Stochastic%20Processes

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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 Goldratts game.)
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A stochastic process often has the following
structureThe 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 X0 , X1 , X2 ,
provides a mathematical representation of how the
states of the physical system evolves over time.
Stochastic Processes
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Examples of Stochastic Processes

• Scheduling Radar Warning Receivers
• Developing Optimal Geometries/Routing for
  Sweeping Minefields

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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?
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Developing Optimal Geometries/Routing for
Sweeping Minefields

• Develop a route(s) for MCM assets to search a
  specified area in the minimum time.

• Size and shape of search area may change over
  time Previously searched cell may become
  unvisited with probability.

• Stochastic Nature Arrival time is variable
  Cell search time variable Asset may become
  inactive