In performance engineering of composed services, coordinated provisioning can reduce the amount of resources required to meet end-to-end response time objectives. To this aim, various intertwined aspects of the application architecture need to be taken into account, notably including precedence constraints in the composition of elementary services, along with their durations and sensitivity to the scaling of provisioned resources. We address coordinated provisioning of resources for elementary services with stochastic durations with general distributions (i.e., including non-exponential distributions). We compose services in a workflow where precedence constraints define a Directed Acyclic Graph (DAG) and the distribution of the end-to-end (E2E) response time is subject to a Service Level Objective (SLO). We leverage a surrogate model of service performance, assuming a low workload of workflow requests (i.e., a single-request scenario) and service durations inversely proportional to provisioned resources. Given the total amount of resources, our approach derives the service provisioning that optimizes the workflow E2E response time distribution, by exploiting a compositional approach and by using stochastically ordered approximations to manage dependencies in non-well-nested precedence DAGs. Then, the approach scales provisioned resources up or down to determine the minimum amount of resources needed to satisfy the SLO, while leaving the remaining resources for horizontal scaling in order to manage multiple workflow requests at high workloads. Experiments consider low-workload and high-workload scenarios, different relations between elementary service durations and provisioned resources, and workflow topologies taken from benchmarks or randomly generated with controlled statistics, using elementary service durations from a dataset of the literature. Results show that the technique is feasible also for workflows with a thousand of services and that it outperforms other provisioning methods in fitting the SLO using the same resource amount and in minimizing the resource amount needed to fit the SLO.

Workflows are patterns of orchestrated activities designed to deliver some specific output, with application in various relevant contexts including software services, business processes, supply chain management. In most of these scenarios, durational properties of individual activities can be identified from logged data and cast in stochastic models, enabling quantitative evaluation of time behavior for diagnostic and predictive analytics. However, effective fitting of observed durations commonly requires that distributions break the limits of memoryless behavior and unbounded support of Exponential distributions, casting the problem in the class of non-Markovian models. This results in a major hurdle for numerical solution, largely exacerbated by the concurrency structure of workflows, which natively subtend concurrent activities with overlapping execution intervals and a limited number of regeneration points, i.e., time points at which the Markov property is satisfied and analysis can be decomposed according to a renewal argument. We propose a compositional method for quantitative evaluation of end-to-end response time of complex workflows. The workflow is modeled through Stochastic Time Petri Nets (STPNs), associating activity durations with Exponential distributions truncated over bilateral firmly bounded supports that fit mean and coefficient of variation of real logged histograms. Based on the model structure, the workflow is decomposed into a hierarchy of subworkflows, each amenable to efficient numerical solution through Markov regenerative transient analysis. In this step, the grain of decomposition is driven by non-deterministic analysis of the space of feasible behaviors in the underlying Time Petri Net (TPN) model, which permits efficient characterization of the factors that affect behavior complexity between regeneration points. Duration distributions of the subworkflows obtained through separate analyses are then repeatedly recomposed in numerical form to compute the response time distribution of the overall workflow.