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RETRIAL NETWORKS WITH FINITE BUFFERS AND THEIR APPLICATION TO INTERNET DATA TRAFFIC

Published online by Cambridge University Press:  25 September 2008

Kostia Avrachenkov  and
Uri Yechiali
Kostia Avrachenkov
Affiliation:
INRIA, Sophia Antipolis, France E-mail: k.avrachenkov@sophia.inria.fr
Uri Yechiali
Affiliation:
Tel Aviv University, Tel Aviv, Israel E-mail: uriy@post.tau.ac.il
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Abstract

Data on the Internet is sent by packets that go through a network of routers. A router drops packets either when its buffer is full or when it uses the Active Queue Management. Currently, the majority of the Internet routers use a simple Drop Tail strategy. The rate at which a user injects the data into the network is determined by transmission control protocol (TCP). However, most connections in the Internet consist only of few packets, and TCP does not really have an opportunity to adjust the sending rate. Thus, the data flow generated by short TCP connections appears to be some uncontrolled stochastic process. In the present work we try to describe the interaction of the data flow generated by short TCP connections with a network of finite buffers. The framework of retrial queues and networks seems to be an adequate approach for this problem. The effect of packet retransmission becomes essential when the network congestion level is high. We consider several benchmark retrial network models. In some particular cases, an explicit analytic solution is possible. If the analytic solution is not available or too entangled, we suggest using a fixed-point approximation scheme. In particular, we consider a network of one or two tandem M/M/1/K-type queues with blocking and with an M/M/1/∞-type retrial (orbit) queue. We explicitly solve the models with particular choices of K, derive stability conditions for K≥1, and present several graphs based on numerical results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 4 , October 2008 , pp. 519 - 536
Copyright
Copyright © Cambridge University Press 2008

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