October 9, 2017 –
Title: Linear Algebraic Methods in RESTART Failure Problems in Markovian Systems
Student: Stephen Thompson
Major Advisor: Dr. Robert McCartney
Associate Advisors: Dr. Lester Lipsky, Dr. Swapna Gokhale
Date/Time: Thursday, October 5th, 2017 at 11:30 am in Babbidge 1947 meeting room
Consider a task with ideal execution time T such as the transmission of information on a data link or the machining of a 3D object that is subject to failure. When a system fails during execution of a task there are three general scenarios of recovery protocols: RESUME, REPLACE and RESTART. RESUME is where the task is continued from the point of failure once the system has been repaired. No work is lost and the task characteristics remain the same. REPLACE discards the work so far and starts from scratch, thereby replacing everything. The work is lost and the task characteristics change. The RESUME and REPLACE scenarios are amenable to mathematical treatment and can usually be analyzed by Markov models. The remaining paradigm of RESTART has shown to be difficult to analyze. Here all of the work is lost and the task must start from the beginning, retracing all of the steps previously taken to the point of failure. The task characteristics remain the same although the task has restarted. Clearly, it is not a memoryless process, and Markov methods have fallen short. The objective of this thesis is to develop and extend the Linear Algebraic Queueing Theory (LAQT) framework
to develop an analytic model of the RESTART paradigm. There are three independent goals of this work. The first aim is to propose a novel method that implements the RESTART paradigm in the analysis of the steady state M/G/1 queue. The second aim is to extend the linear algebraic approach of RESTART to include server redundancy and repair. The final aim is to analyze the RESTART scenario with emphasis on checkpointing.