No abstract

Commercial cloud offerings, such as Amazon's EC2, let users allocate compute resources on demand, charging based on reserved time intervals. While this gives great flexibility to elastic applications, users lack guidance for choosing between multiple offerings, in order to complete their computations within given budget constraints. In this work, we present BaTS, our budget-constrained scheduler. Using a small task sample, BaTS can estimate costs and makespan for a given bag on different cloud offerings. It provides the user with a choice of options before execution and then schedules the bag according to the user's preferences. BaTS requires no a-priori information about task completion times. We evaluate BaTS by emulating different cloud environments on the DAS-3 multicluster system. Our results show that BaTS correctly estimates budget and makespan for the scenarios investigated; the user-selected schedule is then executed within the given budget limitations.

Abstract-Elastic applications like bags of tasks benefit greatly from Infrastructure as a Service (IaaS) clouds that let users allocate compute resources on demand, charging based on reserved time intervals. Users, however, still need guidance for mapping their applications onto multiple IaaS offerings, both minimizing execution time and respecting budget limitations. For budgetcontrolled execution of bags of tasks, we built BaTS, a scheduler that estimates possible budget and makespan combinations using a tiny task sample, and then executes a bag within the user's budget constraints. Previous work has shown the efficacy of this approach. There remains, however, the risk of outlier tasks causing the execution to exceed the predicted makespan.In this work, we present a stochastic optimization of the tail phase for BaTS' execution. The main idea is to use the otherwise idling machines up until the end of their (already paidfor) allocation time. Using the task completion time information acquired during the execution, BaTS decides which tasks to replicate onto idle machines in the tail phase, reducing the makespan and improving the tolerance to outlier tasks. Our evaluation results show that this effect is robust w.r.t. the quality of runtime predictions and is the strongest with more expensive schedules in which many fast machines are available.

The Multi-class Queueing Network (McQN) arises as a natural multi-class extension of the traditional (single-class) Jackson network. In a single-class network subcriticality (i.e. subunitary nominal workload at every station) entails stability, but this is no longer sufficient when jobs/customers of different classes (i.e. with different service requirements and/or routing scheme) visit the same server; therefore, analytical conditions for stability of McQNs are lacking, in general. In this note we design a numerical (simulation-based) method for determining the stability region of a McQN, in terms of arrival rate(s). Our method exploits certain (stochastic) monotonicity properties enjoyed by the associated Markovian queue-configuration process. Stochastic monotonicity is a quite common feature of queueing models and can be easily established in the single-class framework (Jackson networks); recently, also for a wide class of McQNs, including first-come-first-serve (FCFS) networks, monotonicity properties have been established. Here, we provide a minimal set of conditions under which the method performs correctly. Eventually, we illustrate the use of our numerical method by presenting a set of numerical experiments, covering both single and multi-class networks.

In this paper we provide a perturbation analysis of finite time-inhomogeneous Markov processes. We derive closed-form representations for the derivative of the transition probability at time t, with t > 0. Elaborating on this result, we derive simple gradient estimators for transient performance characteristics either taken at some fixed point in time t, or for the integrated performance over a time interval [0 , t]. Bounds for transient performance sensitivities are presented as well. Eventually, we identify a structural property of the derivative of the generator matrix of a Markov chain that leads to a significant simplification of the estimators.