Michael J. Ferguson

Exact Results for Nonsymmetric Token Ring Systems

This paper derives exact results for a token ring system with exhaustive or gated service. There are N nodes on the ring and control is passed sequentially from one to the next. Messages with random lengths arrive at each node and are placed on the ring when the control arrives at that node. Exhaustive service means that the queue at a node is empty before the token is released and gated means that only those messages in the queue at the arrival of the token are served at that cycle. Generating function recursions for the terminal service time (the total sojourn time of a token at a node) and, from this, joint cycle and intervisit times are derived. Using known results relating the marginal generating functions of the waiting time and the cycle and intervisit time, it is shown that the N mean waiting times at the nodes require the solution of N(N - 1) and N2equations for the exhaustive and gated cases, respectively. The arrival processes are assumed to be Poisson with different rates and the service processes are general and different at each node. In addition the token overhead is allowed to have an arbitrary but independent distribution at each node. Explicit, simply programmed equations are given. It is shown, arguing from the form of the equations, that there is a conservation law in effect in this system. If the nodal mean waiting times are weighted by the relative intensity, defined here as the intensity weighted mean, then the sum takes on a particularly simple form and is independent of the placement of the nodes on the ring. When the service means at each node are equal, this quantity is just the system mean waiting time.

Computation of the Variance of the Waiting Time for Token Rings

The main new result in this paper is a simple expression for the variance of the waiting time for a token ring with an infinite number of stations, nonsymmetric Poisson traffic, deterministic ring delays, and virtually identical service distributions. These results can be considered as an approximation to the large ring where no individual station dominates the traffic. In the process, the exact equations for obtaining the variance of the waiting time for arbitrary traffics and service densities are found. In general, if there are n nonsymmetric stations, about n3equations need to be solved.

Adaptive control of Markov chains with local updates

Abstract An iterative algorithm is proposed for adaptive expected average cost control of finite state Markov chains. The algorithm estimates the unknown parameter using a strongly consistent parameter estimator, and uses this estimate to update the control policy. Each update may apply to as few as one or as many as all states as long as all states are updated infinitely often as the number of iterations goes to infinity; in this sense the algorithm does local updates. No prior knowledge of the optimal control policy is assumed. The algorithm requires only a small amount of computation at each step, is easily implementable, and converges to the optimal policy in finite time. Its complexity, for queueing systems governed by birth-death processes, is comparable to that of a learning automaton but is based on the optimality equation of dynamic programming.

A multilingual TÊX

This paper discusses a modification to TEX that allows for multilingual hyphenation on a paragraph by paragraph basis using standard TEX fonts. Although this is a sufficient for most applications, it does not of itself solve spacing, linguistically unique characters, text input, nor multilingual message problems. A discussion of these problems, with special emphasis on solutions through TEX modifications, is included. These suggestions are followed with a plea for standardization.

On the operational semantics of nondeterminism and divergence

Abstract An operational model of nondeterministic processes coupled with a novel theory of divergence is presented. The operational model represents internal nondeterminism without using explicit internal transitions. Here the notion of internal state effectively replaces the familiar notion of internal transition, giving rise to an alternative operational view of processes: the weak process. Roughly, a weak process is a collection of stable internal states together with a set of transitions each of which is defined from an internal state to another weak process. Internal nondeterminism arises from such refinement of processes into multiple internal states. A simple extension to the basic weak process model gives rise to an elaborate operational theory of divergence. According to this theory, the ability of a process to undertake an infinite internal computation which is pathological, or persistent, is distinguished from its ability to undertake an infinite internal computation which is not. Although applicable to process algebraic languages with an internal action construct, the resulting model is most suitable for supplying operational semantics to process algebras which express internal nondeterminism by an internal choice construct. The distinction between the two forms of divergence is in particular taken into account when the hiding construct of such a process algebra is assigned a weak process semantics.

A TLA Solution to the Specification and Verification of the RLP1 Retransmission Protocol

This paper presents a series of TLA+ specification/implementations that lead to an implementation of the retransmission policy of RLP1, the Radio Link Protocol proposed for TDMA (Time Division Multiple Access) digital cellular radio. Both safety and liveness properties are proved for SWPInitial, a very abstract, but formal, specification of a sliding window protocol. The rest of the work consists of a series of refinements which finally result in a model of RLP1. Each refinement step is formally proved. In all cases the most difficult part of the proof is for liveness. We prove, formally and rigorously, and parametrised by the window size N, that the model of RLP1 obtained from the last refinement step is an implementation of the initial specification SWPInitial, and thus inherits safety and liveness properties proved for all the higherlevel specifications. The specifications are written in TLA+, a formal language based on TLA, and proofs are given in Lamports hierarchical proof-style. Most proof steps are checked mechanically in Eves.

INRSTÊX: a document preparation system for multiple languages

This paper discusses a system for the preparation of documents, primarily but not exclusively scientific, in several languages. It can be viewed as a very large extension of Plain or as a simpler version of LATEX. Care has been taken to maintain syntactic consistency and to separate the document formatting chores from the document preparation housekeeping chores. This paper is not a complete description of INRSTEX but rather describes its capabilities and chooses lists and combined text/graphics for some detailed comments.

Combining Formal Methods: An Exercise in Integration

Formal methods can rarely capture all the dimensions of a software project. Different aspects of a project are thus typically formalized separately, with little or no integration. We study here the integration of a formal specification methods and a validation method. The methods that we use are Larch and PROMELA/spin. Larch is an algebraic specification method, specialized in the specification of abstract data types and their properties. PROMELA/spin is a modeling and verification package for concurrent systems, based on a process/communication channel abstraction.