Probability
On computing per-session performance bounds in high-speed multi-hop computer networks
SIGMETRICS '92/PERFORMANCE '92 Proceedings of the 1992 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Performance and stability of communication networks via robust exponential bounds
IEEE/ACM Transactions on Networking (TON)
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Performance bonds for flow control protocols
IEEE/ACM Transactions on Networking (TON)
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Performance Guarantees in Communication Networks
Performance Guarantees in Communication Networks
Computer Networks: The International Journal of Computer and Telecommunications Networking - Network processors
A basic stochastic network calculus
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
Buffer overflow asymptotics for multiplexed regulated traffic
Performance Evaluation
Stochastic Network Calculus
A methodology for computing end-to-end delay bounds in FIFO-multiplexing tandems
Performance Evaluation
Demultiplexing in Network Calculus- A Stochastic Scaling Approach
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Network calculus and queueing theory: two sides of one coin: invited paper
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Network calculus delay bounds in queueing networks with exact solutions
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
A system-theoretic approach to bandwidth estimation
IEEE/ACM Transactions on Networking (TON)
On superlinear scaling of network delays
IEEE/ACM Transactions on Networking (TON)
A survey of envelope processes and their applications in quality of service provisioning
IEEE Communications Surveys & Tutorials
Survey of deterministic and stochastic service curve models in the network calculus
IEEE Communications Surveys & Tutorials
Stochastically bounded burstiness for communication networks
IEEE Transactions on Information Theory
Scaling properties of statistical end-to-end bounds in the network calculus
IEEE Transactions on Information Theory
A Min-Plus Calculus for End-to-End Statistical Service Guarantees
IEEE Transactions on Information Theory
Statistical service assurances for traffic scheduling algorithms
IEEE Journal on Selected Areas in Communications
Delay Bounds in Communication Networks With Heavy-Tailed and Self-Similar Traffic
IEEE Transactions on Information Theory
Sharp bounds in stochastic network calculus
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
On applying stochastic network calculus
Frontiers of Computer Science: Selected Publications from Chinese Universities
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ACM Sigcomm 2006 published a paper [26] which was perceived to unify the deterministic and stochastic branches of the network calculus (abbreviated throughout as DNC and SNC) [39]. Unfortunately, this seemingly fundamental unification---which has raised the hope of a straightforward transfer of all results from DNC to SNC---is invalid. To substantiate this claim, we demonstrate that for the class of stationary and ergodic processes, which is prevalent in traffic modelling, the probabilistic arrival model from [26] is quasi-deterministic, i.e., the underlying probabilities are either zero or one. Thus, the probabilistic framework from [26] is unable to account for statistical multiplexing gain, which is in fact the raison d'être of packet-switched networks. Other previous formulations of SNC can capture statistical multiplexing gain, yet require additional assumptions [12], [22] or are more involved [14], [9] [28], and do not allow for a straightforward transfer of results from DNC. So, in essence, there is no free lunch in this endeavor. Our intention in this paper is to go beyond presenting a negative result by providing a comprehensive perspective on network calculus. To that end, we attempt to illustrate the fundamental concepts and features of network calculus in a systematic way, and also to rigorously clarify some key facts as well as misconceptions. We touch in particular on the relationship between linear systems, classical queueing theory, and network calculus, and on the lingering issue of tightness of network calculus bounds. We give a rigorous result illustrating that the statistical multiplexing gain scales as Ω(√N), as long as some small violations of system performance constraints are tolerable. This demonstrates that the network calculus can capture actual system behavior tightly when applied carefully. Thus, we positively conclude that it still holds promise as a valuable systematic methodology for the performance analysis of computer and communication systems, though the unification of DNC and SNC remains an open, yet quite elusive task.