Activity-Based Abstraction Refinement for Timed Systems

Formal analysis of real time systems is important as they are widely used in safety critical domains. Such systems combine discrete behaviours represented by locations and timed behaviours represented by clock variables. The counterexample-guided abstraction refinement (CEGAR) algorithm utilizes the fundamental technique of abstraction to system verification. We propose a CEGAR-based algorithm for reachability analysis of timed systems. The algorithm is specialized to handle the time related behaviours efficiently by introducing a refinement technique tailored specially to clock variables. The performance of the presented algorithm is demonstrated by runtime measurements on models commonly used for benchmarking such algorithms

Energy-efficient thermal-aware multiprocessor scheduling for real-time tasks using TCPNs

We present an energy-effcient thermal-aware real-time global scheduler for a set of hard real-time (HRT) tasks running on a multiprocessor system. This global scheduler fulfills the thermal and temporal constraints by handling two independent variables, the task allocation time and the selection of clock frequency. To achieve its goal, the proposed scheduler is split into two stages. An off-line stage, based on a deadline partitioning scheme, computes the cycles that the HRT tasks must run per deadline interval at the minimum clock frequency to save energy while honoring the temporal and thermal constraints, and computes the maximum frequency at which the system can run below the maximum temperature. Then, an on-line, event-driven stage performs global task allocation applying a Fixed-Priority Zero-Laxity policy, reducing the overhead of quantum-based or interval-based global schedulers. The on-line stage embodies an adaptive scheduler that accepts or rejects soft RT aperiodic tasks throttling CPU frequency to the upper lowest available one to minimize power consumption while meeting time and thermal constraints. This approach leverages the best of two worlds: the off-line stage computes an ideal discrete HRT multiprocessor schedule, while the on-line stage manage soft real-time aperiodic tasks with minimum power consumption and maximum CPU utilization

1-Synchronous Programming of Large Scale, Multi-Periodic Real-Time Applications with Functional Degrees of Freedom

The design and implementation of reactive, hard real-time systems involves modeling and generating efficient code for the integration of harmonic multi-periodic tasks. Such a reactive system can be modeled as a synchronous program orchestrating computations, state machine transitions and communications. In a harmonic multi-periodic integration program, task execution rates are related through integral ratios. This paper aims at providing a scalable way to implement large systems composed of modular, synchronous reactive tasks, and to generate efficient code satisfying real-time constraints.The paper describes three incremental extensions to the Lustre language and evaluates them on production applications. First, we propose a clock calculus for 1-synchronous clocks, i.e. strictly periodic clocks with a single activation on their period; we show how the compiler can exploit this information to raise the level of abstraction when integrating tasks at the system level. Second, we allow some variables to have unknown phases, extending the clock inference to gather constraints on unknown phases, using a solver for load balancing over multi-periodic real-time schedules, before instantiating this solution to assign clocks to all reactions of the system. Third, we propose temporally underspecified operations, relevant to many discrete control scenarii, for example on variables with low temporal variability; we show how to express this in a composable way, retaining the Kahn semantics of the synchronous program outside these controlled relaxations, and exploiting slack in the computation to relax the constraints of the real-time load-balancing problem

Safe Schedulability of Bounded-Rate Multi-Mode Systems

Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. The schedulability problem for BMMS is defined as an infinite-round game between two players---the scheduler and the environment---where in each round the scheduler proposes a time and a mode while the environment chooses an allowable rate for that mode, and the state of the system changes linearly in the direction of the rate vector. The goal of the scheduler is to keep the state of the system within a pre-specified safe set using a non-Zeno schedule, while the goal of the environment is the opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS where a winning strategy of the scheduler corresponds to a robust energy-optimal policy. We present an algorithm to decide whether the scheduler has a winning strategy from an arbitrary starting state, and give an algorithm to compute such a winning strategy, if it exists. We show that the schedulability problem for BMMS is co-NP complete in general, but for two variables it is in PTIME. We also study the discrete schedulability problem where the environment has only finitely many choices of rate vectors in each mode and the scheduler can make decisions only at multiples of a given clock period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201

Optimal High Frequency Trading with limit and market orders

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market ordersMarket making; limit order book; inventory risk; point process; stochastic control

Optimal High Frequency Trading with limit and market orders

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market ordersComment: 22 page

Model Checking One-clock Priced Timed Automata

We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions, and we study various model-checking problems for that model based on extensions of classical temporal logics with cost constraints on modalities. We prove that, under the assumption that the model has only one clock, model-checking this class of models against the logic WCTL, CTL with cost-constrained modalities, is PSPACE-complete (while it has been shown undecidable as soon as the model has three clocks). We also prove that model-checking WMTL, LTL with cost-constrained modalities, is decidable only if there is a single clock in the model and a single stopwatch cost variable (i.e., whose slopes lie in {0,1}).Comment: 28 page