Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a time-bounded until operator to express probabilistic timing properties over paths as well as an operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady-state operator) and a Volterra integral equation system (for time-bounded until). We then show that the problem of model-checking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all formulas in the logic.

Abstract not found

. The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P# #p(#1 U I #2 ), for state formulas #1 and #2 , comparison operator ##, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using e#cient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all CSL-formulas. In 12th Annual Symposium on Computer Aided Verification, CAV 2000, c # Springer-Verlag 2000 Chicago,...

Markovian Process Algebra (MPA) is a process algebra enhanced with exponential timing which allows the mapping of specifications on continuous time Markov chains (CTMCs). This paper introduces a compositional approach to compute the generator matrix of the CTMC underlying a MPA specification which consists of the parallel composition of finite state agents. Furthermore two different equivalence relations covering quantitative and qualitative aspects are introduced. These equivalence relations are shown to be congruences according to parallel composition of agents.

This thesis develops the Sporadic Server (SS) algorithm for scheduling aperiodic tasks in real-time systems. The SS algorithm is an extension of the rate monotonic algorithm which was designed to schedule periodic tasks. This thesis demonstrates that the SS algorithm is able to guarantee deadlines for hard-deadline aperiodic tasks and provide good responsiveness for soft-deadline aperiodic tasks while avoiding the schedulability penalty and implementation complexity of previous aperiodic service algorithms. It is also proven that the aperiodic servers created by the SS algorithm can be treated as equivalently-sized periodic tasks when assessing schedulability. This allows all the scheduling theories developed for the rate monotonic algorithm to be used to schedule aperiodic tasks. For scheduling aperiodic and periodic tasks that share data, this thesis defines the interactions and schedulability impact of using the SS algorithm with the priority inheritance protocols. For scheduling ha...

This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures.

This paper describes an approach to discrete event simulation modeling that appears to be effective for developing portable and efficient parallel execution of models of large distributed systems and communication networks. In this approach, the modeler develops sub-models with an existing sequential simulation modeling tool, using the full expressive power of the tool. A set of modeling language extensions permit automatically synchronized communication between sub-models; however, the automation requires that any such communication must take a non-zero amount of simulation time. Within this modeling paradigm, a variety of conservative synchronization protocols can transparently support conservative execution of sub-models on potentially different processors. A specific implementation of this approach, U.P.S. (Utilitarian Parallel Simulator), is described, along with performance results on the Intel Paragon and on the IBM SP2. Portions of this paper are reproduced with permission fr...

Dependability evaluation is an important, but difficult, aspect of the design of fault-tolerant parallel and distributed computing systems. One possible technique is to use Markov models, but if applied directly to realistic designs, this often results in large and intractable models. Many authors have investigated methods to avoid this explosive state-space growth, but have typically either solved the problem for a specific system design, or required manipulation of the model at the state-space level. Stochastic activity networks (SANs), a stochastic extension of Petri nets, together with recently developed reduced base model construction techniques, have the potential to avoid this state space growth at the SAN level for many parallel and distributed systems. This paper investigates this claim, by considering their application to three different systems: a fault-tolerant parallel computing system, a distributed database architecture, and a multiprocessor-multimemory system. We show that this method does indeed result in tractable Markov models for these systems, and argue that it can be applied to the dependability evaluation of many parallel and distributed systems.

This thesis has been submitted in partial fulfillment of requirements for an advanced

We present a time and space efficient algorithm for computing steady state solutions of deterministic and stochastic Petri nets (DSPNs) with both stochastic and structural extensions. The algorithm can deal with different execution policies associated with deterministic transitions of a DSPN. The definition of a subordinated Markov chain (SMC) is refined to reduce the computational cost of deriving the transition probabilities of the embedded Markov chain (EMC) underlying a DSPN. Closed-form expressions of these transition probabilities are presented for some SMC topologies. Moreover, we propose to make use of the reward structure defined on the DSPN to reduce memory requirements. The usefulness of the proposed extensions and the steps of the solution algorithm are illustrated using a DSPN of a simple communication protocol. 1