Dimensioning WDM Networks for Dynamic Routing of Evolving Traffic

Xiaolan J. Zhang; Sun-il Kim; Steven S. Lumetta

doi:10.1364/JOCN.2.000730

Journal of Optical Communications and Networking
Vol. 2,
Issue 9,
pp. 730-744
(2010)
•https://doi.org/10.1364/JOCN.2.000730

Dimensioning WDM Networks for Dynamic Routing of Evolving Traffic

Xiaolan J. Zhang, Sun-il Kim, and Steven S. Lumetta

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Xiaolan J. Zhang, Sun-il Kim, and Steven S. Lumetta, "Dimensioning WDM Networks for Dynamic Routing of Evolving Traffic," J. Opt. Commun. Netw. 2, 730-744 (2010)

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Abstract

New Internet applications are increasingly generating high-bandwidth and short-lived demands. If network resources are available, establishing a lightpath on demand only takes a few minutes on today’s reconfigurable optical networks. These demands thus create a more variable and unpredictable environment for long-term network planning. At the same time, upgrading backbone networks remains expensive and infrequent. Dimensioning network resources to sustain variable traffic demands for a long time, while requiring fewer upgrades to achieve high performance, has become a challenging problem. Two kinds of dimensioning problems for optical opaque networks are proposed and studied in this paper: basic dimensioning allocates network resources for a newly built network, and incremental dimensioning allocates extra resources for future demand growth and variations. We propose new metrics to quantify the traffic load and the traffic pattern evolution for dynamically routed networks. We evaluate the performance under load scaling, traffic evolution, and misdimensioning. We show that a dimensioned network can sustain a much higher load while providing the same performance compared with misdimensioned ones. Our approach is better adapted to traffic evolution than a uniform allocation and an asymptotic optimization approach proposed earlier.

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N	Set of nodes.
E	Set of links.
$C_{e}$	Current residual capacity of link $e ∊ E$ . C is the set of all links’ capacity.
$B_{e}$	Basic dimensioning capacity for each link. B is the set of all links’ capacity.
$X_{e}$	Incremental dimensioning capacity for each link. X is the set of all links’ capacity.
$σ_{e}$	Statistic standard deviation of link capacity $B_{e}$ . σ is the set of all links’ standard deviation.
R	Set of all end-to-end request pairs. $R \subseteq N \times N$ .
r	Mean capacity rate of a pair. $r_{i}$ is a capacity rate for a pair $i ∊ R$ .
λ	Mean arrival rate per pair. $λ_{i}$ is a random arrival rate for a pair.
μ	Mean departure rate per pair. The average holding time is $1 ∕ μ$ . $μ_{i}$ is a random departure rate for a pair.
T	Traffic matrix.
${TSL}_{i}$	Topological shortest path length for a pair i.
u	Projected traffic load ratio. $u ∊ (0, 1]$ .
l	Offered traffic load ratio. $l > 0$ .
ϵ	Traffic evolution factor. $ϵ ∊ [0, 1]$ .
α	Network misdimensioning factor. $α ∊ [0, 1]$ .
ξ	Incremental dimensioning scheme in ${MEAN, SD}$ .
β	Routing scheme in ${SPF, WSP, LRW, RFR}$ .
$P_{i} (C)$	Set of all available paths of a pair i based on current residual capacity C.
${SPF}_{i} (C)$	Set of all shortest available paths of a pair i based on current residual capacity C.
${SPG}_{i}$	Shortest path graph for a pair i. It is a subgraph containing all paths of length ${TSL}_{i}$ .
$f_{i} (C)$	Maximum flow on ${SPG}_{i}$ with link residual capacity C for the graph.

SD and MEAN
u	0.75	0.80	0.85	0.90	1.00
ARPANET	64.81	40.00	23.31	10.00	0
COST 239	50.22	30.70	18.27	8.32	0
SD and UNI
u	0.75	0.80	0.85	0.90	1.00
ARPANET	4018.81	4003.69	4001.00	3998.94	3939.19
COST 239	3401.89	3369.89	3390.59	3400.92	3332.59


N	Set of nodes.
E	Set of links.
$C_{e}$	Current residual capacity of link $e ∊ E$ . C is the set of all links’ capacity.
$B_{e}$	Basic dimensioning capacity for each link. B is the set of all links’ capacity.
$X_{e}$	Incremental dimensioning capacity for each link. X is the set of all links’ capacity.
$σ_{e}$	Statistic standard deviation of link capacity $B_{e}$ . σ is the set of all links’ standard deviation.
R	Set of all end-to-end request pairs. $R \subseteq N \times N$ .
r	Mean capacity rate of a pair. $r_{i}$ is a capacity rate for a pair $i ∊ R$ .
λ	Mean arrival rate per pair. $λ_{i}$ is a random arrival rate for a pair.
μ	Mean departure rate per pair. The average holding time is $1 ∕ μ$ . $μ_{i}$ is a random departure rate for a pair.
T	Traffic matrix.
${TSL}_{i}$	Topological shortest path length for a pair i.
u	Projected traffic load ratio. $u ∊ (0, 1]$ .
l	Offered traffic load ratio. $l > 0$ .
ϵ	Traffic evolution factor. $ϵ ∊ [0, 1]$ .
α	Network misdimensioning factor. $α ∊ [0, 1]$ .
ξ	Incremental dimensioning scheme in ${MEAN, SD}$ .
β	Routing scheme in ${SPF, WSP, LRW, RFR}$ .
$P_{i} (C)$	Set of all available paths of a pair i based on current residual capacity C.
${SPF}_{i} (C)$	Set of all shortest available paths of a pair i based on current residual capacity C.
${SPG}_{i}$	Shortest path graph for a pair i. It is a subgraph containing all paths of length ${TSL}_{i}$ .
$f_{i} (C)$	Maximum flow on ${SPG}_{i}$ with link residual capacity C for the graph.

SD and MEAN
u	0.75	0.80	0.85	0.90	1.00
ARPANET	64.81	40.00	23.31	10.00	0
COST 239	50.22	30.70	18.27	8.32	0
SD and UNI
u	0.75	0.80	0.85	0.90	1.00
ARPANET	4018.81	4003.69	4001.00	3998.94	3939.19
COST 239	3401.89	3369.89	3390.59	3400.92	3332.59

Abstract

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Equations (6)

Journal of Optical Communications and Networking