Performance Evaluation最新文献

We consider the restless bandits with general finite state space under partial observability with two observational models: first, the state of each bandit is not observable at all, and second, the state of each bandit is observable when it is selected. Under the assumption that the models satisfy a restart property, we prove that both models are indexable. For the first model, we derive a closed-form expression for the Whittle index. For the second model, we propose an efficient algorithm to compute the Whittle index by exploiting the qualitative properties of the optimal policy. We present detailed numerical experiments for multiple instances of machine maintenance problem. The result indicates that the Whittle index policy outperforms myopic policy and can be close to optimal in different setups.

We present a new stochastic model for the evolution of Directed Acyclic Graphs (DAG)-based distributed ledgers (DL), under the presence of heterogeneous delay. This model is used to analyse the performance metrics of the DL, showing in particular that the number of unapproved messages, in expectation, does not diverge to infinity, even under the presence of delay. We propose an analysis based on conveniently defined sets, as well as an alternative drift-based analysis. The former allows to get a bound on the average number of unapproved messages, while the latter, through a simpler analysis, allows to prove the existence of such bound. For particular scenarios, we are able to derive the expected value of the drift of unapproved messages, through a Markov process-based approach. State-of-the-art mathematical models trying to capture the impact of delays on the performance of such DLs rely on some particular simplifications. In contrast, through our model, we are able to analytically derive similar performance guarantees, in a more realistic setup. In particular, we focus on IOTA foundation’s tangle, while our results can be extended to other DAG-based distributed ledgers. We compare our results to results obtained in a real testbed, showing good accordance between them.

In this paper, we introduce the Laplace–Stieltjes transform (LST) of the inter-departure time distribution in a PH/PH/c queue, and the two-dimensional joint LST of two consecutive inter-departure times to construct their correlation structure. We exploit the properties of phase-type (PH) random variables, as well as the steady-state distribution of the underlying continuous-time Markov chain in a PH/PH/c queue to construct these LSTs. We demonstrate our approach through numerical examples, while validating the results. Later, we analyze the correlation between two consecutive inter-departure times for various PH/PH/c queues. We observe that, if the fundamental elements of the queue have high (low) variability, then the correlation is positive (negative).

Our aim is to estimate the largest community (a.k.a., mode) in a population composed of multiple disjoint communities. This estimation is performed in a fixed confidence setting via sequential sampling of individuals with replacement. We consider two sampling models: (i) an identityless model, wherein only the community of each sampled individual is revealed, and (ii) an identity-based model, wherein the learner is able to discern whether or not each sampled individual has been sampled before, in addition to the community of that individual. The former model corresponds to the classical problem of identifying the mode of a discrete distribution, whereas the latter seeks to capture the utility of identity information in mode estimation. For each of these models, we establish information theoretic lower bounds on the expected number of samples needed to meet the prescribed confidence level, and propose sound algorithms with a sample complexity that is provably asymptotically optimal. Our analysis highlights that identity information can indeed be utilized to improve the efficiency of community mode estimation.

The viral propagation of fake posts on online social networks (OSNs) has become an alarming concern. The paper aims to design control mechanisms for fake post detection while negligibly affecting the propagation of real posts. Towards this, a warning mechanism based on crowd-signals was recently proposed, where all users actively declare the post as real or fake. In this paper, we consider a more realistic framework where users exhibit different adversarial or non-cooperative behaviour: (i) they can independently decide whether to provide their response, (ii) they can choose not to consider the warning signal while providing the response, and (iii) they can be real-coloring adversaries who deliberately declare any post as real. To analyse the post-propagation process in this complex system, we propose and study a new branching process, namely total-current population-dependent branching process with multiple death types. At first, we compare and show that the existing warning mechanism significantly under-performs in the presence of adversaries. Then, we design new mechanisms which remarkably perform better than the existing mechanism by cleverly eliminating the influence of the responses of the adversaries. Finally, we propose another enhanced mechanism which assumes minimal knowledge about the user-specific parameters. The theoretical results are validated using Monte-Carlo simulations.

