Results 1  10
of
33
On the autocorrelation structure of TCP traffic
, 2000
"... The statistical characteristics of network traffic in particular the observation that it can exhibit long range dependence have received considerable attention from the research community over the past few years. In addition, the recent claims that the TCP protocol can generate traffic with long r ..."
Abstract

Cited by 47 (6 self)
 Add to MetaCart
(Show Context)
The statistical characteristics of network traffic in particular the observation that it can exhibit long range dependence have received considerable attention from the research community over the past few years. In addition, the recent claims that the TCP protocol can generate traffic with long rage dependent behavior has also received much attention. Contrary to the latter claims, in this paper we show that the TCP protocol can generate traffic with correlation structures that spans only an analytically predictable finite range of timescales. We identify and analyze separately the two mechanisms within TCP that are responsible for this scaling behavior: timeouts and congestion avoidance. We provide analytical models for both mechanisms that, under the proper loss probabilities, accurately predict the range in timescales and the strength of the sustained correlation structure of the traffic sending rate of a single TCP source. We also analyze an existing comprehensive model of TCP that accounts for both mechanisms and show that TCP itself exhibits a predictable finite range of timescales under which traffic presents sustained correlations. Our claims and results are derived from Markovian models that are supported by simulations. We note that traffic generated by TCP can be misinterpreted to have long range dependence, but that long range dependence is not possible due to inherent finite timescales of the mechanisms of TCP.
Fluid Queues with Longtailed Activity Period Distributions
, 1997
"... This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like longrange dependence. The central model of the paper is a fluid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the a ..."
Abstract

Cited by 42 (2 self)
 Add to MetaCart
This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like longrange dependence. The central model of the paper is a fluid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the activity periods of at least one source is assumed to be longtailed, which may give rise to longrange dependence. We consider the effect of this tail behaviour on the steadystate distributions of the buffer content at embedded points in time and at arbitrary time, and on the busy period distribution. Both exact results and bounds are discussed.
Activity Periods of an Infinite Server Queue and Performance of Certain Heavy Tailed Fluid Queues
, 1997
"... . A fluid queue with ON periods arriving according to a Poisson process and having a longtailed distribution has long range dependence. As a result, its performance deteriorates. The extent of this performance deterioration depends on a quantity determined by the average values of the system param ..."
Abstract

