Transient properties of manyserver queues and related QBD's
Søren Asmussen and Mats Pihlsgård
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2002
ISSN 14039338

Abstract:

The time t(n) of first passage from queue length x to queue length n >
x in an MAP/M/c queue is considered. The mean and the Laplace transform is
computed as solutions of systems of linear equations coming out byoptional
stopping of a martingale obtained as an stochastic integral of the exponential
Wald martingale for Markov additive processes. Compared to existing techniques
for QBD's, the approach has the advantage ofbeing far more efficient for
large n.




Key words:

birthdeath process, buffer overflow, exponential martingale, first passage
problem, heterogeneous servers, KellaWhitt martingale, Laplace transform,
Lévy process, MAP/M/c queue, Markov additive process, optional stopping
