Consider a tandem queuing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stations with the goal of maximizing the long-run average throughput. Our main conclusion is that the presence of server failures does not have a major impact on the optimal assignment of servers to stations for the systems we consider. More specifically, we show that when the servers are generalists, any nonidling policy is optimal, irrespective of the reliability of the servers. We also provide theoretical and numerical results for Markovian systems with two stations and two or three servers that suggest that the structure of the optimal server assignment policy does not depend on the reliability of the servers and that ignoring server failures when assigning servers to stations yields near-optimal throughput. Finally, we present numerical results that illustrate that simple server assignment heuristics designed for larger systems with reliable servers also yield good throughput performance in Markovian systems with three stations and three failure-prone servers.

This article investigates TP2 dependence of sample spacings. It is proved that TP2 (RR2) dependence between a general spacing and a nonadjacent order statistic might be characterized by the DLR (ILR) property of the parent distribution, and TP2 dependence between any pair of consecutive spacings might be characterized by the DLR aging property of the population. Furthermore, TP2 dependence between any two consecutive spacings in multiple outliers exponential models is also derived. In addition, some applications in reliability and business auction are presented as well.

We consider two multiclass discriminatory process sharing (DPS)-like time-shared M/G/1 queuing systems in which the weight assigned to a customer is a function of its class as well as (1) the attained service of the customer in the first system and (2) the residual processing time of the customer in the second system. We study the asymptotic slowdown, the ratio of expected sojourn time to the service requirement, of customers with very large service requirements. We also provide various results dealing with ordering of conditional mean sojourn times of any two given classes. We also show that the sojourn time of an arbitrary customer of a particular class in the standard DPS system (static weights) with heavy-tailed service requirements has a tail behavior similar to that of a customer from the same class that starts a busy period.

This paper describes a technique for assembling both data types and functions from isolated individual components. We also explore how the same technology can be used to combine free monads and, as a result, structure Haskell's monolithic IO monad.

Design by analogy is a powerful part of the design process across the wide variety of modalities used by designers such as linguistic descriptions, sketches, and diagrams. We need tools to support people's ability to find and use analogies. A deeper understanding of the cognitive mechanisms underlying design and analogy is a crucial step in developing these tools. This paper presents an experiment that explores the effects of representation within the modality of sketching, the effects of functional models, and the retrieval and use of analogies. We find that the level of abstraction for the representation of prior knowledge and the representation of a current design problem both affect people's ability to retrieve and use analogous solutions. A general semantic description in memory facilitates retrieval of that prior knowledge. The ability to find and use an analogy is also facilitated by having an appropriate functional model of the problem. These studies result in a number of important implications for the development of tools to support design by analogy. Foremost among these implications is the ability to provide multiple representations of design problems by which designers may reason across, where the verb construct in the English language is a preferred mode for these representations.

This paper deals with the system of agents treated as a concurrent modular system, which is able to support the designer in solving complex design tasks. The behavior of design agents is modeled by sets of grammar rules. Each agent manages a graph grammar and a database of facts concerning the subtask for which it is responsible. The course of designing is determined by the interaction between cooperating specialized agents. The design context is expressed by the environment in which agents act and predicates describing design criteria. The organization, design methodology, and a semantic model of a grammar-based multiagent design system are presented. The notions of a valid design solution and a design solution consistent with the design criteria are also introduced. The proposed approach is illustrated by the example of designing a house estate.

This work is aimed at establishing a common frame and understanding of function modeling (FM) for our ongoing research activities. A comparative review of the literature is performed to grasp the various FM approaches with their commonalities and differences. The relations of FM with the research fields of artificial intelligence, design theory, and maintenance are discussed. In this discussion the goals are to highlight the features of various classical approaches in relation to FM, to delineate what FM introduces to these fields, and to discuss the applicability of various FM approaches in these fields. Finally, the basic ideas underlying our projects are introduced with reference to the general framework of FM.

Creativity of designers can be enhanced by the application of appropriate triggers. The presence of triggers helps designers to search solution spaces. The searching of a solution space increases the possibility of finding creative solutions. Both representation and content of the triggers or stimulus to which the designers are exposed are believed to play a vital role in the representation and content of the outcome of the designers during problem solving. We studied the effect of representation of triggers on ideas generated by six design engineers while trying to solve a given problem. A variety of representations (video/animation and audio, text, explanation, and others) that are potentially useful to designers for five prespecified triggers were administered to each designer, who generated ideas in response to each trigger–representation combination individually. The effect of representations of these triggers on the content and representation of the solutions generated by the design engineers was studied. The results showed significant influence of the representation of the triggers on the representations, number, and quality of the resulting ideas that were generated.

We describe a method for constructing a structural model of an unlabeled target two-dimensional line drawing by analogy to a known source model of a drawing with similar structure. The source case is represented as a schema that contains its line drawing and its structural model represented at multiple levels of abstraction: the lines and intersections in the drawing, the shapes, the structural components, and connections of the device are depicted in the drawing. Given a target drawing and a relevant source case, our method of compositional analogy first constructs a representation of the lines and the intersections in the target drawing, then uses the mappings at the level of line intersections to transfer the shape representations from the source case to the target; next, it uses the mappings at the level of shapes to transfer the full structural model of the depicted system from the source to the target.

We show that any positive integer is the least period of a factor of the Thue-Morse word.We also characterize the set of least periods of factors of a Sturmian word. In particular,the corresponding set for the Fibonacci word is the set of Fibonacci numbers.As a by-product of our results, we give several new proofs and tighteningsof well-known properties of Sturmian words.

We study the palindromic complexity of infinite words uβ ,the fixed points of the substitution over a binary alphabet,φ(0) = 0a1, φ(1) = 0b1, with a - 1 ≥ b ≥ 1,which are canonically associated with quadratic non-simple Parrynumbers β.