40109015
Busy Periods of Poisson Arrival Queues with Loss
We consider two queues with loss, one is the finite dam with Poisson arrivals and the other is the M/G/1 queue with impatient customers. We use the method of Kolmogorov's backward differential equation and construct a type of renewal equation to obtain the Laplace transform of busy(or wet) period in both queues. As a consequence, we provide the explicit forms of expected busy periods.
2880434
The Virtual Waiting Time of the M/G/1 Queue with Impatient Customers
The M/G/1 queue with impatient customers is studied. The complete formula of the limiting distribution of the virtual waiting time is derived explicitly. The expected busy period of the queue is also obtained by using a martingale argument.
15601356
An optimal proportion of perfect repair
At each failure of a system, with probability p it is perfectly repaired, and with probability 1-p it is restored to its condition just prior to failure. It is shown that there exists a unique p minimizing the long-run repair cost, provided the failure time distribution of the system has strictly DMRL.
19038002
Computational Experience of an Interior-Point Algorithm in a Parallel Branch-and-Cut Framework
An interior-point algorithm within a branch-and-bound framework for solving nonlinear mixed integer programs is described. In contrast to solving the relaxation to optimality at each tree node, the relaxation is only solved to near-optimality. Analogous to using advanced bases for warmstart solutions in the case of linear MIP, a \dynamic" collection of warmstart vectors is kept. Computational results on various classes of nonlinear mixed integer programs are presented.
36039309
Consistency in Dataflow Graphs
Analytical properties of programming languages with dataflow graph semantics are discussed. It is shown that one of the most serious problems with these languages is that subtle inconsistencies between parts of the dataflow graph can be inadvertently created. These inconsistencies can lead to deadlock, or in the case of nonterminating programs, to unbounded memory requirements. Consistency is defined to mean that the same number of tokens is consumed as produced on any arc, in the long run. A token-flow model is developed for testing for inconsistency. The method is a generalization of consistency checks for synchronous dataflow (SDF) graphs. The token-flow model is compared to similar tests applied to hybrid dynamical systems. It is argued that dataflow semantics make steady-state analysis possible, leading to a simpler method in most cases. >
858750
Operational Semantics of Hybrid Systems
Hybrid systems are heterogeneous systems that include continuous-time (CT) subsystems interacting with discrete-event (DE) subsystems. They are effective models for physical systems interacting with software or experiencing discrete mode changes. 
This dissertation discusses an interpretation of hybrid systems as executable programs written in a programming language with a hybrid system semantics. The semantic properties of such a programming language affect our ability to understand, execute, and analyze a hybrid system model. This dissertation focuses on a few semantic issues that come in defining such a programming language, such as the interpretation of discontinuities in CT signals and simultaneous discrete events in DE signals, liveness property, and the consequences of numerical ODE solver techniques. 
The interactions between CT and DE subsystems and between DE subsystems themselves are captured by discontinuities in continuous-time signals and simultaneous discrete events in discrete-event signals. In order to precisely represent them in compute execution results, a two-dimension domain, called "super-dense time," is used as the domain for defining signals. This domain allows a signal to have multiple values at the same time point while keeping the values ordered. 
CT and DE subsystems are modeled as actors, which are functions that map a set of signals to another set of signals. In this way, a hybrid system model is just a network of actors interacting via signals. We can always transform a network of actors into a composite actor with feedback, where the function of the composition actor is the composition of functions of the component actors. The least fixed point solution to the function of the composite actor, which is a set of signals, gives the denotational semantics of the hybrid system model. 
The operational semantics takes the denotational semantics as a mathematical foundation and defines a set of rules for evaluating actors such that the least fixed point solution can be constructed. Rather than constructing the whole signals, the operational semantics only computes a discrete subset of the signals called a discrete representation of the signals. The constructive procedure is formalized with the Abstract State Machine semantics, where a hybrid system is treated as a state transition system and the rules specify how state transformations are performed. 
This operational semantics supports heterogeneous and hierarchical composition of different models of computation, such as CT, DE, finite state machines, and synchronous languages, and modular execution of the composition as a whole. This ability makes it easy to jointly model and design software controlled systems. 
The operational semantics proposed in this dissertation has been implemented in HyVisual, which is a software tool for modeling and simulating hybrid systems. HyVisual is part of the Ptolemy II software framework, which is available in open-source form at http://ptolemy.org.
13888487
Hierarchical finite state machines with multiple concurrency models
This paper studies the semantics of hierarchical finite state machines (FSM's) that are composed using various concurrency models, particularly dataflow, discrete-events, and synchronous/reactive modeling. It is argued that all three combinations are useful, and that the concurrency model can be selected independently of the decision to use hierarchical FSM's. In contrast, most formalisms that combine FSM's with concurrency models, such as statecharts (and its variants) and hybrid systems, tightly integrate the FSM semantics with the concurrency semantics. An implementation that supports three combinations is described.
7453458
Designing time-based interactions with multimedia
The current model of time in multimedia frameworks poses particular problems when designing multimedia systems with time-based interaction. We propose to expand and extend an existing distinction between semantic time and real time from music and film theory to multimedia systems design. The semantic time concept also forms the foundation of a new software framework for multimedia systems that we are building, that, unlike most existing frameworks, includes mechanisms for time-based effects such as time-stretching.