Henrik C. Bohnenkamp

On the efficient sequential and distributed generation of very large Markov chains from stochastic Petri nets

In this paper we present efficient techniques for the generation of very large continuous-time Markov chains (CTMCs) specified as stochastic Petri nets (SPNs). In particular, we investigate how the storage efficiency of the reachability graph generation can be improved by using good state coding techniques and by using hashing tables instead of tree-based data structures. These techniques allow us to analyse SPNs with almost 55 million states on a single workstation. The size of the SPNs that can be handled is then further enlarged by using a cluster of workstations. With 16 workstations, connected via a 100 Mbps Ethernet, we can generate reachability graphs with over 400 million states in reasonable time. The presented techniques have been realised in a prototype tool (PARSECS) implemented in C++ using the libraries STL and MPICH. The SPNs to be input to PARSECS are specified using CSPL, known from the tool SPNP. In the paper we present our techniques and study their performance for a number of case studies. We also present comparisons with SPNP.

Cost-optimization of the IPv4 zeroconf protocol

This paper investigates the tradeoff between reliability and effectiveness for the IPv4 Zeroconf protocol, proposed by Cheshire/Adoba/Guttman in 2002, dedicated to the selfconfiguration of IP network interfaces. We develop a simple stochastic cost model of the protocol, where reliability is measured in terms of the probability to avoid an address collision after configuration, while effectiveness is viewed as the average penalty perceived by a user. We derive an analytical expression for the user penalty which we use to derive optimal configuration parameters of the network, restricting to those parameters which are under the control of a consumer electronics manufacturer. In particular we show that minimal cost and maximal reliability are qualities that cannot be achieved at the same time.

Computing Optimal Schedules of Battery Usage in Embedded Systems

The use of mobile devices is often limited by the battery lifetime. Some devices have the option to connect an extra battery, or to use smart battery-packs with multiple cells to extend the lifetime. In these cases, scheduling the batteries or battery cells over the load to exploit the recovery properties of the batteries helps to extend the overall systems lifetime. Straightforward scheduling schemes, like round-robin or choosing the best battery available, already provide a big improvement compared to a sequential discharge of the batteries. In this paper, we compare these scheduling schemes with the optimal scheduling scheme produced with two different modeling approaches: an approach based on a priced-timed automaton model (implemented and evaluated in Uppaal Cora), as well as an analytical approach (partly formulated as nonlinear optimization problem) for a slightly adapted scheduling problem. We show that in some cases the results of the simple scheduling schemes (round-robin, and best-first) are close to optimal. However, the optimal schedules, computed according to both methods, also clearly show that in a variety of scenarios, the simple schedules are far from optimal.

Maximizing system lifetime by battery scheduling

The use of mobile devices is limited by the battery lifetime. Some devices have the option to connect an extra battery, or to use smart battery-packs with multiple cells to extend the lifetime. In these cases, scheduling the batteries over the load to exploit recovery properties usually extends the system lifetime. Straightforward scheduling schemes, like round robin or choosing the best battery available, already provide a big improvement compared to a sequential discharge of the batteries. In this paper we compare these scheduling schemes with the optimal scheduling scheme produced with a priced-timed automaton battery model (implemented and evaluated in Uppaal Cora). We see that in some cases the results of the simple scheduling schemes are close to optimal. However, the optimal schedules also clearly show that there is still room for improving the battery lifetimes.

The Modest Modeling Tool and Its Implementation

This paper is about the tool-suite Motor that supports the modeling and analysis of Modest specifications. In particular, we discuss its tool architecture, and the implementation details of the tool components that do already exist, in particular, the parser, the SOS implementation, an interactive simulator, and a state-space generator. As the expressiveness of Modest goes beyond existing notations for real-time as well as probabilistic systems, the implementation of these tool components has a non-trivial intrinsic complexity.

Synthesis and stochastic assessment of schedules for lacquer production

The Modest modeling language pairs modeling features from stochastic process algebra and from timed and probabilistic automata with light-weight notations such as exception handling. It is supported by the Motor tool, which facilitates the execution and evaluation of Modest specifications by means of the discrete event simulation engine of the Mobius tool. This paper describes the application of Modest, Motor and Mobius to a highly nontrivial case. We investigate the effect of faulty behavior on a hard real-time scheduling problem from the domain of lacquer production. The scheduling problem is first solved using the timed model-checker Uppaal. The resulting schedules are then embedded in a Modest failure model of the lacquer production line, and analyzed with the discrete event simulator of Mobius. This approach allows one to assess the quality of the schedules with respect to timeliness, utilization of resources, and sensitivity to different assumptions about the reliability of the production line.

Timed testing with torx

We describe an approach to on-the-fly real-time testing based on non-deterministic timed automata. The approach is based on standard computations on zone automata. We present algorithms for practical testing, as they were implemented in the testing tool TorX.

On integrating the MOBIUS and MODEST modeling tools

frame-work components. This translation preserves the structureof the models, allowing efficient solutions. The frameworkis implementedin the toolby a well-definedAbstract Func-tional Interface (AFI). Models and solution techniques in-teract with one another through the use of the standardinterface, allowing them to interact with M

Semi-numerical Solution of Stochastic Process Algebra Models

A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the complete global state space of the CTMC. The method works for a fixed number of sequential processes running in parallel and which all synchronize on the same global set of actions. The behaviour of the processes is expressed by the embedded Markov chain of a semi-Markov process and by distribution functions (exponomials) which describe the times between synchronizations. The solution method is exact, hence, the state space explosion problem for this class of processes has been solved. A distributed implementation of the solution technique is straightforward.

Synthesis and stochastic assessment of cost-optimal schedules

We treat the problem of generating cost-optimal schedules for orders with individual due dates and cost functions based on earliness/tardiness. Orders can run in parallel in a resource-constrained manufacturing environment, where resources are subject to stochastic breakdowns. The goal is to generate schedules while minimizing the expected costs. First, we estimate the distribution of each order type by simulation (assuming a reasonable machine/load model) and derive from the cost-function an optimal offset from the due date of each individual order. Second, these optimal offsets are then used to guide the generation of schedules which are responsible to resolve resource conflicts. Third, we evaluate the generated schedules by simulation. The approach is demonstrated by means of a non-trivial case-study from lacquer production. Optimal offsets are derived with the Modest/Möbius tool, schedules are generated using Uppaal Cora. The experimental results show that our approach achieves good results in all considered scenarios, and better results than an approach based on adding slack to processing times.