Martingale Methods in Queueing
Theory
Mats Pihlsgård
Handledare: Sören Asmussen
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2001:E5

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 KellaWhitt 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.




