On performance bounds for the integration of elastic and adaptive streaming flows

We study in this paper the integration of elastic and streaming traffic on a same link in an IP network. We are specifically interested in the computation of the mean bit rate obtained by a data transfer. For this purpose, we consider that the bit rate offered by streaming traffic is low, of the order of magnitude of a small parameter ε ≪ 1 and related to an auxiliary stationary Markovian process (X(t)). Under the assumption that data transfers are exponentially distributed, arrive according to a Poisson process, and share the available bandwidth according to the ideal processor sharing discipline, we derive the mean bit rate of a data transfer as a power series expansion in ε. Since the system can be described by means of an M/M/1 queue with a time-varying server rate, which depends upon the parameter ε and process (X(t)), the key issue is to compute an expansion of the area swept under the occupation process of this queue in a busy period. We obtain closed formulas for the power series expansion in ε of the mean bit rate, which allow us to verify the validity of the so-called reduced service rate at the first order. The second order term yields more insight into the negative impact of the variability of streaming flows.

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“…Since E (B 2 ) = 2/µ 2 (1 − ρ) 3 and E(A B 1 ) = µ/(µ − λ) 2 (see for instance standard books such as Cohen (13))). The lemma is proved.…”

Section: It Follows Thatmentioning

confidence: 99%

Integration of streaming services and TCP data transmission in the Internet

Antunes

Fricker

Guillemin

et al. 2005

Performance Evaluation

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“…Bandwidth-sharing network models (Massoulié and Roberts, 2002;Bonald and Proutière, 2003;Gromoll and Williams, 2009) have become quite a standard modeling tool over the past decade for modeling communication networks. In particular, they have been used extensively to represent the flow level dynamics of data traffic in wired or wireless networks (Bonald et al, 2006), as well as for the integration of voice and data traffic (Bonald and Proutière, 2004), hence generalizing more traditional voice traffic models, e.g. Kelly (1979).…”

Section: Inria Conicet and Laas-cnrsmentioning

confidence: 99%

“…Consider now a system where two intrinsically different types of traffic -"streaming" and "elastic" traffic -coexist and share a link of capacity 1. Such models have been considered by Núñez-Queija, van den Berg and Mandjes (1999); Delcoigne, Proutière and Régnié (2004); Bonald and Proutière (2004).…”

Section: Usingmentioning

confidence: 99%

Bandwidth Sharing Networks with Multiscale Traffic

2014

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In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms that conserve the quality of service experienced by the affected classes, while ensuring that the temporarily unstable class is not entirely neglected. In this paper, we examine the complex interaction occurring between several classes of traffic when classes obtain bandwidth proportionally to their incoming traffic. We characterize the evolution of the performance measures of the network from the moment the initial surge takes place until the system reaches its equilibrium. Using a time-space-transition-scaling, we show that the trajectories of the temporarily unstable class can be described by a differential equation, while those of the stable classes retain their stochastic nature. In particular, we show that the temporarily unstable class evolves at a time-scale which is much slower than that of the stable classes. Although the time-scales decouple, the dynamics of the temporarily unstable and the stable classes continue to influence one another. We further proceed to characterize the obtained differential equations for several simple network examples. In particular, the macroscopic asymptotic behavior of the unstable class allows us to gain important qualitative insights on how the bandwidth allocation affects performance. We illustrate these results on several toy examples and we finally build a penalization rule using these results for a network integrating streaming and surging elastic traffic.

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“…The processor sharing discipline has been used to model many aspects of computer systems, including the quantum-based time sharing of the CPU by computer operating systems (see Kleinrock [10]) and (elastic) traffic modeling in communication networks (see Nunez-Queija [16], Roberts [18] and Bonald and Proutiere [2]) and scheduling in Web servers [6].…”

Section: Introductionmentioning

confidence: 99%

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

Hampshire

Massey

2006

Queueing Syst

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We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M t /M t /1 processor-sharing queue. Our analysis is enabled by the introduction of a "virtual customer" which differs from the notion of a "tagged customer" in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.

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On performance bounds for the integration of elastic and adaptive streaming flows

Cited by 39 publications

References 21 publications

Integration of streaming services and TCP data transmission in the Internet

Integration of streaming services and TCP data transmission in the Internet

Bandwidth Sharing Networks with Multiscale Traffic

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

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