Analysis of GI/M/s/c queues using uniformisation

We combine uniformisation, a powerful numerical technique for the analysis of continuous time Markov chains, with the Markov chain embedding technique to analyze GI/M/s/c queues. The main steps of the proposed approach are the computation of

• (1)the mixed-Poisson probabilities associated to the number of arrival epochs in the uniformising Poisson process between consecutive customer arrivals to the system; and
• (2)the conditional embedded uniformised transition probabilities of the number of customers in the queueing system immediately before customer arrivals to the system.

To show the performance of the approach, we analyze queues with Pareto interarrival times using a stable recursion for the associated mixed-Poisson probabilities whose computation time is linear in the number of computed coefficients. The results for queues with Pareto interarrival times are compared with those obtained for queues with other interarrival time distributions, including exponential, Erlang, uniform and deterministic interarrival times. The obtained results show that much higher loss probabilities and mean waiting times in queue may be obtained for queues with Pareto interarrival times than for queues with the other mentioned interarrival time distributions, specially for small traffic intensities.     

On one top news list model

We introduce a top news list model based on extremal shot noise with Poisson arrival flow. We find one- and multi-dimensional distributions of popularity of current news (at arbitrary time and at infinity), as well as distributions of places of news in a top list and their sojourn times in a stationary regime. We consider in detail the case where the popularity of a news item is Pareto distributed at the initial time and then decreases exponentially.     

Expressions for Rényi and Shannon entropies for bivariate distributions

Exact forms of Rényi and Shannon entropies are determined for 27 continuous bivariate distributions, including the Kotz type distribution, truncated normal distribution, distributions with normal and centered normal conditionals, natural exponential distribution, Freund's exponential distribution, Marshall and Olkin's exponential distribution, exponential mixture distribution, Arnold and Strauss's exponential distribution, McKay's gamma distribution, distribution with gamma conditionals, gamma exponential distribution, Dirichlet distribution, inverted beta distribution, distribution with beta conditionals, beta stacy distribution, Cuadras and Augé's distribution, Farlie Gumbel Morgenstern distribution, logistic distribution, Pearson type VII distribution, Pearson type II distribution, distribution with Cauchy conditionals, bilateral Pareto distribution, Muliere and Scarsini's Pareto distribution, distribution with Pareto conditionals and the distribution with Gumbel conditionals. We believe that the results presented here will serve as an important reference for scientists and engineers in many areas.     

Some properties of fuzzy random renewal processes

Fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables. Based on the fuzzy random theory, this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed (iid) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the /spl alpha/-pessimistic values and /spl alpha/-optimistic values of the interarrival times is discussed. Furthermore, the fuzzy random style of renewal equation is provided. Finally, fuzzy random Blackwell's renewal theorem and Smith's key renewal theorem are also given.     

基于Pareto分布的IP骨干节点输入通信量模型

输入通信量的行为特性对于IP骨干网节点的性能和设计有重要的影响.本文从IP骨干网络节点输入通信量角度出发,提出了一个基于Pareto和指数分布的混合通信量模型,其中数据包到达间隔为Pareto分布,包大小为指数分布.该模型克服了传统网络通信量模型中没有显式考虑数据包大小的缺点,从数据包级对网络通信量进行了精确的描述,从而能够更好地进行路由器结构设计和性能分析.仿真实验验证了我们模型的有效性.     

Preventive replacement policies with time of operations,mission durations,minimal repairs and maintenance triggering approaches

When a mission arrives at a random time and lasts for a duration, it becomes an interesting problem to plan replacement policies according to the health condition and repair history of the operating unit, as the reliability is required at mission time and no replacement can be done preventively during the mission duration. From this viewpoint, this paper proposes that effective replacement policies should be collaborative ones gathering data from time of operations, mission durations, minimal repairs and maintenance triggering approaches. We firstly discuss replacement policies with time of operations and random arrival times of mission durations, model the policies and find optimum replacement times and mission durations to minimize the expected replacement cost rates analytically. Secondly, replacement policies with minimal repairs and mission durations are discussed in a similar analytical way. Furthermore, the maintenance triggering approaches, i.e., replacement first and last, are also considered into respective replacement policies. Numerical examples are illustrated when the arrival time of the mission has a gamma distribution and the failure time of the unit has a Weibull distribution. In addition, simple case illustrations of maintaining the production system in glass factories are given based on the assumed data.     