Cited by 40 (10 self)
 Add to MetaCart
. A fluid queue with ON periods arriving according to a Poisson process and having a longtailed distribution has long range dependence. As a result, its performance deteriorates. The extent of this performance deterioration depends on a quantity determined by the average values of the system parameters. In the case when the the performance deterioration is the most extreme, we quantify it by studying the time until the amount of work in the system causes an overflow of a large buffer. This turns out to be strongly related to the tail behavior of the increase in the buffer content during a busy period of the M=G=1 queue feeding the buffer. A large deviation approach provides a powerful method of studying such tail behavior. 1. Introduction We consider the following fluid queuing model. Sessions arrive to a network server (multiplexer) according to a Poisson process with rate ? 0. Each session remains active for a random length of time with distribution F and a finite mean ¯. We assum...
Subexponential loss rates in a GI/GI/1 queue with applications
 QUEUEING SYSTEMS 33
, 1999
"... Consider a single server queue with i.i.d. arrival and service processes, {A, An, n � 0} and {C, Cn, n � 0}, respectively, and a finite buffer B. The queue content process {Q B n, n � 0} is recursively defined as Q B n+1 = min((Q B n + An+1 − Cn+1) +, B), q + = max(0, q). When E(A − C) < 0, and A ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
Consider a single server queue with i.i.d. arrival and service processes, {A, An, n � 0} and {C, Cn, n � 0}, respectively, and a finite buffer B. The queue content process {Q B n, n � 0} is recursively defined as Q B n+1 = min((Q B n + An+1 − Cn+1) +, B), q + = max(0, q). When E(A − C) < 0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue E(Q B n + An+1 − Cn+1 − B) + has the following explicit asymptotic characterization: E(Q B n + An+1 − Cn+1 − B) + ∼ E(A − B) + as B →∞, independently of the server process Cn. For a fluid queue with capacity c, M/G/ ∞ arrival process At, characterized by intermediately regularly varying on periods τ on, which arrive with Poisson rate Λ, the average loss rate λ B loss satisfies λ B loss ∼ Λ E(τ on η − B) + as B →∞, where η = r + ρ − c, ρ = EAt <c; r (c � r) is the rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with longtailed characteristics, e.g., Internet data services.
Capacity Regions for Network Multiplexers with HeavyTailed Fluid OnOff Sources
, 2001
"... Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous OnOff sources. An OnOff 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 ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
Consider a network multiplexer with a finite buffer fed by a superposition of independent heterogeneous OnOff sources. An OnOff 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. KeywordsNetwork multiplexer, Finite buffer fluid queue, OnOff process, Heavytailed distributions, Subexponential distributions, Longrange dependence I.
How System Performance is Affected by the Interplay of Averages in a Fluid Queue with Long Range Dependence Induced by Heavy Tails
 Ann. Appl. Probab
, 1999
"... . We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonet ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
. We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonetheless, the extent of this performance deterioration is shown to depend crucially on the average values of the system parameters. 1. Introduction We consider the following fluid queuing model. Sessions (ON periods) are initiated at a network server or multiplexer according to a Poisson process with rate ? 0. Each session is active for a random length of time with distribution F and a finite mean ; during this time it generates network traffic at unit rate. We assume that the lengths of different sessions are independent, and they are also independent of the Poisson arrival process. The service rate is r ? 0 units of traffic per unit time. If X(t) denotes the amount of work (measured in unit...
Overflow Behavior in Queues with Many LongTailed Inputs
 ADVANCES IN APPLIED PROBABILITY
, 1999
"... We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponenti ..."
Abstract

Cited by 16 (7 self)
 Add to MetaCart
We consider a fluid queue fed by a superposition of n homogeneous onoff sources with generally distributed on and offperiods. We scale buffer space B and link rate C by n, such that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n; we specifically examine the situation in which also b is large. We explicitly compute asymptotics for the case in which the onperiods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull. We provide a detailed interpretation of our results. Crucial is the shape of the function v(t) := log P(A* > t) for large t, A* being the residual onperiod. If v(&middot;) is slowly varying (e.g., Pareto, Lognormal), then, during the trajectory to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill `slowly', and the typical time to overflow will be `more than linear' in the buffer size. In contrast, if v(&middot;) ...
Scheduling Strategies and LongRange Dependence
 Queueing Systems
, 1999
"... This paper is another contribution to understanding the effect that longrange 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 ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
This paper is another contribution to understanding the effect that longrange 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 longtailed sources
 IN PROC. IEEE INFOCOM
, 2001
"... In this paper we consider a multibuffered 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 ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
In this paper we consider a multibuffered 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 samplepath description of the workload evolution under GPS as well as the marked Poisson structure of the inputs.
Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous HeavyTailed OnOff Processes
, 2000
"... Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent OnOff processes. An OnOff process consists of a sequence of alternating independent activity and silence periods. Successive activity, as well as silence, periods are identically distributed. The p ..."
Abstract

Cited by 14 (5 self)
 Add to MetaCart
(Show Context)
Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent OnOff processes. An OnOff process consists of a sequence of alternating independent activity and silence periods. Successive activity, as well as silence, periods are identically distributed. The process is active with probability p on and during its activity period produces fluid with constant rate r. For this queueing system, under the assumption that the residual activity periods are intermediately regularly varying, we derive explicit and asymptotically exact formulas for approximating the stationary loss probability and loss rate. In the case of homogeneous sources with residual activity periods equal in distribution to on r , the queue overflow probability is asymptotically, as B !1, equal to P[Q B = B] = ` N k 0 ' p k 0 on P on r ? B k 0 (r \Gamma ae) +N ae \Gamma c k 0 (1 + o(1)); where ae = rp on , N ae ! c and k 0 is the smallest integer greater than (c...