Modelling Stochastic Communications: Reversible Discrete-Time Markov Chains

In course

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.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_gxo2hy66

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (21)

Related concepts (21)

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).

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.

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 (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.

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.