Maximum Remaining Service Time in Infinite-Server Queues

We study the maximum remaining service time in infinite-server queues of type M|G|∞ (at a given time and in a stationary regime). The following cases for the arrival flow rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a random process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In the case of a constant rate, we study effects that arise when the average service time is infinite (for power-law distribution tails). We find the extremal index of the sequence of maximum remaining service times. The results are extended to queues of type M^X|G|∞, including those with dependent service times within a batch.     

Simple reinforcement learning agents: Pareto beats Nash in an algorithmic game theory study

Repeated play in games by simple adaptive agents is investigated. The agents use Q-learning, a special form of reinforcement learning, to direct learning of behavioral strategies in a number of 2×2 games. The agents are able effectively to maximize the total wealth extracted. This often leads to Pareto optimal outcomes. When the rewards signals are sufficiently clear, Pareto optimal outcomes will largely be achieved. The effect can select Pareto outcomes that are not Nash equilibria and it can select Pareto optimal outcomes among Nash equilibria.Acknowledgement This material is based upon work supported by, or in part by, NSF grant number SES-9709548. We wish to thank an anonymous referee for a number of very helpful suggestions.     

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.     

Multi-objective α-reliable path finding in stochastic networks with correlated link costs: A simulation-based multi-objective genetic algorithm approach (SMOGA)

In this study, we propose a new simulation-based multi-objective genetic algorithm (SMOGA) approach to find a portfolio of reliable nondominant (Pareto) paths, a set of paths that is equally good or better at least in one objective space compared to all other paths, in stochastic networks while considering link travel time uncertainties and correlations among link travel times. Our SMOGA model consists of a Monte Carlo simulation, a genetic algorithm, and a Pareto filter module to find a set of Pareto paths that minimize the travel time budgets required to satisfy multiple requirements of travel time reliability pre-determined by users. For our purposes, an alpha (and beta) reliable path finding problem is first formulated as a variant of Chance Constrained Multi-objective Programming (CCMOP) model. Then the simulation module is used to simulate stochastic networks with correlations among link travel times, and genetic algorithm and Pareto filter module are used to effectively search for Pareto paths that satisfy multiple reliability requirements in combinatorial solution space. Numerical results on the Chicago Sketch network demonstrate that our carefully designed genetic representation (a variable-length chromosome and two ways of generating initial population) and genetic operators (a crossover and a mutation operator) effectively explore solution space and ensure the feasibility and diversity of offspring paths. Further, our graphical representations of Pareto paths on the same network indicate that simplified models that do not consider correlations among link travel time distributions may find Pareto paths with a significant bias in travel time budgets and hence provide travelers sub-optimal paths.     

Process Arrival Pattern Aware Alltoall and Allgather on InfiniBand Clusters

Recent studies show that MPI processes in real applications could arrive at an MPI collective operation at different times. This imbalanced process arrival pattern can significantly affect the performance of the collective operation. MPI_Alltoall() and MPI_Allgather() are communication-intensive collective operations that are used in many scientific applications. Therefore, their efficient implementations under different process arrival patterns are critical to the performance of scientific applications running on modern clusters. In this paper, we propose novel RDMA-based process arrival pattern aware MPI_Alltoall() and MPI_Allgather() for different message sizes over InfiniBand clusters. We also extend the algorithms to be shared memory aware for small to medium size messages under process arrival patterns. The performance results indicate that the proposed algorithms outperform the native MVAPICH implementations as well as other non-process arrival pattern aware algorithms when processes arrive at different times. Specifically, the RDMA-based process arrival pattern aware MPI_Alltoall() and MPI_Allgather() are 3.1 times faster than MVAPICH for 8 KB messages. On average, the applications studied in this paper (FT, RADIX, and N-BODY) achieve a speedup of 1.44 using the proposed algorithms.     

