Cost-aware scheduling of deadline-constrained task workflows in public cloud environments

Public cloud computing infrastructure offers resources on-demand, and makes it possible to develop applications that elastically scale when demand changes. This capacity can be used to schedule highly parallellizable task workflows, where individual tasks consist of many small steps. By dynamically scaling the number of virtual machines used, based on varying resource requirements of different steps, lower costs can be achieved, and workflows that would previously have been infeasible can be executed. In this paper, we describe how task workflows consisting of large numbers of distributable steps can be provisioned on public cloud infrastructure in a cost-efficient way, taking into account workflow deadlines. We formally define the problem, and describe an ILP-based algorithm and two heuristic algorithms to solve it. We simulate how the three algorithms perform when scheduling these task workflows on public cloud infrastructure, using the various instance types of the Amazon EC2 cloud, and we evaluate the achieved cost and execution speed of the three algorithms using two different task workflows based on a document processing application

A functional central limit theorem for a Markov-modulated infinite-server queue

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\alpha$ is observed. For $\alpha\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.Comment: 4 figure

Markov-modulated infinite-server queues driven by a common background process

International audienceThis paper studies a system with multiple infinite-server queues which are modulated by a common background process. If this background process, being modeled as a finite-state continuous-time Markov chain, is in state j, then the arrival rate into the i-th queue is λi,j, whereas the service times of customers present in this queue are exponentially distributed with mean µ −1 i,j ; at each of the individual queues all customers present are served in parallel (thus reflecting their infinite-server nature). Three types of results are presented: in the first place (i) we derive differential equations for the probability generating functions corresponding to the distributions of the transient and stationary numbers of customers (jointly in all queues), then (ii) we set up recursions for the (joint) moments, and finally (iii) we establish a central limit theorem in the asymptotic regime in which the arrival rates as well as the transition rates of the background process are simultaneously growing large

Discovery of the potential role of sensors in a personal emergency response system: what can we learn from a single workshop?

Capturing knowledge from domain experts is important to effectively integrate novel technological support in existing care processes. In this paper, we present our experiences in using a specific type of workshop, which we identified as a decision-tree workshop, to determine the process and information exchange during the usage of a Personal Emergency Response System (PERS). We conducted the workshop with current and possible future users of a PERS system to investigate the potential of context-and social awareness for such a system. We discuss the workshop format as well as the results and reflection on this workshop

Refined large deviations asymptotics for Markov-modulated infinite-server systems

Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers’ arrival rates and service rates are modulated by a Markovian background process; additionally, there are infinitely many servers (and consequently the resulting model is often used as a proxy for the corresponding many-server model). The Markov-modulated infinite-server model hardly allows any explicit analysis, apart from results in terms of systems of (ordinary or partial) differential equations for the underlying probability generating functions, and recursions to obtain all moments. As a consequence, recent research efforts have pursued an asymptotic analysis in various limiting regimes, notably the central-limit regime (describing fluctuations around the average behavior) and the large-deviations regime (focusing on rare events). Many of these results use the property that the number of customers in the system obeys a Poisson distribution with a random parameter. The objective of this paper is to develop techniques to accurately approximate tail probabilities in the large-deviations regime. We consider the scaling in which the arrival rates are inflated by a factor N, and we are interested in the probability that the number of customers exceeds a given level Na. Where earlier contributions focused on so-called logarithmic asymptotics of this exceedance probability (which are inherently imprecise), the present paper improves upon those results in that exact asymptotics are established. These are found in two steps: first the distribution of the random parameter of the Poisson distribution is characterized, and then this knowledge is used to identify the exact asymptotics. The paper is concluded by a set of numerical experiments, in which the accuracy of the asymptotic results is assessed

Analysis of Markov-modulated infinite-server queues in the central-limit regime

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\ge 0$, in the asymptotic regime in which the arrival rates $\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\alpha$, with $\alpha \in \mathbb R^+$. The specific value of $\alpha$ has a crucial impact on the result: (i)~for $\alpha>1$ the system essentially behaves as an M/M/$\infty$ queue, and in the central limit theorem the centered process has to be normalized by $\sqrt{N}$; (ii)~for $\alpha<1$, the centered process has to be normalized by $N^{{1-}\alpha/2}$, with the deviation matrix appearing in the expression for the variance