Bottlenecks in Two-Hop Ad Hoc Networks - Dividing Radio Capacity in a Smart Way

In two-hop ad hoc networks the available radio capacity tends to be equally shard among the contending stations, which may lead to bottleneck situations in case of unbalanced traffic routing. We propose a generic model for evaluating adaptive capacity sharing strategies. We use infinite-state stochastic Petri nets for modeling the system and use the logic CSRL for specifying the measures of interest

Computing Battery Lifetime Distributions

The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetime depends naturally on the rate at which energy is consumed, however, it also depends on the usage pattern of the battery. Continuous drawing of a high current results in an excessive drop of residual capacity. However, during \ud intervals with no or very small currents, batteries do recover to a certain extend. We model this complex behaviour with an inhomogeneous Markov reward model, following the approach of the so-called Kinetic battery Model (KiBaM). \ud The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop a tailored numerical algorithm for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery

Model checking algorithms for Markov reward models

Model checking Markov reward models unites two dierent approaches of model-based system validation. On the one hand, Markov reward models have a long tradition in model-based performance and dependability evaluation. On the other hand, a formal method like model checking allows for the precise specication and verication of complex qualitative system properties. The logic CSRL (an extension of CTL) provides the specic means to formulate desired properties of Markov reward models, including constraints on time and accumulated reward. The most involved operator of CSRL is the so-called until operator with quantitative constraints in the form of a time and a reward interval. Its model checking is closely connected to the computation of the distribution of accumulated reward in the Markov reward model. So far, suitable numerical algorithms have only been published for the restricted case where the time and the reward interval have lower bounds equal to zero. In this thesis we close the gap and present the theoretical basis as well as the numerical algorithms needed for model checking CSRL until formulas with arbitrary time and reward intervals

A versatile infinite-state Markov reward model to study bottlenecks in 2-hop ad hoc networks

In a 2-hop IEEE 801.11-based wireless LAN, the distributed coordination function (DCF) tends to equally share the available capacity among the contending stations. Recently alternative capacity sharing strategies have been made possible. We propose a versatile infinite-state Markov reward model to study the bottleneck node in a 2-hop IEEE 801.11-based ad hoc network for different adaptive capacity sharing strategies. We use infinite-state stochastic Petri nets (iSPNs) to specify our model, from which the underlying QBD-type Markov-reward models are automatically derived. The impact of the different capacity sharing strategies is analyzed by CSRL model checking of the underlying infinite-state QBD, for which we provide new techniques. Our modeling approach helps in deciding under which circumstances which adaptive capacity sharing strategy is most appropriate

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

Efficient CSL Model Checking Using Stratification

For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.Comment: 18 pages, preprint for LMCS. An extended abstract appeared in ICALP 201