Evaluating the Robustness of Resource Allocations Obtained through Performance Modeling with Stochastic Process Algebra

Recent developments in the field of parallel and distributed computing has led to a proliferation of solving large and computationally intensive mathematical, science, or engineering problems, that consist of several parallelizable parts and several non-parallelizable (sequential) parts. In a parallel and distributed computing environment, the performance goal is to optimize the execution of parallelizable parts of an application on concurrent processors. This requires efficient application scheduling and resource allocation for mapping applications to a set of suitable parallel processors such that the overall performance goal is achieved. However, such computational environments are often prone to unpredictable variations in application (problem and algorithm) and system characteristics. Therefore, a robustness study is required to guarantee a desired level of performance. Given an initial workload, a mapping of applications to resources is considered to be robust if that mapping optimizes execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research, a stochastic process algebra, Performance Evaluation Process Algebra (PEPA), is used for obtaining resource allocations via a numerical analysis of performance modeling of the parallel execution of applications on parallel computing resources. The PEPA performance model is translated into an underlying mathematical Markov chain model for obtaining performance measures. Further, a robustness analysis of the allocation techniques is performed for finding a robustmapping from a set of initial mapping schemes. The numerical analysis of the performance models have confirmed similarity with the simulation results of earlier research available in existing literature. When compared to direct experiments and simulations, numerical models and the corresponding analyses are easier to reproduce, do not incur any setup or installation costs, do not impose any prerequisites for learning a simulation framework, and are not limited by the complexity of the underlying infrastructure or simulation libraries

A Stochastic Multiple Players Multi-Issues Bargaining Model for the Piave River Basin

The objective of this paper is to investigate the usefulness of non-cooperative bargaining theory for the analysis of negotiations on water allocation and management. We explore the impacts of different economic incentives, a stochastic environment and varying individual preferences on players’ strategies and equilibrium outcomes through numerical simulations of a multilateral, multiple issues, non-cooperative bargaining model of water allocation in the Piave River Basin, in the North East of Italy. Players negotiate in an alternating-offer manner over the sharing of water resources (quantity and quality). Exogenous uncertainty over the size of the negotiated amount of water is introduced to capture the fact that water availability is not known with certainty to negotiating players. We construct the players’ objective function with their direct input. We then test the applicability of our multiple players, multi-issues, stochastic framework to a specific water allocation problem and conduct comparative static analyses to assess sources of bargaining power. Finally, we explore the implications of different attitudes and beliefs over water availability.Bargaining, Non-Cooperative Game Theory, Simulation Models, Uncertainty