Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions

NoC performance parameters estimation at design stage

Nowadays different types of communication systems are used in designing of data transmission systems. Performance and operating characteristics of communication systems are crucial. System-on-chip (SoC) communication system can be built based on a bus, switch or network-on-chip (NoC). Type of communication system is selected according to user requirements for bandwidth, time delays, hardware cost of communication systems implementation and technology limitations. In this paper we consider the problem of different communication systems characteristics estimation. Formulas for average and maximum data transmission time calculation of different flows will be presented for different types of communication systems. Load estimation for each transfer point will be presented also. Proposed network calculator includes mechanisms based on the queuing systems to calculate the parameters of communication system. Attention will be paid to NoC communication system characteristics calculation

Exact Worst-case Delay in FIFO-multiplexing Feed-forward Networks

In this paper, we compute the actual worst-case end-to-end delay for a flow in a feed-forward network of first-in–first-out (FIFO)-multiplexing service curve nodes, where flows are shaped by piecewise-affine concave arrival curves, and service curves are piecewise affine and convex. We show that the worst-case delay problem can be formulated as a mixed integer linear programming problem, whose size grows exponentially with the number of nodes involved. Furthermore, we present approximate solution schemes to find upper and lower delay bounds on the worst-case delay. Both only require to solve just one linear programming problem and yield bounds that are generally more accurate than those found in the previous work, which are computed under more restrictive assumptions

Stability and performance guarantees in networks with cyclic dependencies

With the development of real-time networks such as reactive embedded systems, there is a need to compute deterministic performance bounds. This paper focuses on the performance guarantees and stability conditions in networks with cyclic dependencies in the network calculus framework. We first propose an algorithm that computes tight backlog bounds in tree networks for any set of flows crossing a server. Then, we show how this algorithm can be applied to improve bounds from the literature fir any topology, including cyclic networks. In particular, we show that the ring is stable in the network calculus framework