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Approximation models for the evaluation of TCP/AQM networks

Marek Dariusz, Domański Adam, Domańska Joanna, Szyguła Jakub, Czachórski Tadeusz, Klamka Jerzy, Filus Katarzyna

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 4

art. no. e141986

EN

The article proposes a model in which Diffusion Approximation is used to analyse the TCP/AQM transmission mechanism in a multinode computer network. In order to prevent traffic congestion, routers implement AQM (Active Queue Management) algorithms. We investigate the influence of using RED-based AQM mechanisms and the fractional controller PIγ on the transport layer. Additionally, we examine the cases in which the TCP and the UDP flows occur and analyse their mutual influence. Both transport protocols used are independent and work simultaneously. We compare our solution with the Fluid Flow approximation, demonstrating the advantages of Diffusion Approximation.

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Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Tikhonenko O., Kempa W. M.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

841--854

EN

A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.

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On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping

Zhernovyi Y., Kopytko B., Zhernovyi K.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 4

163--175

EN

We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk’s potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

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Active queue management with discrete sliding modes in TCP networks

Ignaciuk P., Karbowańczyk M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2014

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Vol. 62, nr 4

701--711

EN

In this paper, a new active queue management (AQM) algorithm for data traffic control in TCP/IP networks is developed. The algorithm design is based on the principles of discrete sliding-mode control. Unlike majority of earlier studies, the design procedure considers the effects of both non-negligible delay in transferring data and feedback information and unpredictable capacity variations. The switching function is selected to incorporate a delay compensation mechanism, which ensures efficient network operation even for large bandwidthdelay product connections. The proposed algorithm, implemented as a packet marking scheme, is tested in discrete event ns-2 simulator. The results show that the algorithm provides fast convergence to steady state after sudden, unanticipated capacity changes. By generating smaller overshoots, the proposed algorithm also allows for reducing buffer space requirements to avoid packet loss as compared to the benchmark AQM solutions.

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Analysis of AQM queues with queue size based packet dropping

Chydziński A., Chróst Ł.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 3

567-577

EN

Queueing systems in which an arriving job is blocked and lost with a probability that depends on the queue size are studied. The study is motivated by the popularity of Active Queue Management (AQM) algorithms proposed for packet queueing in Internet routers. AQM algorithms often exploit the idea of queue-size based packet dropping. The main results include analytical solutions for queue size distribution, loss ratio and throughput. The analytical results are illustrated via numerical examples that include some commonly used blocking probabilities (dropping functions).