Betsy S. Greenberg

Model Libraries: Knowledge Representation and Reasoning

We propose a knowledge representation and operators for large, diverse model libraries. The knowledge representation distinguishes between model types that are classes of models defined by a collection of assumptions and model templates and instances that instantiate model types through decomposition and specialization of components. Underlying the knowledge representation are inheritance to represent the level of generalization and multiple levels of instantiation to represent the level of details among models. For inheritance, we define partial order relations for models and their components including domains, classes, units, assumptions, metrics, and constraints. For instantiation, we define constraints on transformations between model types, templates, and instances. The inexact search operators support content-based retrieval especially when it is difficult for a user to exactly specify the characteristics of models of interest. The operators use similarity functions to measure the closeness of a mat...

Repetitive Testing in the Presence of inspection Errors

This article considers a problem posed by a semiconductor manufacturer. The manufacturer wished to design the most cost-efficient final functionality test procedure possible for its semiconductor devices while maintaining high outgoing quality. The problem is that its test procedure is imperfect. Although the manufacturer believes that the tests probability of incorrectly accepting a defective device is very close to 0, they know that it frequently rejects devices that are functioning correctly. Every device must be tested once to ensure high quality. Items that fail can be retested to reduce the cost of discarding good devices. The manufacturer wished to determine whether retesting is beneficial and if so how many retests to conduct. We construct a model from which the expected benefit of n retests may be calculated and then maximized. Expected benefit is a function of both the probability that a device is defective and the probability that the test is incorrect. Thus we suggest methods of estimating th...

An upper bound on the performance of queues with returning customers

Multiple channel queues with Poisson arrivals, exponential service distributions, and finite capacity are studied. A customer who finds the system at capacity either leaves the system for ever or may return to try again after an exponentially distributed time. Steady state probabilities are approximated by assuming that the returning customers see time averages. The approximation is shown to result in an upper bound on system performance.

PREDICTING DISPATCHING DELAYS ON A LOW SPEED, SINGLE TRACK RAILROAD

This paper presents queueing models for predicting dispatching delays on single track, low speed rail lines with widely spaced passing locations. Because of scheduling unpredictabilities, we assume Poisson arrivals of trains. Because of the slow transit speeds, we assume that trains traveling in the same direction can do so on close headways. We also assume siding capacity at passing locations is not limiting. Under these assumptions, we calculate expected delays on individual segments of single track and for segments of single track with an alternate route.

Perishable inventory systems with batch demand and arrivals

In this paper we consider a perishable inventory system in which stored items have finite lifetimes. We assume that both the arrival of and demand for items are batch Poisson processes with geometrically sized batches. We find the Laplace transform and first two moments for the times between shortages and the times between outdates of inventory.

Bowl Shapes Are Better with Buffers–Sometimes

We consider tandem queueing systems with a general arrival process and exponential service distribution. The queueing system consists of several stations with finite intermediate buffer capacity between the stations. We address the problem of determining the optimal arrangement for the stations. We find that considering the last two stations, the departure process is stochastically faster if the slower station is last. Our results are consistent with the “bowl shape” phenomenon that has been observed in serial queueing systems with zero buffer capacity.

Inheritance and instantiation in model management

The authors define a knowledge representation that supports large, diverse model bases. The knowledge representation distinguishes between model types which are classes of models defined by a collection of assumptions, and model templates and instances that instantiate model types through decomposition and specialization of components. Underlying the knowledge representation are inheritance, representing the level of generalization, and multiple levels of instantiation, representing the level of details among models. For inheritance, the authors define partial order relations for model characteristics including domains, classes, units, assumptions, metrics, and constraints, as well as models composed of these characteristics. For instantiation, the authors define constraints between models at different levels of detail. They also briefly discuss how the model management environment can manipulate the knowledge representation in search, explanation, instantiation, and classification of models.<<ETX>>

Measurement theoretic representation of large, diverse model bases: the unified modeling language

The philosophy and features of the Unified Modeling Language LU are presented with emphasis on the support of large, diverse model bases. We argue that measurement theory stressing homomorphic mappings from empirical to mathematical systems is an ideal foundation for integrated modeling environments. Homomorphic mappings are an integral part of the semantics of the LU and motivate a number of language features that support large, diverse model bases. The LU provides a separate but uniform representation of domain worlds and mathematical systems known as model types. Domain worlds are composed of empirical objects, relations, and functions organized into classes and attributes, while model types are defined by standard queries and a rich collection of assumptions. To emphasize the importance of homomorphic mappings, unification constraints combine common patterns of domain and mathematical knowledge in model templates. Reusability and incremental refinement are supported by inheritance based on partial order relations for classes, attributes, assumptions, and model types. Together, the semantic foundation and language features provide a practical and formal knowledge representation for large, diverse model bases.

M/G/1 queueing systems with returning customers

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

Optimal Order for Servers in Series with No Queue Capacity

In this paper we consider the problem of finding the optimal order for two servers in series when there is no queue capacity. We show that it is better for the faster server to be first. The strength of this conclusion will depend on the strength of the assumption made about the service distribution. We also find the optimal order for some systems where both servers have the same average service time and different service distributions.