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Stochastic service curve and delay bound analysis: a single node case
- Computer Science from University of Kaiserslautern
, 2013
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On computing bounds on average backlogs and delays with network calculus
- in IEEE ICC
, 2010
"... Abstract—The stochastic network calculus is an analytical tool which was mainly developed to compute tail bounds on backlogs and delays. From these, bounds on average backlogs and delays are derived in the literature by integration. This paper improves such bounds on average backlogs by using Jensen ..."
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Abstract—The stochastic network calculus is an analytical tool which was mainly developed to compute tail bounds on backlogs and delays. From these, bounds on average backlogs and delays are derived in the literature by integration. This paper improves such bounds on average backlogs by using Jensen’s inequality; furthermore, improved bounds on average delays follow imme-diately from Little’s Law. The gain factor can be substantial especially at high utilizations, e.g., of order Ω 1
On the Calculation of Sample-Path Backlog Bounds in Queueing Systems over Finite Time Horizons
"... The ability to calculate backlog bounds is of key importance for buffer sizing in packet-switched networks. In particular, it is critical to capture the statisti-cal multiplexing gains which, in turn, calls for stochastic backlog bounds. The stochastic network calculus (SNC) is a promising methodolo ..."
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The ability to calculate backlog bounds is of key importance for buffer sizing in packet-switched networks. In particular, it is critical to capture the statisti-cal multiplexing gains which, in turn, calls for stochastic backlog bounds. The stochastic network calculus (SNC) is a promising methodology to compute such stochastic backlog bounds. So far in the literature SNC-based backlog bounds apply only to an arbitrary, but fixed single point in time. Yet, from the network engineering perspective, one would rather like to have a sample path backlog bound, i.e., a bound that applies (with a certain fixed violation probability) all of the time. While, in general, such bounds are hard to obtain we investigate in this paper how sample path backlog bounds can be computed over finite time horizons. In particular, we show how a simple extension of the known SNC re-sults can lead to sub-optimal bounds by deriving an alternative methodology (based on extreme value theory) for bounding the backlog over finite time hori-zons. Interestingly, none of the two methods completely dominates the other. For the new method we also discuss how it can be evolved into a corresponding calculus for network analysis analogous to the existing SNC. 2
End-to-end delay analysis for networks with partial assumptions of statistical independence
- IN PROCEEDINGS OF THE FOURTH INTERNATIONAL ICST CONFERENCE ON PERFORMANCE EVALUATION METHODOLOGIES AND TOOLS (VALUETOOLS), 2009
, 2009
"... By accounting for statistical properties of arrivals and service, stochastic formulations of the network calculus yield significantly tighter backlog and delay bounds than those obtained in a purely deterministic framework. This paper proposes a stochastic network calculus formulation which can acco ..."
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By accounting for statistical properties of arrivals and service, stochastic formulations of the network calculus yield significantly tighter backlog and delay bounds than those obtained in a purely deterministic framework. This paper proposes a stochastic network calculus formulation which can account for partial assumptions on statistical independence of arrivals and service across multiple network nodes. Scenarios where this can be useful are packet tandem networks with cross traffic and independent arrivals, where identical packet sizes create correlations across the nodes. As an application, the paper investigates the role of partial statistical independence on end-to-end delay bounds in four main scenarios arising by combining assumptions on the statistical independence of arrivals and packet sizes at different network nodes.
Statistical End-to-end Performance Bounds for Networks under Long Memory FBM Cross Traffic
, 2009
"... Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Approximate performance measures are known from large deviations theory for single queuing systems with fBm through traffic. In this paper we derive end-to-end performance bounds f ..."
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Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Approximate performance measures are known from large deviations theory for single queuing systems with fBm through traffic. In this paper we derive end-to-end performance bounds for a through flow in a network of tandem queues under fBm cross traffic. To this end, we prove a rigorous sample path envelope for fBm that complements previous approximate results. We find that both approaches agree in their outcome that overflow probabilities for fBm traffic have a Weibullian tail. We employ the sample path envelope and the concept of leftover service curves to model the remaining service after scheduling fBm cross traffic at a system. Using composition results for tandem systems from the stochastic network calculus we derive end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic. We discover that these bounds grow in O ` 1 ´ n(log n) 2−2H for n systems in series where H is the Hurst parameter of the fBm cross traffic. We show numerical results on the impact of the variability and the correlation of fBm traffic on network performance.
Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems
"... Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sus-tain certain statistical delay guarantees with a small probability of error. We use a stochastic non-equilibr ..."
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Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sus-tain certain statistical delay guarantees with a small probability of error. We use a stochastic non-equilibrium approach that models the variability of traffic and service to formalize the influence of delay constraints on the effective capacity. Permitting unbounded delays, known ergodic capacity results from information theory are recovered in the limit. We prove that the model has the property of additivity, which enables composing CDE boundaries obtained for sources and systems as if in isolation. A method for construction of CDE boundaries is devised based on moment-generating functions, which includes the large body of results from the theory of effective bandwidths. Solutions for essential sources, channels, and respective coders are derived, including Huffman coding, MPEG video, Rayleigh fading, and hybrid automatic re-peat request. Results for tandem channels and for the composition of sources and channels are shown. Index Terms—Queueing analysis, information theory, channel models, time varying channels, quality of service. I.
