An Eclectic Survey of Bounding Methodsfor

Markov models are often used for performance mod-eling. However most models do not have closed form solutions, and numerical solutions are often not feasible due to the large (or even innnite) state space of models of practical interest. One can sometimes take advantage of special structures such as nearly completely decomposable models or models with matrix analytic solutions. This paper presents a brief survey of some work over the past few years on nding bounds on performance measures for models that are otherwise intractable. The bounds are found by modifying the original model such that: (a) the modiied model is eeciently solvable and (b) the modiied model is proven to provide an upper (lower) bound on the value of the performance measure in the original model. We have successfully applied this methodology in a number of studies which are brieey surveyed here. This is not meant to be a broad, inclusive survey but rather we concentrate on an approach that the authors' have been exploring.