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Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows
- Ann. Appl. Probab
"... We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant ” subset of the flows, ..."
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Cited by 22 (10 self)
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We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant ” subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a “minimally critical ” set of On– Off flows with regularly varying On periods. In case the dominant set contains just a single On–Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On–Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios.
Asymptotic Behavior of Generalized Processor Sharing with Long-Tailed Traffic Sources
- IN: PROC. INFOCOM 2000 CONFERENCE
, 1999
"... We analyze the asymptotic behavior of long-tailed traffic sources under the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing, have emerged as an important mechanism for achieving differentiated quality-of-service in integrated-services n ..."
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Cited by 22 (9 self)
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We analyze the asymptotic behavior of long-tailed traffic sources under the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing, have emerged as an important mechanism for achieving differentiated quality-of-service in integrated-services networks. Under certain conditions, we prove that in an asymptotic sense an individual source with longtailed traffic characteristics is effectively served at a constant rate, which may be interpreted as the maximum feasible average rate for that source to be stable. Thus, asymptotically, the source is only affected by the traffic characteristics of the other sources through their average rate. In particular, the source is essentially immune from excessive activity of sources with `heavier'-tailed traffic characteristics. This suggests that GPS-based scheduling algorithms provide an effective mechanism for extracting high multiplexing gains, while protecting individual connections.
Self-Similar Communication Models And Very Heavy Tails
, 1998
"... Several studies of file sizes either being downloaded or stored in the world wide web have commented that tails can be so heavy that not only are variances infinite, but so are means. Motivated by this fact, we study the infinite node Poisson model under the assumption that transmission times are h ..."
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Cited by 19 (6 self)
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Several studies of file sizes either being downloaded or stored in the world wide web have commented that tails can be so heavy that not only are variances infinite, but so are means. Motivated by this fact, we study the infinite node Poisson model under the assumption that transmission times are heavy tailed with infinite mean. The model is unstable but we are able to provide growth rates. Self-similar but non-stationary Gaussian process approximations are provided for the number of active sources, cumulative input, buffer content and time to buffer overflow.
Empirical Testing Of The Infinite Source Poisson Data Traffic Model
, 2000
"... The infinite source Poisson model is a fluid queue approximation of network data transmission that assumes that sources begin constant rate transmissions of data at Poisson time points for random lengths of time. This model has been a popular one as analysts attempt to provide explanations for obser ..."
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Cited by 17 (5 self)
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The infinite source Poisson model is a fluid queue approximation of network data transmission that assumes that sources begin constant rate transmissions of data at Poisson time points for random lengths of time. This model has been a popular one as analysts attempt to provide explanations for observed features in telecommunications data such as self-similarity, long range dependence and heavy tails. We survey some features of this model in cases where transmission length distributions have (a) tails so heavy that means are infinite, (b) heavy tails with finite mean and infinite variance and (c) finite variance. We survey the self-similarity properties of various descriptor processes in this model and then present analyses of four data sets which show that certain features of the model are consistent with the data while others are contradicted. The data sets are 1) the Boston University 1995 study of web sessions, 2) the UC Berkeley home IP HTTP data collected in November 1996, 3) tr...
Capacity Regions for Network Multiplexers with Heavy-Tailed Fluid On-Off Sources
, 2001
"... Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous On-Off sources. An On-Off source consists of a sequence of alternating independent activity and silence periods. During its activity period a source produces fluid with constant rate. For this sys ..."
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Cited by 17 (6 self)
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Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous On-Off sources. An On-Off source consists of a sequence of alternating independent activity and silence periods. During its activity period a source produces fluid with constant rate. For this system, under the assumption that the residual activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate. The derived asymptotic formulas, in addition to their analytical tractability, exhibit excellent quantitative accuracy, which is illustrated by a number of simulation experiments. We demonstrate through examples how these results can be used for efficient computing of capacity regions for network switching elements. Furthermore, the results provide important insight into qualitative tradeoffs between the overflow probability, offered traffic load, available capacity, and buffer space. Overall, they provide a new set of tools for designing and provisioning of networks with heavytailed traffic streams. Keywords---Network multiplexer, Finite buffer fluid queue, On-Off process, Heavy-tailed distributions, Subexponential distributions, Long-range dependence I.