A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem

To better reflect the uncertainty existing in the actual disassembly environment, the multi-objective disassembly line balancing problem with fuzzy disassembly times is investigated in this paper. First, a mathematical model of the multi-objective fuzzy disassembly line balancing problem (MFDLBP) is presented, in which task disassembly times are assumed as triangular fuzzy numbers (TFNs). Then a Pareto improved artificial fish swarm algorithm (IAFSA) is proposed to solve the problem. The proposed algorithm is inspired from the food searching behaviors of fish including prey, swarm and follow behaviors. An order crossover operator of the traditional genetic algorithm is employed in the prey stage. The Pareto optimal solutions filter mechanism is adopted to filter non-inferior solutions. The proposed model after the defuzzification is validated by the LINGO solver. And the validity and the superiority of the proposed algorithm are proved by comparing with a kind of hybrid discrete artificial bee colony (HDABC) algorithm using two test problems. Finally, the proposed algorithm is applied to a printer disassembly instance including 55 disassembly tasks, for which the computational results containing 12 non-inferior solutions further confirm the practicality of the proposed Pareto IAFSA in solving the MFDLBP.     

Pareto optimization for the two-agent scheduling problems with linear non-increasing deterioration based on Internet of Things

The Internet of Things (IoT) enables these objects to collect and exchange data and it is an important character of smart city. Multi-agent scheduling is one necessary part of Internet of Things. In this paper, we investigate the Pareto optimization scheduling on a single machine with two competing agents and linear non-increasing deterioration, which is Multi-agent scheduling problems often occurred in the Internet of Things. In the scheduling setting, each of the two competing agents wants to optimize its own objective which depends on the completion times of its jobs only. The assumption of linear non-increasing deterioration means that the actual processing time of a job will decrease linearly with the starting time. The objective functions in consideration are the maximum earliness cost and the total earliness. Two Pareto optimization scheduling problems are studied in this paper. In the first problem, each agent has the maximum earliness cost as its objective function. In the second problem, one agent has the maximum earliness cost as its objective function and the other agent has the total earliness as its objective function. The goal of a Pareto optimization scheduling problem is to find all Pareto optimal points and, for each Pareto optimal point, a corresponding Pareto optimal schedule. In the literature, the two corresponding constrained optimization scheduling problems are solved in polynomial time under the assumption that the inverse cost function of each job is available. In this paper, we extend these results to the setting without the availability assumption. Furthermore, by estimating the number of Pareto optimal points, we show that the above two Pareto optimization scheduling problems are solved in polynomial time. Hence, our results have much more theoretically meaningful constructs. Experimentation results show that the algorithms presented in this paper are efficient.     

Analysis and control of correlated web server queues

The research literature is rich with studies that demonstrate various degrees of correlation in the arrival processes found in Web server environments. All of these previous studies either have assumed the arrival process of each Web server to be independent of the corresponding service process or have completely ignored this important issue. Using data from commercial Web servers, we demonstrate the existence of considerable dependencies between arrival times and service times, in addition to a strong dependence structure within the arrival process, and then we explore a likely causal model of this cross correlation. A mathematical approximation of Web server performance is derived, based on heavy-traffic stochastic-process limits, that captures both the correlations within the arrival process and the correlations between the arrival and service processes. We then demonstrate that the results from our approximation, which is asymptotically exact, are in very good agreement with simulation results across all traffic intensities. Our mathematical analysis is further exploited to revisit certain scheduling issues in Web server environments. In particular, we consider a scheduling approach that provides expected response times relatively close to those under the optimal shortest remaining processing time policy while also maintaining better variance properties.     

基于分层抽样算法的异常攻击流量检测

在高速互联网应用中,海量数据无法逐包检测分析,异常攻击流量也不易被识别。为解决该问题,利用泊松帕累托突发过程的经典流量模型对网络流量自相似特性进行分析,将网络流量分为长流与短流,并根据数据流到达时间的抽样比增量进行分层抽样,由此实现异常攻击流量的检测。在基于数据报文级检测的snort异常入侵检测系统上对该方法进行仿真实验,结果证明其能有效缩小异常攻击数据范围,快速准度地检测出攻击。     

A multi-start local search heuristic for an energy efficient VMs assignment on top of the OpenNebula cloud manager

