On computing per-session performance bounds in high-speed multi-hop computer networks

Abstract

We present a technique for computing upper bounds on the distribution of individual per-session performance measures such as delay and buffer occupancy for networks in which sessions may be routed over several “hops.” Our approach is based on first stochastically bounding the distribution of the number of packets (or cells) which can be generated by each traffic source over various lengths of time and then “pushing” these bounds (which are then shown to hold over new time interval lengths at various network queues) through the network on a per-session basis. Session performance bounds can then be computed once the stochastic bounds on the arrival process have been characterized for each session at all network nodes. A numerical example is presented and the resulting distributional bounds compared with simulation as well as with a point-valued worst-case performance bound.

Tradeoffs in designing networks with end-to-end statistical QoS guarantees

“…(7) (10) The assumption in Eqn. (10) is similar to an assumption made in [3], as well as in related work [6,19,20,21,22]. A theoretical justification for this assumption is made in [21], and the assumption has been supported by numerical examples [3,6,21].…”

“…One group of work on end-to-end statistical QoS, attempts to achieve a characterization of correlated traffic inside a network [5,22,36,40]. An alternative approach, which we adopt in Section 3, is to reconstruct traffic characteristics inside the network so that arrivals to core nodes satisfy the same properties as the arrivals to an edge node.…”

A calculus for information-driven networks

“…For stochastic network calculus, its research can also be tracked back to early 1990s (e.g. [13], [21]). However, due to some difficulties specific to stochastic networks [10], [11], [15], it is only in recent years when critical network calculus properties such as concatenation property [5], [10], [11] and independent case analysis [10], [11] have been proved for stochastic network calculus.…”

A Case for Decomposition of FIFO Networks

“…Envelope functions provide bounds limiting the amount of traffic entering or leaving a network node. Envelopes can be either deterministic (strict and never violated) [10], or have some statistical structure allowing for small violation probabilities [21], [27]. Statistical envelopes capture the multiplexing gain characteristic to aggregates of many independent arrivals [3], and are available for many traffic types, e.g., deterministically regulated, Markov-modulated processes, or fractional Brownian motion [23].…”