doi:10.1016/j.peva.2006.08.001
Copyright © 2006 Elsevier Ltd All rights reserved.
An analytic model of TCP performance over multi-hop wireless links with correlated channel fading
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S.P. Kima and K. Mitchell
, a, 
aSchool of Computing and Engineering, University of Missouri-Kansas City, 5100 Rockhill Road, Kansas City, MO 64110, USA
Received 9 January 2004;
revised 17 July 2006.
Available online 18 September 2006.
Abstract
In this paper, we present an analytic model for TCP performance over wireless channels with highly correlated fading characteristics. The wireless channel TCP segment loss process is modeled using a Linear Algebraic Queueing Theory representation of a hidden Markov chain that can incorporate autocorrelations in successive segment losses. The segment loss model is then used in the development of a discrete time Markov chain representation of the evolution of the TCP congestion window. Variability in the round-trip time (RTT) distribution and sublinear congestion window growth is also incorporated into the model. We derive transient and steady-state performance measures such as the mean and variance of the congestion window size and throughput for various error autocorrelation and RTTs.
Keywords: TCP; Correlated wireless channels; Throughput; Markov chain; Hidden Markov model; Linear algebraic queueing theory
Fig. 1. An example of the window evolution.
Fig. 2. Markov chain of window evolution.
(a) When w≤R.
(b) When w>R.
Fig. 3. A representation of slot and an embedded point.
Fig. 4. A sequence of TOs.
Fig. 5. TO state transition model.
Fig. 6. Comparison of throughput with [13] model and simulation.
Fig. 7. Comparison of throughput with [16] and simulation.
Fig. 8. Distribution of window size with
.
Fig. 9. Squared coefficient of variation of the throughput.
Fig. 10. Window size distribution,
.
Fig. 11. Squared coefficient of variation of the throughput.
Fig. 12. Window size distribution,
.
Fig. 13. Squared coefficient of variation of the throughput.
(a) When w≤R.
(b) When w can be greater than R.
(c) When w can be greater than R and RTT is a function of w.
Fig. 14. Three congestion window scenarios.
Fig. 15. Scenario 1: Effect of RTT variance on the c2 of the throughput.
Fig. 16. Scenario 2: Effect of RTT variance on the mean of the throughput.
Fig. 17. Scenario 2: Effect of RTT variance on the c2 of the throughput.
Fig. 18. Scenario 3: Effect of RTT variance on the mean of the throughput.
Fig. 19. Scenario 3: Effect of RTT variance on the c2 of the throughput.
Fig. 20. Throughput over a two-hop wireless connection.
Fig. 21. Transient behavior of the mean window size w.
This work has been supported in part by a grant from the University of Missouri Research Board and the National Science Foundation NSF ANI-0106640.

Corresponding author. Tel.: +1 816 235 1227; fax: +1 816 235 5159.