CTMCII-beamer - Dealing with Some Assumptions Computation...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Dealing with Some Assumptions Computation of Transition Probabilities Solving the Backward or Forward Equations Introductory Engineering Stochastic Processes, ORIE 3510 Instructor: Mark E. Lewis, Associate Professor School of Operations Research and Information Engineering Cornell University Disclaimer : Notes are only meant as a lecture supplement not substitute! 1/ 19 Dealing with Some Assumptions Computation of Transition Probabilities Solving the Backward or Forward Equations Embedded DTMC has No Self-Loops Explosiveness (no need for finite state space) Embedded DTMC has No Self-Loops We assumed that the embedded DTMC has Q ii = 0. Is this required? Recall we are trying to model a natural phenomenon by CTMCs...and so we would not actually view self loops (it would just stay in the same state at time t ). Just for fun, suppose we want a CTMC from an embedded DTMC with Q ii > 0 for some i and some rates v i for the exponential times between jumps (including self-loops) So the rate at which we see jumps from i to j (for i 6 = j ) should be Q ij v i (as before) But the rate at which actually leave state i is not v i 2/ 19 Dealing with Some Assumptions Computation of Transition Probabilities Solving the Backward or Forward Equations Embedded DTMC has No Self-Loops Explosiveness (no need for finite state space) Embedded DTMC has No Self-Loops We assumed that the embedded DTMC has Q ii = 0. Is this required? Recall we are trying to model a natural phenomenon by CTMCs...and so we would not actually view self loops (it would just stay in the same state at time t ). Just for fun, suppose we want a CTMC from an embedded DTMC with Q ii > 0 for some i and some rates v i for the exponential times between jumps (including self-loops) So the rate at which we see jumps from i to j (for i 6 = j ) should be Q ij v i (as before) But the rate at which actually leave state i is not v i 2/ 19 Dealing with Some Assumptions Computation of Transition Probabilities Solving the Backward or Forward Equations Embedded DTMC has No Self-Loops Explosiveness (no need for finite state space) Embedded DTMC has No Self-Loops We assumed that the embedded DTMC has Q ii = 0. Is this required? Recall we are trying to model a natural phenomenon by CTMCs...and so we would not actually view self loops (it would just stay in the same state at time t ). Just for fun, suppose we want a CTMC from an embedded DTMC with Q ii > 0 for some i and some rates v i for the exponential times between jumps (including self-loops) So the rate at which we see jumps from i to j (for i 6 = j ) should be Q ij v i (as before) But the rate at which actually leave state i is not v i 2/ 19 Dealing with Some Assumptions Computation of Transition Probabilities Solving the Backward or Forward Equations Embedded DTMC has No Self-Loops Explosiveness (no need for finite state space) Embedded DTMC has No Self-Loops We assumed that the embedded DTMC has Q ii = 0. Is this required?...
View Full Document

This note was uploaded on 10/07/2010 for the course ORIE 3510 taught by Professor Resnik during the Spring '09 term at Cornell University (Engineering School).

Page1 / 65

CTMCII-beamer - Dealing with Some Assumptions Computation...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online