Reducing energy consumption is an increasingly important issue in cloud computing, more specifically when dealing with a large-scale cloud. Minimizing energy consumption can significantly reduce the amount of energy bills and the greenhouse gas emissions. Therefore, many researches are carried out to develop new methods in order to consume less energy. In this paper, we present an Energy-aware Multi-start Local Search algorithm (EMLS-ONC) that optimizes the energy consumption of an OpenNebula-based Cloud. Moreover, we propose a Pareto Multi-Objective version of the EMLS-ONC called EMLS-ONC-MO dealing with both the energy consumption and the Service Level Agreement (SLA). The objective is to find a Pareto tradeoff between reducing the energy consumption of the cloud while preserving the performance of Virtual Machines (VMs). The different schedulers have been experimented using different arrival scenarios of VMs and different hardware configurations (artificial and real). The results show that EMLS-ONC and EMLS-ONC-MO outperform the other energy- and performance-aware algorithms in addition to the one provided in OpenNebula by a significant margin on the considered criteria. Besides, EMLS-ONC and EMLS-ONC-MO are proved to be able to assign at least as many VMs as the other algorithms.     

Air cargo pickup schedule for single delivery location

In this paper, various deterministic models for determining optimal pickup times for air cargo from an airport and delivering it to a local distribution center for a global manufacturer are presented. The arrival times of the flights that can potentially bring air cargo are assumed to be deterministic and known. In addition, the custom clearance time for the air cargo and the traveling time from the airport to the local distribution center are assumed to be deterministic and known. These models are formulated mathematically as linear binary integer programming models without air cargo weight considerations. Deterministic formulations without air cargo weight information are shown to be related to the p-Median problem. The deterministic formulation of air cargo pickup times with air cargo weight consideration is shown to be a nonlinear binary integer programming model. The solutions of these models serve as an initial starting point to solve the stochastic problem with random arrival times of the flights and random custom clearance times and travel times.     

Motion extrapolation of auditory–visual targets

Many tasks involve the precise estimation of speed and position of moving objects, for instance to catch or avoid objects that cohabit in our environment. Many of these objects are characterised by signal representations in more than one modality, such as hearing and vision. The aim of this study was to investigate the extent to which the simultaneous presentation of auditory and visual signals enhances the estimation of motion speed and instantaneous position. Observers are asked to estimate the instant when a moving object arrives at a target spatial position by pressing a response button. This task requires observers to estimate the speed of the moving object and to calibrate the timing of their manual response such that it coincides with the true arrival time of the moving object. When both visual and auditory motion signals are available, the variability in estimating the arrival time of the moving object is significantly reduced compared to the variability in the unimodal conditions. This reduction in variability is consistent with optimal integration of the auditory and visual speed signals. The average bias in the estimated arrival times depends on the motion speed: for medium speeds (17 deg/s) observers’ subjective arrival times are earlier than the true arrival times; for high speeds (47 deg/s) observers exhibit a (much smaller) bias in the other direction. This speed-dependency suggests that the bias is due to an error in estimating the motion speeds rather than an error in calibrating the timing of the motor response. Finally, in this temporal localization task, the bias and variability show similar patterns for motion defined by vision, audition or both.     

Prediction for Pareto distribution based on progressively Type-II censored samples

In this paper, we discuss different predictors of times to failure of units censored in multiple stages in a progressively censored sample from Pareto distribution. The best linear unbiased predictors, maximum likelihood predictors and approximate maximum likelihood predictors are considered. We also present two methods for obtaining prediction intervals for the times to failure of units. A numerical simulation study involving two data sets is presented to illustrate the methods of prediction.     

Aperiodic task scheduling for Hard-Real-Time systems

A real-time system consists of both aperiodic and periodic tasks. Periodic tasks have regular arrival times and hard deadlines. Aperiodic tasks have irregular arrival times and either soft or hard deadlines. In this article, we present a new algorithm, the Sporadic Server algorithm, which greatly improves response times for soft deadline aperiodic tasks and can guarantee hard deadlines for both periodic and aperiodic tasks. The operation of the Sporadic Server algorithm, its performance, and schedulability analysis are discussed and compared with previously published aperiodic service algorithms.