We propose a formal timing analysis of an extension of the AFDX standard, incorporating the TSN BLS shaper, to homogenize the avionics communication architecture, and enable the interconnection of different avionics domains with mixed-criticality levels, e.g., current AFDX traffic, Flight Control and In-Flight Entertainment. Existing Network Calculus models are limited to three classes, but applications with heterogeneous traffic require additional classes. Hence, we propose to generalize an existing Network Calculus model to do a worst-case timing analysis of an architecture with multiple BLS on multi-hop networks, to infer real-time bounds. Then, we conduct the performance analysis of such a proposal. First we evaluate the model on a simple 3-classes single-hop network to assess the sensitivity and tightness of the model, and compare it to existing models (CPA and Network Calculus). Secondly, we study a realistic AFDX configuration with six classes and two BLS. Finally, we compute a real use-case to add A350 flight control traffic to the AFDX. Results show the good properties of the generalized Network Calculus model compared to the CPA model and the efficiency of the extended AFDX to noticeably enhance the medium priority level delay bounds, while respecting the higher priority level constraints, in comparison with the current AFDX standard.
The CPA model @cite_16 computes the impact of the other flows by dividing them in four categories: the lower-priority blocking, the same-priority blocking, the higher priority blocking, and the BLS shaper blocking. The latter is defined as follows for a flow of class @math : @math with: @math , @math and @math BLS parameters of class @math ; @math , with @math the Maximum Frame Size of flow @math , @math the streams with a priority lower than @math : the maximum blocking time, called the replenishment interval @math the shortest service interval for class @math .
@cite_16
2168965212 2117702591 2143488880 2150148016
We consider a multiclass multiplexer with support for multiple service classes and dedicated buffers for each service class. Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buffer overflow probability for each dedicated buffer. We assume dependent arrival and service processes as is usually the case in models of bursty traffic. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We introduce a novel optimal control approach to address these problems. In particular, we relate the lower bound derivation to a deterministic optimal control problem, which we explicitly solve. Optimal state trajectories of the control problem correspond to typical congestion scenarios. We explicitly and in detail characterize the most likely modes of overflow. We specialize our results to the generalized processor sharing policy (GPS) and the generalized longest queue first policy (GLQF). The performance of strict priority policies is obtained as a corollary. We compare the GPS and GLQF policies and conclude that GLQF achieves smaller overflow probabilities than GPS for all arrival and service processes for which our analysis holds. Our results have important implications for traffic management of high-speed networks and can be used as a basis for an admission control mechanism which guarantees a different loss probability for each class. We consider the following natural model: customers arrive as a Poisson stream of rate spl lambda n, spl lambda <1, at a collection of n servers. Each customer chooses some constant d servers independently and uniformly at random from the n servers and waits for service at the one with the fewest customers. Customers are served according to the first-in first-out (FIFO) protocol and the service time for a customer is exponentially distributed with mean 1. We call this problem the supermarket model. We wish to know how the system behaves and in particular we are interested in the effect that the parameter d has on the expected time a customer spends in the system in equilibrium. Our approach uses a limiting, deterministic model representing the behavior as n spl rarr spl infin to approximate the behavior of finite systems. The analysis of the deterministic model is interesting in its own right. Along with a theoretical justification of this approach, we provide simulations that demonstrate that the method accurately predicts system behavior, even for relatively small systems. Our analysis provides surprising implications. Having d=2 choices leads to exponential improvements in the expected time a customer spends in the system over d=1, whereas having d=3 choices is only a constant factor better than d=2. We discuss the possible implications for system design. The maximum flow problem is a fundamental graph theory problem with many important applications. Max-flow algorithms based on the push-relabel method are known to have better complexity bound and faster practical execution speed than others. However, existing push-relabel algorithms are designed for uniprocessors or parallel processors that support locking primitives, thus making it very difficult to apply the push-relabel technique to CUDA-based GPUs. We present a first generic parallel push-relabel algorithm for CUDA devices. We model the parallelization efficiency of the algorithm, which reveals that, for a given input graph, the level of parallelism varies during the execution of the algorithm. To maximize the execution efficiency, we develop a dynamically tuned algorithm that utilizes both CPU and GPU by adaptively switching between the two computing units during run time. We show that algorithm finds the maximum flow with O(|V |2|E|) operations (summed over both the CPU and the GPU). Extensive experimental results show that the new algorithm is up to 2 times faster than the push-relabel algorithm by In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity):