Perturbation analysis of a variable M/M/1 queue: a probabilistic approach

Citation
Antunes, Nelson et al., Perturbation analysis of a variable M/M/1 queue: a probabilistic approach, Advances in applied probability , 38(1), 2006, pp. 263-283
ISSN journal
00018678
Volume
38
Issue
1
Year of publication
2006
Pages
263 - 283
Database
ACNP
SICI code
Abstract
In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter . . 1. We specifically compute the two first terms of the power series expansion in . of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.