Reduced Load Equivalence under Subexponentiality
, 2001
"... A+B of a queue with capacity # loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and e - , we show that W A+B is asymptotically equal to the reduced load queue W A , where b is the mean rate of B. This co ..."
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Cited by 16 (3 self)
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A+B of a queue with capacity # loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and e - , we show that W A+B is asymptotically equal to the reduced load queue W A , where b is the mean rate of B. This complements the known result that this property does not hold when both processes have lighter than e - deviation decay rates. Furthermore, using the same methodology, we show that under an equivalent set of conditions the results on sampling at subexponential times hold. Keywords: Large deviations, non-Cramer type conditions, reduced load equivalence, independent sampling, subexponential distributions 1
Dynamic bandwidth allocation algorithms for high-speed data wireless networks,” tech
, 2000
"... Next-generation wireless networks are expected to support a wide range of highspeed data services, with Web browsing as one of the major applications. Although high data rates have been shown feasible in a single-user setting, the resource allocation issues that arise in a multiple-user context rema ..."
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Cited by 16 (1 self)
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Next-generation wireless networks are expected to support a wide range of highspeed data services, with Web browsing as one of the major applications. Although high data rates have been shown feasible in a single-user setting, the resource allocation issues that arise in a multiple-user context remain extremely challenging. Compared with voice, data traffic is typically more bursty, while the users are less sensitive to delay. These characteristics require resource allocation strategies to operate in a fundamentally different manner if the spectrum is to be used efficiently. In this paper we propose several algorithms for scheduling the efficient transmission of data to multiple users. As a new feature, the various schemes exploit knowledge of the buffer contents to achieve high throughput, while maintaining fairness by providing quality of service (QoS) to individual users. The proposed algorithms are backward compatible with existing cellular and personal communications services (PCS) standards such as IS-136. They provide a powerful approach to improving spectrum efficiency in forthcoming high-speed data cellular services. The extensive simulation experiments we present in this paper demonstrate that the algorithms significantly outperform conventional schemes.
Scheduling Strategies and Long-Range Dependence
- Queueing Systems
, 1999
"... This paper is another contribution to understanding the effect that long-range dependent traffic can have on the performance of communication networks. Our goal here is to investigate the role of scheduling policies in controlling such effects. We carry out this investigation in the framework of a s ..."
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Cited by 15 (0 self)
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This paper is another contribution to understanding the effect that long-range dependent traffic can have on the performance of communication networks. Our goal here is to investigate the role of scheduling policies in controlling such effects. We carry out this investigation in the framework of a single server queuing model, described below
Asymptotic analysis of GPS systems fed by heterogeneous long-tailed sources
- IN PROC. IEEE INFOCOM
, 2001
"... In this paper we consider a multi-buffered system consisting of N buffers accessed by heterogeneous longtailed sessions and served according to the Generalized Processor Sharing (GPS) discipline with weights fOE i g. We assume that sessions arrive according to a Poisson process. A session of type i ..."
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Cited by 15 (0 self)
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In this paper we consider a multi-buffered system consisting of N buffers accessed by heterogeneous longtailed sessions and served according to the Generalized Processor Sharing (GPS) discipline with weights fOE i g. We assume that sessions arrive according to a Poisson process. A session of type i transmits at rate r i and has a duration whose distribution is longtailed of the form P ( i ? t) ff i t \Gamma(1+fi i ) where ff i , fi i ? 0. We obtain the large buffer asymptotics under very general stability hypotheses. In particular we show that recent results on the GPS asymptotics obtained by Borst, Boxma and Jelenkovic can be recovered and there are important cases for which we obtain exact asymptotes for which the previous results do not apply. The methodology exploits the sample-path description of the workload evolution under GPS as well as the marked Poisson structure of the inputs.
