Stochastic Processes Definition A stochastic process is defined

Stochastic Processes Definition: A stochastic process is defined to be an indexed collection of random variables {Xt}, where the index t runs through a given set T. Often T is taken to be the set of non-negative integers, and Xt represents a measurable characteristic of interest at time t. (example: Xt – size of queue between machine 3 and 4 in Goldratt’s game. )

Stochastic Processes A stochastic process often has the following structure: The current status of the system can fall into any one of M + 1 mutually exclusive categories called states. For notational convenience, these states are labeled 0, 1, …. . , M. The random variable represents the state of the system at time t, so its only possible values are 0, 1, …. , M. The system is observed at particular points of time, labeled t = 0, 1, 2, …. Thus, the stochastic process {Xt} = {X 0 , X 1 , X 2 , …} provides a mathematical representation of how the states of the physical system evolves over time.

Examples of Stochastic Processes • Scheduling Radar Warning Receivers • Developing Optimal Geometries/Routing for Sweeping Minefields

Scheduling Radar Warning Receivers PROBLEM STATEMENT § Develop an RWR scheduler that minimizes the time to detect multiple threats across multiple frequency bands. Stochastic Nature – What is the initial angle/time offset for each of the threats?

Developing Optimal Geometries/Routing for Sweeping Minefields § Develop a route(s) for MCM assets to search a specified area in the minimum time. Stochastic Nature: • Arrival time is variable • Cell search time variable • Asset may become inactive • Size and shape of search area may change over time • Previously searched cell may become “unvisited” with probability.