Datacenter capacity is growing exponentially to satisfy the increasing demand for many emerging computationally-intensive applications, such as deep learning. This trend has led to concerns over datacenters’ increasing energy consumption and carbon footprint. The most basic prerequisite for optimizing a datacenter’s energy- and carbon-efficiency is accurately monitoring and attributing energy consumption to specific users and applications. Since datacenter servers tend to be multi-tenant, i.e., they host many applications, server- and rack-level power monitoring alone does not provide insight into the energy usage and carbon emissions of their resident applications. At the same time, current application-level energy monitoring and attribution techniques are intrusive: they require privileged access to servers and necessitate coordinated support in hardware and software, neither of which is always possible in cloud environments. To address the problem, we design WattScope, a system for non-intrusively estimating the power consumption of individual applications using external measurements of a server’s aggregate power usage and without requiring direct access to the server’s operating system or applications. Our key insight is that, based on an analysis of production traces, the power characteristics of datacenter workloads, e.g., low variability, low magnitude, and high periodicity, are highly amenable to disaggregation of a server’s total power consumption into application-specific values. WattScope adapts and extends a machine learning-based technique for disaggregating building power and applies it to server- and rack-level power meter measurements that are already available in data centers. We evaluate WattScope’s accuracy on a production workload and show that it yields high accuracy, e.g., often $<\sim$10% normalized mean absolute error, and is thus a potentially useful tool for datacenters in externally monitoring application-level power usage.

How should we schedule jobs to minimize mean queue length? In the preemptive M/G/1 queue, we know the optimal policy is the Gittins policy, which uses any available information about jobs’ remaining service times to dynamically prioritize jobs. For models more complex than the M/G/1, optimal scheduling is generally intractable. This leads us to ask: beyond the M/G/1, does Gittins still perform well?

Recent results show Gittins performs well in the M/G/k, meaning that its additive suboptimality gap is bounded by an expression which is negligible in heavy traffic. But allowing multiple servers is just one way to extend the M/G/1, and most other extensions remain open. Does Gittins still perform well with non-Poisson arrival processes? Or if servers require setup times when transitioning from idle to busy?

In this paper, we give the first analysis of the Gittins policy that can handle any combination of (a) multiple servers, (b) non-Poisson arrivals, and (c) setup times. Our results thus cover the G/G/1 and G/G/k, with and without setup times, bounding Gittins’s suboptimality gap in each case. Each of (a), (b), and (c) adds a term to our bound, but all the terms are negligible in heavy traffic, thus implying Gittins’s heavy-traffic optimality in all the systems we consider. Another consequence of our results is that Gittins is optimal in the M/G/1 with setup times at all loads.

The Asymmetric Inclusion Process (ASIP) tandem queue is a model of stations in series with a gate after each station. At a gate opening, all customers in that station instantaneously move to the next station unidirectionally. In our study, we enhance the ASIP model by introducing the capability for individual customers to independently move from one station to the next, and by allowing both individual customers and batches of customers from any station to exit the system. The model is inspired by the process by which macromolecules are transported within cells.

We present a comprehensive analysis of various aspects of the queue length in the ASIP tandem model. Specifically, we provide an exact analysis of queue length moments and correlations and, under certain circumstances, of the queue length distribution. Furthermore, we propose an approximation for the joint queue length distribution. This approximation is derived using three different approaches, one of which employs the concept of the replica mean-field limit. Among other results, our analysis offers insight into the extent to which nutrients can support the survival of a cell.

We consider the online convex optimization (OCO) problem with quadratic and linear switching cost in the limited information setting, where an online algorithm can choose its action using only gradient information about the previous objective function. For $L$-smooth and $\mu$-strongly convex objective functions, we propose an online multiple gradient descent (OMGD) algorithm and show that its competitive ratio for the OCO problem with quadratic switching cost is at most $4(L+5)+\frac{16(L+5)}{\mu }$. The competitive ratio upper bound for OMGD is also shown to be order-wise tight in terms of $L,\mu$. In addition, we show that the competitive ratio of any online algorithm is $max\{\Omega \left(L\right),\Omega \left(\frac{L}{\sqrt{\mu }}\right)\}$ in the limited information setting when the switching cost is quadratic. We also show that the OMGD algorithm achieves the optimal (order-wise) dynamic regret in the limited information setting. For the linear switching cost, the competitive ratio upper bound of the OMGD algorithm is shown to depend on both the path length and the squared path length of the problem instance, in addition to $L,\mu$, and is shown to be order-wise, the best competitive ratio any online algorithm can achieve. Consequently, we conclude that the optimal competitive ratio for the quadratic and linear switching costs are fundamentally different in the limited information setting.