Simple and explicit bounds for multi-server queues with 1/(1−ρ)1/(1 - \rho) (and sometimes better) scaling

We consider the FCFS $GI/GI/n$ queue, and prove the first simple and explicit bounds that scale as $\frac{1}{1-\rho}$ (and sometimes better). Here $\rho$ denotes the corresponding traffic intensity. Conceptually, our results can be viewed as a multi-server analogue of Kingman's bound. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay. The strength of our bounds (e.g. in the form of tail decay rate) is a function of how many moments of the inter-arrival and service distributions are assumed finite. More formally, suppose that the inter-arrival and service times (distributed as random variables $A$ and $S$ respectively) have finite $r$th moment for some $r > 2.$ Let $\mu_A$ (respectively $\mu_S$) denote $\frac{1}{\mathbb{E}[A]}$ (respectively $\frac{1}{\mathbb{E}[S]}$). Then our bounds (also for higher moments) are simple and explicit functions of $\mathbb{E}\big[(A \mu_A)^r\big], \mathbb{E}\big[(S \mu_S)^r\big], r$, and $\frac{1}{1-\rho}$ only. Our bounds scale gracefully even when the number of servers grows large and the traffic intensity converges to unity simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale better than $\frac{1}{1-\rho}$ in certain asymptotic regimes. More precisely, they scale as $\frac{1}{1-\rho}$ multiplied by an inverse polynomial in $n(1 - \rho)^2.$ These results formalize the intuition that bounds should be tighter in light traffic as well as certain heavy-traffic regimes (e.g. with $\rho$ fixed and $n$ large). In these same asymptotic regimes we also prove bounds for the tail of the steady-state number in service. Our main proofs proceed by explicitly analyzing the bounding process which arises in the stochastic comparison bounds of amarnik and Goldberg for multi-server queues. Along the way we derive several novel results for suprema of random walks and pooled renewal processes which may be of independent interest. We also prove several additional bounds using drift arguments (which have much smaller pre-factors), and make several conjectures which would imply further related bounds and generalizations

Large deviations analysis for the M/H2/n+MM/H_2/n + M queue in the Halfin-Whitt regime

We consider the FCFS $M/H_2/n + M$ queue in the Halfin-Whitt heavy traffic regime. It is known that the normalized sequence of steady-state queue length distributions is tight and converges weakly to a limiting random variable W. However, those works only describe W implicitly as the invariant measure of a complicated diffusion. Although it was proven by Gamarnik and Stolyar that the tail of W is sub-Gaussian, the actual value of $\lim_{x \rightarrow \infty}x^{-2}\log(P(W >x))$ was left open. In subsequent work, Dai and He conjectured an explicit form for this exponent, which was insensitive to the higher moments of the service distribution. We explicitly compute the true large deviations exponent for W when the abandonment rate is less than the minimum service rate, the first such result for non-Markovian queues with abandonments. Interestingly, our results resolve the conjecture of Dai and He in the negative. Our main approach is to extend the stochastic comparison framework of Gamarnik and Goldberg to the setting of abandonments, requiring several novel and non-trivial contributions. Our approach sheds light on several novel ways to think about multi-server queues with abandonments in the Halfin-Whitt regime, which should hold in considerable generality and provide new tools for analyzing these systems

Consensus Division in an Arbitrary Ratio

We consider the problem of partitioning a line segment into two subsets, so that n finite measures all have the same ratio of values for the subsets. Letting ? ? [0,1] denote the desired ratio, this generalises the PPA-complete consensus-halving problem, in which ? = 1/2. Stromquist and Woodall [Stromquist and Woodall, 1985] showed that for any ?, there exists a solution using 2n cuts of the segment. They also showed that if ? is irrational, that upper bound is almost optimal. In this work, we elaborate the bounds for rational values ?. For ? = ?/k, we show a lower bound of (k-1)/k ? 2n - O(1) cuts; we also obtain almost matching upper bounds for a large subset of rational ?. On the computational side, we explore its dependence on the number of cuts available. More specifically, 1) when using the minimal number of cuts for each instance is required, the problem is NP-hard for any ?; 2) for a large subset of rational ? = ?/k, when (k-1)/k ? 2n cuts are available, the problem is in PPA-k under Turing reduction; 3) when 2n cuts are allowed, the problem belongs to PPA for any ?; more generally, the problem belong to PPA-p for any prime p if 2(p-1)??p/2?/?p/2? ? n cuts are available

Performance-based control system design automation via evolutionary computing

This paper develops an evolutionary algorithm (EA) based methodology for computer-aided control system design (CACSD) automation in both the time and frequency domains under performance satisfactions. The approach is automated by efficient evolution from plant step response data, bypassing the system identification or linearization stage as required by conventional designs. Intelligently guided by the evolutionary optimization, control engineers are able to obtain a near-optimal ‘‘off-thecomputer’’ controller by feeding the developed CACSD system with plant I/O data and customer specifications without the need of a differentiable performance index. A speedup of near-linear pipelineability is also observed for the EA parallelism implemented on a network of transputers of Parsytec SuperCluster. Validation results against linear and nonlinear physical plants are convincing, with good closed-loop performance and robustness in the presence of practical constraints and perturbations

Nonlinear system identification and control using state transition algorithm

By transforming identification and control for nonlinear system into optimization problems, a novel optimization method named state transition algorithm (STA) is introduced to solve the problems. In the proposed STA, a solution to a optimization problem is considered as a state, and the updating of a solution equates to a state transition, which makes it easy to understand and convenient to implement. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results have demonstrated the validity of the methodology, and comparisons to STA with other optimization algorithms have testified that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence rate and more stable performance.Comment: 20 pages, 18 figure

Generalizing Minimal Supergravity

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5) and SO(10) models, and calculate the corresponding indices k. Especially, the index k is 5/3 in the traditional SU(5) and SO(10) models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1) flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.Comment: RevTex4, 14 pages, 4 tables, references added, version in PL

A First Look at the Crypto-Mining Malware Ecosystem: A Decade of Unrestricted Wealth

Illicit crypto-mining leverages resources stolen from victims to mine cryptocurrencies on behalf of criminals. While recent works have analyzed one side of this threat, i.e.: web-browser cryptojacking, only commercial reports have partially covered binary-based crypto-mining malware. In this paper, we conduct the largest measurement of crypto-mining malware to date, analyzing approximately 4.5 million malware samples (1.2 million malicious miners), over a period of twelve years from 2007 to 2019. Our analysis pipeline applies both static and dynamic analysis to extract information from the samples, such as wallet identifiers and mining pools. Together with OSINT data, this information is used to group samples into campaigns. We then analyze publicly-available payments sent to the wallets from mining-pools as a reward for mining, and estimate profits for the different campaigns. All this together is is done in a fully automated fashion, which enables us to leverage measurement-based findings of illicit crypto-mining at scale. Our profit analysis reveals campaigns with multi-million earnings, associating over 4.4% of Monero with illicit mining. We analyze the infrastructure related with the different campaigns, showing that a high proportion of this ecosystem is supported by underground economies such as Pay-Per-Install services. We also uncover novel techniques that allow criminals to run successful campaigns.Comment: A shorter version of this paper appears in the Proceedings of 19th ACM Internet Measurement Conference (IMC 2019). This is the full versio