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«End-to-End QoS Provision over Heterogeneous IP and non IP Broadband Wired and Wireless Network Environments A dissertation submitted in satisfaction ...»

-- [ Page 15 ] --

[35] H. Koumaras, A. Kourtis, and D. Martakos, “Evaluation od video quality based on objectively estimated metric,” pp. 235–242.

[36] 3GPP, “General packet radio service (gprs),” 3GPP TS23.060m v3.12.0, june 2003.

[37] K. Richardson, “Umts overview,” Journal of Electronics and Communication Engineering, vol. 12, no. 3, pp. 130–136, 2000.

[38] I. 802.11g 2003, “Part11 wireless lan medium access control (mac) and physical layer (phy) specification band,” Supp. IEEE 802.11, 2003.

[39] J. K.-J. P. Schramm, G. Malmgren, and J. Torsner, “Hiperlan2, broadband wireless communication at 5 ghz,” IEEE Communication Magazine, vol. 40, no. 6, pp. 130–136, 2002.

[40] H. Koumaras, A. Kourtis, and D. Martakos, “Evaluation od video quality based on objectively estimated metric,” Journal of Communications and Networking, KICS, vol. 7, no. 3, pp. 235–242, september 2005.

[41] T. Pliakas, G. Kormentzas, and C. Skianis, “Scalable video streaming traffic delivery in ip/umts networking environments,” Journal of Multimedia, vol. 2, no. 2, pp. 37–46, april 2007.

[42] T. Pliakas, G. Kormentzas, C. Skianis, and A. Kourtis, “Mpeg-4 fgs video streaming traffic delivery experimentation in an ip/dvb network,” in IEEE International Conference on Communications (ICC), june 2007.

[43] K. Nichols, S. Blake, F. Baker, and D. Black, “Definition of the differentiated services field (ds field) in the ipv4 and ipv6 header,” IETF RFC 2474, December 1998.

[44] I. 802.11e, “Wireless lan medium access conttrol (mac) enhancements for quality of service (qos),” 802.11e draft, 2004.

[45] J. Reichel, H. Schwarz, and M. Wien, “Joint scalable video model joint draft 6,” Joint Video Team, JVT-S201, Geneva, Switzerland, april 2006.

[46] ——, “Joint scalable video model jsvm-6,” Joint Video Team, JVT-S202, Geneva, Switzerland, april 2006.

[47] T. Wiegand, J. Sullivan, G. Bjontegaard, and A. Luthra, “Overview of the h.264/avc video coding standard,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, no. 7, pp. 550–576, July 2003.

[48] H. Schwarz, D. Marpe, and T. Wiegand, “Overview of the scalable h.264/mpeg–4 avc extension,” in IEEE International Conference on Image Processing, Atlanta, october 2006.

[49] A. Ksentini, M. Naimi, and A. Gueroui, “Toward an improvement of h.264 video transmission over ieee 802.11e through a cross layer architecture,” IEEE Communications Magazine, pp. 487–495, 2006.

[50] S. Park, K. Kim, K. D.C., S. Choi, and S. Hong, “Collaborative qos architecture between diffserv and 802.11e wireless lan,” in The 57th IEEE Semiannual Vehicular Technology Conference, april 2004.

[51] “Network simulator v.2 (ns-2) dcf and edca extensions,” http://www.tkn.tuberlin.de/research/802.11e ns2.

[52] “Scalable extension of h.264/mpeg-4 avc,” Fraunhofer Institute, Image Processing Department, available from http://ip.hhi.de.

[53] H. Schulzrinne, “Rtp: A transport protocol real-time applications,” RFC 1889, 1996.

–  –  –

A.1 Regional and Functional Constraints Throughout this report we have considered optimization problems that were subject to constraints. These include the problem of allocating a finite amounts of bandwidth to maximize total user benefit the social welfare maximization problem, and the time of day pricing problem. We make frequent use of the Langragian method to solve these problem. This appendx provides a tutorial on the method.

Take for example:

–  –  –

Here f is to be maximized subject to constraints that are of two types. The constraint x ∈ X is a regional constraint. For example, it might be x 0. The constraint g(x) = b is a functional constraint Sometimes the functional constraint is an inequeality constraint, like g(x0) b But if it is, we can always add a slack variable z, and re-write it as the equality constraint g(x) + z = b, re-defining the regional constraint as x ∈ X and z geqslant0. To illustrate, we shall use the

NETWORK problem with just on resource constraint:

–  –  –

where b is a positive number.

A.2 The Langragian Method The solution of a constrained optimization problem can often be found by using

the so-called Langragian method. We define the Langragian as:

–  –  –

In general, the Langragian is the sum of the orignal objective function, and a term thal involves the functional constraint add a Langrage multiplier λ. Suppose we ignore the functional constraint and consider the problem of maximizing the Langragina, subject only to the regional constraint. This is often an easier problem than the original one. The value of x that maximizes L(x, λ) depends upon the value of λ. Ket us denote this optimizing value of x by x(λ).

For example, since L1 (x, λ) is a concave function of x, t has a unique maximum

at a point where f is stationary with respect to changes in x, i.e. where:

–  –  –

Suppose there existe x∗ ∈ X and λ∗, such that x∗ maximized L(x, λ∗ ), and g(x∗ ) = b. Then x∗ solves P.

Equality in the first line holds because we have simply added 0 on the right hand side. The inequaliy in the secodn line hoolds because we have enlarged the set over which maximization takes place. In the third line, we use the fact that x∗ maximizes L(x, λ∗ and in the fourth line we use g(x∗ = b. But x∗ is feasible for P, in that it satisfies the regional and functional constraints. Hence x∗ is optimal.

If g and b are vectors, so that g(x) = b expresses more than one constraint, when we would write

–  –  –

B.1 The case of producers and consumers

In this appendix we prove that under the tatonnement mechanism price convergence. Consider first the problem of maximizing social surplus:

–  –  –

A typical instance of this problem is when xr is the flow in route r through the network generateing value ur (xr ). A route is a set of links; Ajr = 1 if route r uses link j. Cj is the capacity if link j.

–  –  –

Since C − Ax is the vector excess demand and µ is the price vector, we can repeat the last steps in previous section, and show that again in this case tatonnement will converge to the socially optimal vector of prices.



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