Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state ({\em killing}) is possible from any state rather than just one state. The purpose of this paper is to investigate to what extent properties of birth-death processes, in particular with regard to the existence of quasi-stationary distributions, remain valid in the generalized setting. It turns out that the elegant structure of the theory of quasi-stationarity for birth-death processes remains intact as long as killing is possible from only finitely many states, but breaks down otherwise

Quasi-stationary distributions for a class of discrete-time Markov chains

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step ({\it killing}) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general

Paramecium: An Extensible Object-Based Kernel

In this paper we describe the design of an extensible kernel, called Paramecium. This kernel uses an object-based software architecture which together with instance naming, late binding and explicit overrides enables easy reconfiguration. Determining which components reside in the kernel protection domain is up to the user. An certification authority or one of its delegates certifies which components are trustworthy and therefore permitted to run in the kernel protection domain. These delegates may include validation programs, correctness provers, and system administrators. The main advantage of certifications is that it can handle trust and sharing in a non-cooperative environment

An Object Model for Flexible Distributed Systems

this paper we describe a new model for constructing operating systems and applications in an integrated fashion. Compared to current approaches we provide high-level primitives for supporting distributed and parallel applications. We also provide the flexibility to configure both applications and kernels to only include the functionality that is actually used. The model we describe is based on objects. Objects are used to structure both applications programs and operating system kernels. They also provide the application interface to the operating system kernel, and access to hardware devices for both kernels and applications. By providing structuring mechanisms for large (distributed) objects, we believe that applications will be are easier to build. At the same time we provide flexibility by allowing extensions of operating system kernels and applications with new objects at run time[8], and by providing a way to bind to objects dynamically. An important aspect of a distributed system is the scalability of the system [6]. A scalable system should not depend on centralized resources or on algorithms that need global information. At the same time, a flexible system can use different algorithms depending on the situation. For example, the use of broadcasting and multicasting on a local Ethernet can be quite effective but should be avoided on a world wide scale. In this paper we discuss an object model that provides two kinds of objects: local objects and distributed objects. In Section 2 we describe the nondistributed (local) objects, followed by distributed objects in Section 3. We compare our work to that of others in Section 4. 2 Local object

Towards Object-based Wide Area Distributed Systems

In order to facilitate the construction of wide area distributed systems, it is necessary that we adopt a model that simplifies application development. In this position paper we advocate an object-based approach. Our approach allows for flexibility because many of the technical details of distribution, such as communication protocols, consistency rules, etc. can be hidden behind the objects' interfaces. In addition, we allow distributed objects to offer alternative implementations for an interface. A client may choose the most suitable implementation. We discuss the use of distributed objects as the means to this end, and compare our approach to existing ones. 1 Introduction Wide area distributed applications pose varying demands on the underlying operating systems, often making the development of the application itself a difficult task. For example, development of distributed applications often requires the following: ffl Support for expressing communication at a sufficiently high..