# Markov decision process

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to the arrival and service processes, one defines a so called network process {E (t), t≥0} on a finite space {1, 2…3} with instantaneous transition rates Sij, 1≤ i ≠ j≤ m. The node controls the arrival and service processes as follows: Suppose time t is such that E(t) = j, then the arrival rate is λj and the service rate is µj, provided that the server is busy at time t. Consider the whole system is a two dimensional time Markov chain { N(t), E(t), t≥0} on the state space { (n, i); n≥0, 1≤i≤m}, where

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Markov Chains Game Introduction Probabilistic reasoning goes a long way in many popular board games. Abbott and Richey [1] and Ash and Bishop [2] identify the most portable properties in Monopoly and Tan [3] derives battle strategies for RISK. In RISK, the stochastic progress of a battle between two players over any of the 42 countries can be described using a Markov Chain. Theory for Markov Chains can be applied to address questions about the probabilities of victory and expected losses in battle

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Given an MDP, the total reward in future may be computed as R = r1 + r2 + …. rn But, future rewards are uncertain and needs to be discounted to ascertain their present value as: R = rt+1 + rt+2 + … rt+n = rt + ɣ *rt+1 + …. + ɣ(n-t) *rn, where discount factor ɣ is in the range of [0, 1] The agent learning is primarily based on maximizing discounted value of all future rewards. Owing to the uncertainty in future, estimation of this value for agent learning is not easy. A popular approach is to use

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simulations combine stochastic modelling and geo-statistics to improve characterization of geospatial phenomena. The behaviour of these can be described by different types of processes such as Poisson and renewal, discrete-time and continuous time Markov processes, Brownian processes and diffusion. 3.1.3 Deterministic VS Stochastic models With Deterministic models the outcome is always assumed to be certain if the input is fixed then regardless of the number of times one may re-calculate its always

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Chance nodes (circles) depict the possible consequence – positive or negative – of the decision. They are referred to as transition states. Transition probabilities are assigned to each transition state and they must always sum to one. Triangles indicate the point at which the analysis ends and the health impact and/or costs of each consequence is quantified. When decision tree analysis is done at the same time as the clinical trial, the payoff may also be expressed as utilities

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MODELING CUSTOMER RELATIONSHIPS AS MARKOV CHAINS Phillip E. Pfeifer Robert L. Carraway f INTRODUCTION The lifetime value of a customer is an important and useful concept in interactive marketing. Courtheaux (1986) illustrates its usefulness for a number of managerial problems—the most obvious if not the most important being the budgeting of marketing expenditures for customer acquisition. It can also be used to help allocate spending across media (mail vs. telephone vs. television), vehicles

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working on this principle: 1.4.1 Markov Model Markov models are very commonly used in the identification of patterns based on the sequence of previously accessed pages [3] [4]. They are the natural candidates for sequential pattern discovery for link prediction due to their suitability to modeling sequential processes. The Markov model process calculates the probability of the page the user will visit next after visiting a sequence of Web pages in the same session. Markov model implementations have been

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Classification of dynamic games according to the level of information available. Information plays a crucial role in Game theory. The high level of importance is due to the fact that it provides us with an outline for different possible strategies that the players might undertake. 4.1. Dynamic Games with Complete Information Complete information implies that each agent knows both the strategies and returns of the other agents participating in the game but they may be not be aware of the particular

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stimuli. For the reason that companies use various marketing activities to attract and influence the consumer’s decision process, marketing stimuli includes the 4P’s being also affected by other forces that play an important part in shaping the purchase decision. Economic, political, cultural, and technological stimuli have a huge influence besides the buyer characteristics and the decision process. Ultimately, the consumer ends up with a response to determine the product, brand, and dealer choices, besides

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A Markov Chain Study on Mortgage Loan Default Stages Ying-Shing Lin, PhD Associate Professor, Dept. of Accounting Information Systems. National Kaohsiung First University of Science and Technology e-mail:yslin@nkfust.edu.tw (NKFUST) Sheng-Jung Li, PhD Assistant Professor, Dept. of Finance Shu-Te University e-mail:botato@stu.edu.tw Shenn-Wen Lin PhD Candidate National Kaohsiung First University of Science and Technology e-mail:059180@landbank.com.tw September, 2012 Abstract Shifting

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