Lecture

Modelling Stochastic Communications: Reversible Discrete-Time Markov Chains

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the topic of reversible discrete-time Markov chains, focusing on stochastic models for communications. The instructor explains the concept of stationarity, transition probabilities, and the reversibility property of Markov chains. The lecture also delves into the calculation of probabilities and the conditions for a chain to be reversible.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (21)

Markov chain

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).

Supply chain

A supply chain, sometimes expressed as a "supply-chain", is a complex logistics system that consists of facilities that convert raw materials into finished products and distribute them to end consumers or end customers. Meanwhile, supply chain management deals with the flow of goods within the supply chain in the most efficient manner. In sophisticated supply chain systems, used products may re-enter the supply chain at any point where residual value is recyclable. Supply chains link value chains.

Supply chain management

In commerce, supply chain management (SCM) deals with a system of procurement (purchasing raw materials/components), operations management (ensuring the production of high-quality products at high speed with good flexibility and low production cost), logistics and marketing channels, so that the raw materials can be converted into a finished product and delivered to the end customer.

Demand-chain management

Demand-chain management (DCM) is the management of relationships between suppliers and customers to deliver the best value to the customer at the least cost to the demand chain as a whole. Demand-chain management is similar to supply-chain management but with special regard to the customers. Demand-chain-management software tools bridge the gap between the customer-relationship management and the supply-chain management. The organization's supply chain processes are managed to deliver best value according to the demand of the customers.

Microscopic reversibility

The principle of microscopic reversibility in physics and chemistry is twofold: First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with respect to inversion in time (T-symmetry); Second, it relates to the statistical description of the kinetics of macroscopic or mesoscopic systems as an ensemble of elementary processes: collisions, elementary transitions or reactions.

Related lectures (64)

Stochastic Processes: Time Reversal

Explores time reversal in stationary Markov chains and the concept of detailed balance conditions.

Markov Chains and Applications

Explores Markov chains and their applications in algorithms, focusing on user impatience and faithful sample generation.

Markov Chains and Algorithm Applications

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.

Markov Chains and Algo Applications

Covers Markov chains, Metropolis algorithm, Glauber dynamics, and heat bath dynamics.

Markov Chains: Reversibility & Convergence