has minimum searchers' existence probability. Now let us assume that q number of searchers are likely to share a block with non-zero searchers' existence probabilities in a particular time-step, where the individual existence probabilities for those searchers are represented as p 1 , p 2 ,…, p q , respectively, then, mutual searchers' existence probabilities (Hazra et al., 2017) in that particular block can be formulated as follows. ...
... By applying Markov chain, the following set of equations is formulated to compute the state vectors in each time step (Hazra et al., 2017). ...
... Accordingly, T computes searchers' existence probabilities of the neighbour blocks and explores the one which has minimum searchers' existence probability. Now let us assume that q number of searchers are likely to share a block with non-zero searchers' existence probabilities in a particular time-step, where the individual existence probabilities for those searchers are represented as p 1 , p 2 ,…, p q , respectively, then, mutual searchers' existence probabilities (Hazra et al., 2017) in that particular block can be formulated as follows. ...
Target searching is widely accepted as a significant area of study by various research communities. This paper addresses four target searching scenarios in a two-dimensional grid with obstacles, where multiple mobile sensors aim to search a single mobile target in a minimal time. The reachability condition of the target is checked before modelling the problem. The proposed work classifies the scenarios based on information-set available to the mobile sensors and the target. The scenarios are modelled as games that involve two adversary players: mobile sensor and target. The search strategies for the mobile sensors are formulated under different circumstances, and the strategic differences between cooperative and non-cooperative strategies are analysed. Later, the proposed work is extended in a new dimension, where information gain for the mobile sensors is determined by information refreshment interval. The proposed work helps the decision makers by facilitating the search operation in different scenarios.
... Number of players A game can have two or more than two players. The problems discussed in this paper can be modeled for different scenarios: SS-ST, single searchermultiple target (SS-MT), multiple searcher-single target (MS-ST) and multiple searchermultiple target (MS-MT) [34], but in our proposed models, the games are played between two players: S and T. Therefore, the problem represents as an SS-ST problem. ...
Target searching is one of the challenging research areas which finds applications in many critical real-time scenarios. The modeling and analysis play a vital role to solve real-time problems. This paper addresses a number of grid-based target searching problems in a single searcher-single target environment applicable to real-time scenarios and various approaches are introduced for modeling and analyzing the problems. The solutions derived from the proposed approaches facilitate the understanding of the problems in detail. We have initially, modeled and analyzed the problems as an extensive-form game and a normal-form game, by deducing appropriate strategies for the respective players (searcher and target) along with expected payoffs. In the paper, a mobile sensor and a mobile object play the role of a searcher and a target, respectively. Later, the problem is viewed from a different dimension by representing it as a state transition diagram and a finite automaton to highlight the differences resulting from varying activities of the searcher and the target. This is further extended to key-based target searching with an aim to minimize the search time. In this paper, we have highlighted few real-time target searching problems similar to the identified problems in the conclusion.
For a productive and healthy life, air quality plays an important role. This paper addresses the requirements to develop a system capable of providing real-time information, predictions, and alerts about the indoor environment using context-awareness. The proposed IoT system serves for data collection, pre-processing, defining rules, and forecasting the predicting states of the indoor environment by giving information to the end-user about the alerts and recommendations. A novel approach based on the indoor pollutants T, RH, CO2, PM 2.5, PM 10, and CO for the determination of the status of the environment is proposed. The pre-processing is used for filtering data using and extended Kalman filter. Further, the system uses an adaptive neuro-fuzzy inference system (ANFIS) and discrete-time Markov chains (DTMC) to predict the state of the indoor environment with the help of daily air pollution concentrations and environmental parameters. The ANFIS model predictor considers the value of indoor pollutants to form a new index: State of indoor air (SIA). For analysis and forecasting of the new index SIA, the DTMC model is used. The collected and measured data is stored in the IoT cloud using the sensing setup, and sensed information is used to develop the SIA transfer matrix, generating return durations corresponding to each SIA and providing alerts based on the data to the end-user. The models are assessed using the expected and actual return durations. The most frequent interior ventilation states, according to the predictions, are poor and moderate. Only 0.08 percent of the time does the IAQ remain in a good state. Two-thirds of the time (66%), the indoor ventilation is severe (poor, very poor, or hazardous); 19% of the time it is very bad, and 15% of the time it is hazardous, suggesting and warning that there is a very high probability of unhealthy AQI in educational institutions in the Delhi-NCR region. Performance is measured by the comparison between actual and forecasted return periods, and the forecast error for our system is low, with an absolute forecast error of 3.47% on an average.
In this article, we present a unique search game model to search/hide an immobile object by/from a mobile sensor in a two-dimensional bounded space. In the proposed model, the mobile sensor is a searcher, the immobile object is a target and the search space is a square/rectangular region. The proposed model is suitable for the case where the searcher has no prior knowledge about the probability distribution of the target location in the region. The game model helps the players (searcher and target) to choose their best response strategies considering all possible strategies of their respective opponents and computes the expected payoffs and Nash Equilibrium of the game. The novelty of the proposed model is to guide both the players to choose their best response strategies. The proposed model is set up as follows: Initially, the search space which is a square/rectangular region is divided into square blocks of equal size to represent it as a grid and the distance is measured from the starting block of the searcher to all other blocks using shortest path followed by which the transition probabilities of each block is determined. Once the payoff matrix is obtained, we use lrslib tool to compute the mixed strategies, Nash equilibria and expected payoffs. The proposed model is applicable in real-time scenarios which involve large square/rectangular grids where the number of blocks is large.
