Theory of linear and integer programming
Theory of linear and integer programming
Algorithmic geometry
Performance Guarantees in Communication Networks
Performance Guarantees in Communication Networks
Introduction to Algorithms
Delay jitter bounds and packet scale rate guarantee for expedited forwarding
IEEE/ACM Transactions on Networking (TON)
Delay bounds for a network of guaranteed rate servers with FIFO aggregation
Computer Networks: The International Journal of Computer and Telecommunications Networking
Embedded Software in Network Processors - Models and Algorithms
EMSOFT '01 Proceedings of the First International Workshop on Embedded Software
Computer Networks: The International Journal of Computer and Telecommunications Networking
Tight end-to-end per-flow delay bounds in FIFO multiplexing sink-tree networks
Performance Evaluation
The DISCO network calculator: a toolbox for worst case analysis
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Instability of FIFO in the permanent sessions model at arbitrarily small network loads
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
End-to-end delay bounds in FIFO-multiplexing tandems
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Optimal routing for end-to-end guarantees: the price of multiplexing
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
An Algorithmic Toolbox for Network Calculus
Discrete Event Dynamic Systems
Network calculus: a theory of deterministic queuing systems for the internet
Network calculus: a theory of deterministic queuing systems for the internet
Sensor network calculus – a framework for worst case analysis
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Flow control with (min,+) algebra
ISoLA'10 Proceedings of the 4th international conference on Leveraging applications of formal methods, verification, and validation - Volume Part I
Container of (min, +)-linear systems
Discrete Event Dynamic Systems
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Network Calculus is an attractive theory to derive deterministic bounds on end-to-end performance measures. Nevertheless bounding tightly and quickly the worst-case delay or backlog of a flow over a path with cross-traffic remains a challenging problem. This paper carries on with the study of configurations where a main flow encounters some cross-traffic flows which interfere over connected sub-paths. We also assume that no information is available about scheduling policies at the nodes (blind multiplexing). Such configurations were first analyzed in [25, 27] where a "Pay Multiplexing Only Once" (PMOO) phenomenon was identified, and then in [6, 7] where a (min, +) multi-dimensional operator was introduced to compute a minimum service curve for the whole path. Under standard assumptions (concave arrival curves and convex service curves), we prove some properties of this new operator and we show how to use it to derive bounds on delays and backlogs in polynomial time. We also discuss the simpler case when there is no cross-traffic. Then the analysis is known to boil down to the (min, +) convolution of all the service curves over the path. For convex and piecewise affine service curves, a specific theorem enables one to compute efficiently the convolution. This theorem has been used by several authors [6, 8, 17, 21, 22, 25, 27], but they all refer to a proof which sets only one part of the theorem [5]. We provide a new proof based on the Legendre-Fenchel Transform. We also investigate the complexity of computing performances bounds in this case.