Absorbing Markov Chain Research Papers (original) (raw)
The paper introduces DILOC, a distributed, iterative algorithm to locate M sensors (with unknown locations) in Rm, m ges 1, with respect to a minimal number of m + 1 anchors with known locations. The sensors and anchors, nodes in the... more
The paper introduces DILOC, a distributed, iterative algorithm to locate M sensors (with unknown locations) in Rm, m ges 1, with respect to a minimal number of m + 1 anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors' locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley-Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors' locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions.
In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still... more
In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise. This paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms. The framework is built on the absorbing Markov chain model of evolutionary algorithms. The first step towards a systematic comparative study among different EAs and their first hitting times has been made in the paper.
We present an algorithm for distributed sensor localization with noisy distance measurements (DILAND) that extends and makes the DLRE more robust. DLRE is a distributed sensor localization algorithm in Rm (m ?? 1) introduced in our... more
We present an algorithm for distributed sensor localization with noisy distance measurements (DILAND) that extends and makes the DLRE more robust. DLRE is a distributed sensor localization algorithm in Rm (m ?? 1) introduced in our previous work (IEEE Trans. Signal Process., vol. 57, no. 5, pp. 2000-2016, May 2009). DILAND operates when: 1) the communication among the sensors is noisy; 2) the communication links in the network may fail with a nonzero probability; and 3) the measurements performed to compute distances among the sensors are corrupted with noise. The sensors (which do not know their locations) lie in the convex hull of at least m + 1 anchors (nodes that know their own locations). Under minimal assumptions on the connectivity and triangulation of each sensor in the network, we show that, under the broad random phenomena described above, DILAND converges almost surely (a.s.) to the exact sensor locations.
This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be... more
This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example.
American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students' final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation... more
American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students' final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a frequentist approach is used. For the standard six-year graduation rate method, the frequentist approach corresponds to counting the number of students who finished their program within six years and dividing by the number of students who entered that year. In the case of absorbing Markov chains, the frequentist approach is used to compute the underlying transition matrix, which is then used to estimate the graduation rate. In this paper, we apply a sensitivity analysis to compare the performance of the standard six-year graduation rate method with that of absorbing Markov chains. Through the analysis, we highlight significant limitations with regards to the estimation accuracy of both approaches when applied to small sample sizes or cohorts at a university. Additionally, we note that the Absorbing Markov chain method introduces a significant bias, which leads to an underestimation of the true graduation rate. To overcome both these challenges, we propose and evaluate the use of a regularly updating multi-level absorbing Markov chain (RUML-AMC) in which the transition matrix is updated year to year. We empirically demonstrate that the proposed RUML-AMC approach nearly eliminates estimation bias while reducing the estimation variation by more than 40%, especially for populations with small sample sizes.
To cope with the increasing demand of wireless communication services multi-carrier systems are being used. Radio resources are very limited and efficient usages of these resources are inevitable to get optimum performance of the system.... more
To cope with the increasing demand of wireless communication services multi-carrier systems are being used. Radio resources are very limited and efficient usages of these resources are inevitable to get optimum performance of the system. Paging channel is a low-bandwidth channel and one of the most important channels on which system performance depends significantly. Therefore it is vulnerable to even moderate overloads. In this paper, an efficient paging algorithm, Concurrent Search, is proposed for efficient use of paging channel in Multi- carrier CDMA system instead of existing sequential searching algorithm. It is shown by the simulation that the paging performance in proposed algorithm is far better than the existing system.
Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. The stronger of... more
Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. The stronger of these forms holds that this is true independent of starting state; the weaker, only for a specified set of starting probabilities. Simple, necessary and sufficient conditions for both forms are developed and applied to several examples.
Abstract- This paper proposes an effective decision support system based on an absorbing Markov, which is used for helping decision makers in Faculty of Computing and Information Technology(FCIT) at King Abdul Aziz University (KAU) in... more
Abstract- This paper proposes an effective decision support system based on an absorbing Markov, which is used for helping decision makers in Faculty of Computing and Information Technology(FCIT) at King Abdul Aziz University (KAU) in controlling student’s flow transition enrollment. Several important controlling criteria that govern student’s flow performance during semesters are evaluated. These include estimating students flow between deferent study levels, the average life time a student spends at each level, the semesters required for graduation, and students graduating probability. A complete performance evaluation comparison between boys and girls at IT College is investigated. Results show that girls achieved better performance than boys. The system has several advantages, such as, helping to find any bottle necks to be solved during students transition study from one semester to another, and helping to know students needed facilities to planning for future required resource...