Performability Studies of Automated Manufacturing Systems with Multiple Part Types

In this paper, we consider the transient performance analysis of failure-prone manufacturing systems producing multiple part types. We decompose the exact monolithic model into (a) slower time scale structure state process modeling the failure and repair and (b) a faster time scale performance model describing the part processing and the material movement. We combine the solution of these two models to show that the accumulated reward over a given time interval is a solution of a set of forward or adjoint multidimensional linear hyperbolic partial differential equations. This result generalizes the existing results on composite performance-dependability analysis of manufacturing systems. We also present efficient numerical methods for computing the distribution of the cumulative operational time, and the mean and variance of the cumulative production over a given time interval. Further, we bring out the significance of these results in the manufacturing systems context through several examples

Path Planning Using Probability Tensor Flows

Probability models are emerging as a promising framework to account for "intelligent" behavior. In this article, probability propagation is discussed to model agent's motion in potentially complex grids that include goals and obstacles. Tensor messages in the state-action space (due to grid structure, states are 2-D and the concomitant probability distributions are represented by 3-D arrays), propagated bi-directionally on a Markov chain, provide crucial information to guide the agent's decisions. The discussion is carried out with reference to a set of simulated grids and includes scenarios with multiple goals and multiple agents. The visualization of the tensor flow reveals interesting clues about how decisions are made by the agents. The emerging behaviors are very realistic and demonstrate great potential for the application of this framework to real environments

Probabilistic Inference and Dynamic Programming: A Unified Approach to Multi-Agent Autonomous Coordination in Complex and Uncertain Environments

We present a unified approach to multi-agent autonomous coordination in complex and uncertain environments, using path planning as a problem context. We start by posing the problem on a probabilistic factor graph, showing how various path planning algorithms can be translated into specific message composition rules. This unified approach provides a very general framework that, in addition to including standard algorithms (such as sum-product, max-product, dynamic programming and mixed Reward/Entropy criteria-based algorithms), expands the design options for smoother or sharper distributions (resulting in a generalized sum/max-product algorithm, a smooth dynamic programming algorithm and a modified versions of the reward/entropy recursions). The main purpose of this contribution is to extend this framework to a multi-agent system, which by its nature defines a totally different context. Indeed, when there are interdependencies among the key elements of a hybrid team (such as goals, changing mission environment, assets and threats/obstacles/constraints), interactive optimization algorithms should provide the tools for producing intelligent courses of action that are congruent with and overcome bounded rationality and cognitive biases inherent in human decision-making. Our work, using path planning as a domain of application, seeks to make progress towards this aim by providing a scientifically rigorous algorithmic framework for proactive agent autonomy

Application-layer multipath data transfer via TCP: Schemes and performance tradeoffs

For applications involving data transmission from multiple sources, an important problem is: when sources are allowed to use multiple paths, how does one select paths and control the sending rates on the paths to maximize the aggregate sending rate of the sources? We consider this problem in the context of an overlay network by allowing a source to send data over k (k ≥ 1) overlay paths to its destination. This problem is NP-hard, and we develop an iterative distributed heuristic to solve it. In each iteration, we first select paths and then control the sending rates on the multiple paths to maximize the aggregate sending rate of the sources. For rate control, we develop an application-level multipath rate controller via TCP. This controller is easy to deploy and maximizes the aggregate sending rate of the sources in certain settings. To the best of our knowledge, this is the first distributed application-level controller with such an optimality property. For path selection, we prove that the problem of optimal overlay path selection is NP-hard and propose randomized pathselection algorithms. Our performance evaluation demonstrates that our iterative heuristic performs very well in a wide range of settings. Furthermore, a small number of paths, 2 to 4, and a small amount of extra bandwidth in the network are sufficient to realize most of the performance gains

Hierarchical test sequencing for complex systems

Testing complex systems, such as the ASML TWINSCAN lithographic machine, is expensive and time consuming. In a previous work, a test sequencing method to calculate time-optimal test sequences has been developed. Because complex systems are composed of several subsystems, which are again composed of several modules, there exists a need to hierarchically model test sequencing problems. Such a hierarchical test sequencing problem consists of a high-level model that describes a test sequencing problem at the system level, and one or more low-level models that describe the test sequencing problems at the subsystem or module level. The tests at the system level correspond to the solutions of low-level problems. This paper describes a hierarchical test sequencing model and proposes two algorithms to compute an optimal test sequence. The benefits of hierarchically modeling a problem are less computational effort and less modeling effort, because not all relations are needed. This is illustrated by a small example. The industrial relevance of this method is illustrated on a case study related to a manufacturing testing phase of a lithographic machine

On the Redundancy of D-Ary Fano Codes

We study the redundancy of D-ary Fano source codes. We show that a novel splitting criterion allows to prove a bound on the redundancy of the resulting code which sharpens the guarantee provided by Shannon’s classical result for the case of an optimal code. In particular we show that, for any D≥ 2 and for every source distribution p= p1, ⋯, pn, there is a D-ary Fano code that satisfies the redundancy bound 1$$\begin{aligned} \overline{L} - H_D(\mathbf{p}) \le 1- p_{\min }, \end{aligned}$$L¯-HD(p)≤1-pmin, where, L¯ denotes the average codeword length, pmin= min ipi, and HD(p)=-∑i=1npilogD(pi) is the D-ary entropy of the source. The existence of D-ary Fano codes achieving such a bound had been conjectured in [ISIT2015], where, however, the construction proposed achieves the bound only for D= 2, 3, 4. In [ISIT2020], a novel construction was proposed leading to the proof that the redundancy bound in (1) above also holds for D= 5 (and some other special cases). This result was attained by a dynamic programming based algorithm with time complexity O(Dn) (per node of the codetree). Here, besides proving that the redundancy bound in (1) can be achieved, unconditionally, for every D> 3, we also significantly improve the time complexity of the algorithm building a D-ary Fano code tree achieving such a bound: We show that, for every D≥ 4, a D-ary Fano code tree satisfying (1) can be constructed by an efficient greedy procedure that has complexity O(Dlog 2n) per node of the codetree (i.e., improving from linear time to logarithmic time in n)