On the one hand, the state space of complex Markovian models can often be partitioned between a small subset with a high steady-state probability and a large subset with a low steady-state probability. On the other hand, performance evaluation and reliability analysis require the computation of performance indices, often defined as functions of instantaneous rewards on the states of the model. ...

We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader’s problem. Both bounding problems are equivalent to explicit mixedinteger linear progra...

Censored Markov chains (CMC) allow to represent the conditional behavior of a system within a subset of observed states. They provide a theoretical framework to study the truncation of a discrete-time Markov chain when the generation of the state-space is too hard or when the number of states is too large. But the stochastic matrix of a CMC may be difficult to obtain. Dayar et al. (2006) have p...

We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on the right{hand{side and has a multivariate Gaussian distribution. Computation of these bounds requires the solution of only as many linear programs as the problem has variables.

Multistage stochastic programs show time-inconsistency in general, if the objective is neither the expectation nor the maximum functional. This paper considers distortion risk measures (in particular the Average Value-at-Risk) at the final stage of a multistage stochastic program. Such problems are not time consistent. However, it is shown that by considering risk parameters at random level and...

Consider (typically large) multistage stochastic programs, which are defined on scenario trees as the basic data structure. It is well known that the computational complexity of the solution depends on the size of the tree, which itself increases typically exponentially fast with its height, i.e. the number of decision stages. For this reason approximations which replace the problem by a simple...

Consistent stochastic orders of processing times and objective functions yield optimal policies in many stochastic scheduling problems. When these orders fail to hold, however, finding optimal values may be difficult. In this paper, we show how to bound these values in general situations including problems with unreliable machines and tardiness-based objectives.

Stochastic bounds are a valuable tool for analysing large Markov chains. If the chain is too large to solve, we can construct upper and lower bounding chains that are easier to solve, and whose steady state solutions will bound that of the original chain. In [Fourneau et al, 2004], an algorithm is presented to construct lumpable bounding chains, which can be aggregated and solved. In a stochast...

The delay characteristics of leaky-bucket constrained sources under Fair Queueing (FQ) policies are evaluated through the worst-case delay bounds. Clearly, these deterministic bounds do not always provide an insight into the underlying system. Moreover, with general stochas-tic source models, there is no analytical method to analyze the delay characteristics. We propose to apply the stochastic ...

We propose several algorithms to obtain bounds based on Censored Markov Chains to analyze partially generated discrete time Markov chains. The main idea is to avoid the generation of a huge (or even infinite) state space and to truncate the state space during the visit. The approach is purely algebraic and provides element-wise and stochastic bounds for the CMC.