Some investigations on FCFS scheduling in hard real-time applications

We investigate some real time behaviour of a (discrete time) single server system with FCFS task scheduling. The main results deal with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadline T. The tree approach used for the derivation of our results is suitable for revisiting problems already solved by queueing theory, too. Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for example, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD(T)]-C • k ' for some x> 1. © 1992 Academic Press, Inc.

Preemptive LCFS scheduling in hard real-time applications, Performance Evaluation

Blieberger, J. and U. Schmid, Preemptive LCFS scheduling in hard real-time applications, Performance Evaluation 1

FCFS-SCHEDULING IN A HARD REAL-TIME ENVIRONMENT UNDER RUSH-HOUR CONDITIONS Abstract.

We investigate some real-time behaviour of a (discrete time) single server system with FCFS (first come first serve) task scheduling under rush-hour conditions. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadline T Relying on a simple general probability model, asymptotic formulas concerning the mean and the variance of SRD (T) are determined; for instance, if the average arrival rate is larger than the departure rate, the expectation of SRD(T) is proved to fulfil E[SRD(T)] = c, + O(T- ') for T-+ m, where c, denotes some constant.- If the arrival rate equals the departure rate, we find E[SRD(T)] c 2 T ' for some i>2

On non-preemptive LCFS scheduling with deadlines

We investigate some real time behaviour of a (discrete time) single server system with nonpreemptive LCFS task scheduling. The main results deal with the probability distribution of a random variable SRD(T), which describes the time the system operates without any violation of a fixed task service time deadline T. A tree approach, similar to those already used for the derivation of the same quantities for other scheduling disciplines (e.g., FCFS) is suitable here again, establishing the power of such techniques once more. Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for example, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD(T)]- CT 3 / 2P T for some p> 1. Our computations rely on a multivariate (asymptotic) coefficient extraction technique which we call asymptotic separation. © 1995 Academic Press, Inc. 1. BASICS In this paper we shall study some aspects concerning the real time behavior of a discrete time single server system with nonpreemptive LCFS task scheduling. Instead of using queueing theory, we apply a special tree approach already used for the derivation of similar results in the case of FCFS and preemptive LCFS scheduling; see [2, 81. Both papers contain a very detailed introduction to the model, as well. The outline of the paper is as follows: After a short description of the underlying model and some questions of interest, we provide the tree approach suitable for the combinatorial and asymptotic computations in Section 3 and 4. Section 5 is devoted to our final results. Finally, some conclusions are appended in Section 6

Symbolic Analysis of Imperative Programming Languages

Abstract. We present a generic symbolic analysis framework for imperative programming languages. Our framework is capable of computing all valid variable bindings of a program at given program points. This information is invaluable for domain-specific static program analyses such as memory leak detection, program parallelisation, and the detection of superfluous bound checks, variable aliases and task deadlocks. We employ path expression algebra to model the control flow information of programs. A homomorphism maps path expressions into the symbolic domain. At the center of the symbolic domain is a compact algebraic structure called supercontext. A supercontext contains the complete control and data flow analysis information valid at a given program point. Our approach to compute supercontexts is based purely on algebra and is fully automated. This novel representation of program semantics closes the gap between program analysis and computer algebra systems, which makes supercontexts an ideal intermediate representation for all domainspecific static program analyses. Our approach is more general than existing methods because it can derive solutions for arbitrary (even intra-loop) nodes of reducible and irreducible control flow graphs. We prove the correctness of our symbolic analysis method. Our experimental results show that the problem sizes arising from real-world applications such as the SPEC95 benchmark suite are tractable for our symbolic analysis framework.

Symbolic Data Flow Analysis for Detecting Deadlocks in Ada Tasking Programs

It is well accepted that designing and analyzing concurrent software-components are tedious tasks. Assuring the quality of such software requires formal methods, which can statically detect deadlocks. This pape