We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Different types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds. 1 Introduction, Concepts and Notations The purpose of this paper is to survey models based on stochastic task graph representations and the solutions techniques that have been developed for them. The reason for doing this in the framework of the QMIPS project is that task graphs appear to be of central importance in the modeling and analysis of parallel programs and architectures. Yet, the solution of task graph problems is difficult in general. No really satisfactory and sufficiently general solutions have been proposed as of today, and research is still active in the area. The term "task graphs" covers now a wide variety of models. We shall begin the survey with what appears to be the initi...

As designers strive to build systems on chips with ever diminishing device sizes, and as clock speeds of gigahertz and above are being contemplated, the limitations of synchronous circuits are beginning to surface. Consequently, there has been a renewed interest in asyn- chronous design techniques that use judicious timing assumptions to obtain fast circuits with low hardware overhead. However, the correct operation of these circuits depend on certain timing constraints being satisfied in the actual implementation. Since statistical variations in manufacturing conditions and operating conditions result in uncertainties in component delays in a chip, it is important to analyze asynchronous systems with uncer- tain component delays to check for timing constraint violations and to determine sufficient conditions for their correct operation. Unfortunately, several timing analysis problems are computationally intractable when component delays are uncertain but bounded. This the- sis presents polynomial-time techniques for approximate timing analysis of asynchronous systems with bounded component delays. Although the algorithms are conservative in the worst case, experiments indicate that they are fairly accurate in practice.

An important question in discrete optimization under uncertainty is to understand the per-sistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path. In the spanning tree and shortest path network problems, when the arc lengths are random, the challenge is to pre-process the network and determine a smaller set of arcs that will most probably be a part of the optimal solution under different realizations of the arc lengths. Building on a character-ization of moment cones for single variate problems, and its associated semidefinite constraint representation, we develop a limited marginal moment model to compute the persistency of a de-cision variable. Under this model, we show that finding the persistency is tractable for zero-one optimization problems with a polynomial sized representation of the convex hull of the feasi-ble region. Through extensive experiments, we show that the persistency computed under the limited marginal moment model is often close to the simulated persistency value under various distributions that satisfy the prescribed marginal moments and are generated independently.

Towards predictable deep-submicron manufacturing