 
Summary: Efficient Simulation of a Tandem Queue
with Server Slowdown
D.I. Miretskiy
, W.R.W. Scheinhardt
, M.R.H. Mandjes
Abstract
Tandem Jackson networks, and more sophisticated variants, have found widespread appli
cation in various domains. One such a variant is the tandem queue with server slowdown,
in which the server of the upstream queue reduces its service speed as soon as the down
stream queue exceeds some prespecified threshold, to provide the downstream queue some
sort of `protection'.
This paper focuses on the overflow probabilities in the downstream queue. Owing to
the Markov structure, these can be solved numerically, but the resulting system of linear
equations is usually large. An attractive alternative could be to resort to simulation,
but this approach is cumbersome due to the rarity of the event under consideration.
A powerful remedy is to use importance sampling, i.e., simulation under an alternative
measure, where unbiasedness of the estimator is retrieved by weighing the observations
by appropriate likelihood ratios.
To find a good alternative measure, we first identify the most likely path to overflow.
For the normal tandem queue (i.e., no slowdown), this path was known, but we develop an
