Raymond Marie

Performability analysis using semi-Markov reward processes

M.D. Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudrys approach are presented. The authors generalize the method to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications. >

Loss formulas and their application to optimization for cellular networks

We develop a performance model of a cell in a wireless communication network where the effect of handoff arrival and the use of guard channels is included. Past recursive formulas for the loss probabilities of new calls and handoff calls are developed. Monotonicity properties of the loss probabilities are proven. Algorithms to determine the optimal number of guard channels and the optimal number of channels are given. Finally, a fixed-point iteration scheme is developed in order to determine the handoff arrival rate into a cell. The uniqueness of the fixed point is shown.

Transient analysis of acyclic markov chains

Abstract Continuous-time Markov chains are commonly used insystem reliability modeling. In this paper, we discuss a method for automatically deriving transient solutions that are symbolic in t for acyclic Markov chains. Our method also includes parametric sensitivity analysis of the transient solution and several cumulative measures associated with Markov chain behavior. We include three examples, one to show the use of our method in evaluating approximate solution techniques, one showing parametric sensitivity analysis of a large Markov model, and one demonstrating the computation of cumulative measures for an acyclic Markov reward process.

System performance with user behavior graphs

Abstract Workload characterization is known to be a difficult and yet a very important facet of performance modeling. User behavior graphs have been advocated as a practical means of workload characterization. Performance modeling with user behavior graphs is for the most part carried out using costly simulations. We present inexpensive and yet accurate analytic performance models based on user behavior graphs.

A simple automata based model for stable routing in dynamic ad hoc networks

This paper focuses on routing protocols for ad hoc networks where nodes can be either awake or sleeping or breakdown and where links can be nonpersistent because of both mobility and the state of the nodes. Routing protocols for ad hoc networks already exist but because of uncertainties they produce a significant traffic overhead. We propose a new algorithm aiming at maximizing the existence probability of a route over a given time period. Our model is based on a dynamic graph where the existence of the nodes and the communication capability between them are modeled by simple two state automata. We exhibit closed form expressions for the existence probabilities of the network elements. Our proposition allows fast computation for stable routes.

A note on the effect of preemptive policies on the stability of a priority queue

We study the stability condition of an M/G/1 priority queue with two classes of jobs. Class 1 jobs have preemptive priority over class 2 jobs. We consider three different types of preemptions and the effects of possible work loss (due to preemption) on the stability condition for the queueing system.

FluidSim: a tool to simulate fluid models of high-speed networks

Abstract In this paper, we present a tool for the simulation of fluid models of high-speed telecommunication networks. The aim of such a simulator is to evaluate measures which cannot be obtained through standard tools in reasonable time or through analytical approaches. We follow an event-driven approach in which events are associated with rate changes in fluid flows. We show that under some loose restrictions on the sources, this suffices to efficiently simulate the evolution in time of fairly complex models. Some examples illustrate the utilization of this approach and the gain that can be observed over standard simulation tools.

An approximation for a multiclass./M/1/FIFO queue imbedded in a closed Queueing Network

A new approximation for the multiclass./M/1/FIFO queue in a closed context is proposed. It consists of replacing the FIFO discipline by a RANDOM one. Compared with other approximations already known, this new one gives very good results. However, its utilization appears more sophisticated than the previous methods.

Stability Oriented Routing in Mobile Ad-Hoc Networks Based on Simple Automatons

Since wireless ad-hoc networks with mobile nodes have not stable topology, the classical network functions as the routing are difficult to realize. The router nodes and the links between them are not stable and can appear and disappear randomly. So, classic routing algorithms can not be used successfully. New approaches should be used which deals with these dynamic changes. To avoid frequent route requests and volatile routes due to uncertain information, the objective of the routing can correspond to the route stability. The route computation can be based on random variables and becomes probabilistic routing. Our book chapter focuses on modeling the resilience of these information for ad hoc networks where topology information is uncertain. Our model is based on a dynamic graph where the existence of the nodes and the communication capability between them are modeled by simple two state automaton where the transitions are initiated by random events.

Point and expected interval availability analysis with stationarity detection

Abstract Interval availability is a dependability measure defined by the fraction of time during which a system is in operation over a finite observation period. The system is assumed to be modeled by a finite Markov process. Because the computation of the distribution of this random variable is very expensive, it is common to compute only its expectation. In this note, we propose a new algorithm to compute the expected interval availability and we compare it with respect to the standard uniformization technique from an execution time point of view. This new method is particularly interesting if the Markov chain is stiff. Moreover, a new algorithm for the stationarity detection is proposed in order to avoid excessive computation. Scope and purpose The advent of fault-tolerant computing systems has led to increased interest in analytic techniques for prediction of dependability measures such as the availability over a given period. Interval availability is defined by the fraction of time during which a system is in operation over a finite observation period. By modeling the system behaviour by a Markov process, we transform the problem of evaluating dependability cumulative measures into the computation of the cumulative measures on a Markov process. In this note we are interested in the expected interval availability. Generally, we are faced with the problem of the execution time, especially when the Markov model is stiff, i.e., when we have a highly available system. This note proposes a new technique which deals efficiently with such a class of processes.