A compositional approach for quantitative evaluation of stochastic workflows

Workflows describe processes of concurrent activities orchestrated by precedence constraints and control-flow constructs and are successfully applied to a large variety of material and digital processes from multiple contexts (e.g supply chain management, composite web services, cloud `functions as a service'. For people employed in this contexts, scientific methods are relevant to enhance the knowledge of the active processes, and to determine what are the better decisions to take to maximize the productivity or to minimize the loss of the considered business. From this perspective, the prediction of the completion time of a workflow is crucial to design and plan the activities of a business. In this thesis, we evaluate a stochastic upper bound on the completion time Probability Density Function (PDF) of complex workflows through an efficient and accurate compositional approach. Workflows are specified as structure trees, a hierarchical representation that is based on Stochastic Time Petri Nets (STPNs), that permits decomposition into a hierarchy of subworkflows with positively correlated response times, guaranteeing that a stochastically larger completion time PDF is obtained when intermediate results are approximated by stochastically larger PDFs and when dependencies are simplified by replicating activities appearing in multiple subworkflows. The method is implemented in Eulero, a novel Java library that enables both modeling of complex workflows through the structure tree and evaluation of their completion time PDF. Predicting the completion time of a workflow can be exploited in an environment of competition, where a set of resource-constrained aggregators selects service providers for the implementation of workflows requested by a set of customers, managing the Service Level Agreement (SLA) on both the sides. In particular, each aggregator selects the implementation of elementary services through a Vickrey-Clarke-Groves-based auction game, where each provider bids Cumulative Distribution Function (CDF) of the offered service completion time. On awarding of the auction, the aggregator can safely predict end-to-end completion times that can guarantee to each customer, and the consequent reward that can obtain. The resource-constrained assignment problem between customers and aggregators is thus solved through a matching game with externalities and incomplete information that aims at maximizing efficient usage of resources in the system according to a collective utility function. The impact of possible cheating strategies to improve the utility of some players is also analyzed, together with the stability of the formulated matching game. Then, the presented methods are then demonstrated in a Model-Driven Engineering (MDE) approach that implements Model-to-Model transformations to map cases of textile manufacturing district production to the proposed scientific application domain, enabling to perform of the methods to real-world contexts.