A stochastic model of TCP/IP with stationary random losses

Altman, Eitan; Avrachenkov, Konstantin; Barakat, Chadi

doi:10.1145/347059.347549

Cited by 132 publications

(189 citation statements)

References 22 publications

(7 reference statements)

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“…Every rounds, the window size of the cumulative flow is increased by , and we have (10) Assuming that and are mutually independent sequences of i.i.d. random variables (as in [1]), from (9) we have (11) Taking into account the assumption that a loss occurs identically distributed over all flows we can say that and are equal for all flows, and from now on we denote them by and . From (2) and (5), we have (12) We assume that at the end of a TD-period , flows experiencing loss in that TDP have the window size , and other flows that experience loss in the previous loss event have the window size , etc.…”

Section: Modelmentioning

confidence: 99%

“…From (2) and (5), we have (12) We assume that at the end of a TD-period , flows experiencing loss in that TDP have the window size , and other flows that experience loss in the previous loss event have the window size , etc. The mean value of the window size of the cumulative flow is (13) From (11)- (13), we have (14) From (10), assuming that a loss occurs independently distributed over the size of the cumulative window in a loss round, hence , we have (15) and including (6), (8), (11), (12), and (14) (16) Solving this equation for , we get (17), shown at the bottom of the page, and including (14), we get (18), shown at the bottom of the page. From (1), (2), (6), (8), and (17), we have (19), shown at the bottom of the page.…”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

An Extension of the TCP Steady-State Throughput Equation for Parallel Flows and Its Application in MulTFRC

Damjanovic

Welzl

2011

IEEE/ACM Trans. Networking

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Abstract-In the first part of this paper, we present a simple extension of the well-known TCP steady-state throughput equation that can be used to calculate the throughput of several flows that share an end-to-end path. The value of this extension, which we show to work well with simulations as well as real-life measurements, is its practical applicability. Thus, in the second part of this paper, we present its application in MulTFRC, a TCP-friendly rate control (TFRC)-based congestion control mechanism that is fair to a number of parallel TCP flows while maintaining a smoother sending rate than multiple real TFRC flows do. MulTFRC enables its users to prioritize transfers by controlling the fairness among them in an almost arbitrary fashion.

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Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

An Extension of the TCP Steady-State Throughput Equation for Parallel Flows and Its Application in MulTFRC

Damjanovic

Welzl

2011

IEEE/ACM Trans. Networking

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“…This situation is quite common in wireless channels in which radio conditions are often the bottlenecks, and not the congestions. It is also a common situation in TCP connections over long distances as was shown by experiments in [3]. In addition, when connections are subject to loss events by exogenous traffic, it has been shown that the losses are independent of the window size (as has been observed in [5]).…”

Section: Introductionmentioning

confidence: 77%

“…Upon loss detection, the window is reduced by a multiplicative factor. TCP modeling has been studied extensively in the literature (see e.g., [2][3][4] and references there), and many authors have been interested in the performance of several parallel TCP connections (see e.g., [5][6][7]). …”

Section: Introductionmentioning

confidence: 99%

Orchestrating parallel TCP connections: Cyclic and probabilistic polling policies

Czerniak

Altman

Yechiali

2012

Performance Evaluation

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t r a c tThe standard Transmission Control Protocol (TCP) is based on an additive rate increase in the absence of congestion, and on multiplicative decrease triggered by congestion signals. However, it does not scale well as the distances, or as the speed of the network, increase. Thus, we study some of the solutions that have been proposed to encounter this problem. These solutions include (i) splitting the transmission from a source to its destination into several parallel connections, and (ii) using Scalable TCP, which is a more aggressive version of TCP. The connection whose rate decreases when a signal arrives is chosen either at random or according to a round robin policy. Our analysis concentrates on a centrally controlled TCP system having N connections. We consider both Additive Increase Multiplicative Decrease (AIMD) and Multiplicative Increase Multiplicative Decrease (MIMD) control mechanisms. The Laplace-Stieltjes Transforms (LST) of the transmission rate of each connection at a polling instant, as well as at an arbitrary moment, are derived. Explicit results are obtained for the mean transmission rate and (in contrast to most polling models) for its second moment. For the AIMD procedure under the cyclic visit policy we show that, for both dynamic (Hamiltonian-type) and static visit orders in each cycle, the connections should be visited following a simple index rule in order to achieve maximum throughput. For the probabilistic visit policy we obtain the set of optimal probabilities that maximizes mean throughput. The analysis of the probabilistic MIMD models uses transformations yielding a system's law of motion equivalent to that of an M/G/1 queue with batch service. The MIMD control mechanism with probabilistic strategy is further analyzed for the case where the transmission rate is bounded above.

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“…For recent papers on growth-collapse models and their applications, see [1], [2], [3], [5], [6], [8], [9], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

Kella

2009

J. Appl. Probab.

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In this paper we generalize existing results for the steady-state distribution of growthcollapse processes. We begin with a stationary setup with some relatively general growth process and observe that, under certain expected conditions, point-and time-stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and necessarily has the marginal distribution of the stationary version. We then specialize to the cases where an independent and identically distributed (i.i.d.) structure holds and where the growth process is a nondecreasing Lévy process, and in particular linear, and the times between collapses form an i.i.d. sequence. Known results can be seen as special cases, for example, when the inter-collapse times form a Poisson process or when the collapse ratio is deterministic. Finally, we comment on the relation between these processes and shot-noise type processes, and observe that, under certain conditions, the steady-state distribution of one may be directly inferred from the other.

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A stochastic model of TCP/IP with stationary random losses

Cited by 132 publications

References 22 publications

An Extension of the TCP Steady-State Throughput Equation for Parallel Flows and Its Application in MulTFRC

An Extension of the TCP Steady-State Throughput Equation for Parallel Flows and Its Application in MulTFRC

Orchestrating parallel TCP connections: Cyclic and probabilistic polling policies

On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

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