Matstat seminar 2.2

Math Pihlsgård presenterar sitt examensarbete

Martingale methods in queueing theory

Abstract.
Let t_n denote the first passage time to level n in a M/M/c queue
The main aim of this thesis is to investigate the expectation
and Laplace transform of t_n. The cases c=1 and c>1 are treated
separately. Important tools in the analysis, in both cases, are
martingales; the Wald martingale and the Kella-Whitt
martingale. These are treated in a separate chapter. Also a chapter on
regenerative processes is included, and the
theory is used to obtain approximate values of Et_n in
two special cases. Although the practical aspects of the problems are
not emphasised, a few equations, rather well suited for computer
visualization, are produced and presented graphically. Finally, the
queue length process and the work load process are simulated in a few
cases.