Lightpath Scheduling and Routing for Traffic Adaptation in WDM Networks

James Yiming Zhang; Hussein Mouftah; Jing Wu; Michel Savoie

doi:10.1364/JOCN.2.000803

Journal of Optical Communications and Networking
Vol. 2,
Issue 10,
pp. 803-819
(2010)
•https://doi.org/10.1364/JOCN.2.000803

Lightpath Scheduling and Routing for Traffic Adaptation in WDM Networks

James Yiming Zhang, Hussein Mouftah, Jing Wu, and Michel Savoie

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James Yiming Zhang, Hussein Mouftah, Jing Wu, and Michel Savoie, "Lightpath Scheduling and Routing for Traffic Adaptation in WDM Networks," J. Opt. Commun. Netw. 2, 803-819 (2010)

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About this Article
History
- Original Manuscript: April 13, 2010
- Revised Manuscript: August 2, 2010
- Manuscript Accepted: August 11, 2010
- Published: September 29, 2010

Abstract

We study the benefits and trade-offs of using scheduled lightpaths for traffic adaptation. We propose a network planning model that allows lightpaths to slide within their desired timing windows with no penalty on the optimization objective and to slide beyond their desired timing windows with a decreasing tolerance level. Our model quantitatively measures the timing satisfactions or violations. We apply the Lagrangian relaxation and subgradient methods to the formulated optimization problem, with which great computational efficiency is demonstrated when compared with other existing algorithms. Our simulation results show how timing flexibility improves network resource utilization and reduces rejections.

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Solution Methods	References	Description of Solution Methods
Heuristic algorithm (for the joint problem)	[3]	Separately solving two subproblems: (1) routing and (2) wavelength assignment. For the routing subproblem, the branch-and-bound method is used to obtain the optimal solution, while Tabu search is used to obtain approximate solutions. For the wavelength assignment subproblem, a greedy vertex coloring algorithm is used. A heuristic algorithm is used to jointly solve the two subproblems, where demands are sorted first and then apply the fixed-alternate routing, followed by a first fit wavelength assignment to each demand.
Heuristic algorithm	[4]	A global random search algorithm to compute RWA schemes that minimize the number of rejected SSLDs
Simulated-annealing-based method	[5]	A simulated-annealing algorithm iteratively explores the solution space until a stopping condition is satisfied
Branch-and-bound method	[6]	Use the branch-and-bound method for solving integer linear programming problems, provided by the CPLEX software package
Heuristic algorithm	[7, 8]	Sort demands by one of the four policies and then assign costs to wavelength links before searching for working and protection paths. Demand sorting policies: earliest-setup demand first, earliest-teardown demand first, most-conflicting demand first, least-conflicting demand first
Heuristic algorithm assisted by CPLEX	[9]	Precompute candidate paths for each demand and then use CPLEX to obtain the best path selection from the candidate paths for all demands
Heuristic algorithm	[10]	Partition demands into disjoint (in time or in edge) groups. The demands in the same group are routed at the same time and are assigned the same wavelength.
Heuristic algorithm	[11]	Sort demands in ascending order of their starting time, then use greedy heuristics to allocate resources to each demand
Heuristic algorithm	[12]	Partition demands into groups (time-disjoint in one algorithm, time-overlapping in the other algorithm) and then route groups of demands
Heuristic algorithm	[13]	Partition demands into time-disjoint groups and then search for paths sharing links of previously selected paths for the demands in the same group to increase the number of link-disjoint paths available to the demands in other groups
Lagrangian-relaxation-based method	[14, 15]	The constraints of no overbooking on any WC at any time slot are relaxed to create a dual problem. The solution to the dual problem is a performance bound of the original problem. Then, the solution to the dual problem and the generated Lagrangian multipliers are used to develop heuristic algorithms for achieving a near-optimal solution to the original problem.

Solution Methods	References	Description of Solution Methods
Heuristic algorithm assisted by CPLEX	[16, 17]	Schedule demands optimally in time by CPLEX and then use existing methods (e.g., methods in Table 1) for the subproblem where a lightpath must start at its specified starting time
Heuristic algorithm	[18, 19]	Three steps: (1) dividing SSLDs into disjoint windows, (2) using a greedy-window-based RWA algorithm on all SSLDs, and (3) rearranging the SSLDs that are not satisfied in step (2)
Heuristic algorithm	[20]	Heuristic algorithm to schedule SSLDs and to assign wavelength to lightpaths in a single-fiber
Heuristic algorithm	[21]	Partitioning SSLDs into time-disjoint groups
Heuristic algorithm	[22, 23, 24]	Heuristic algorithm to jointly schedule lightpaths and to allocate resources

Type of Constraints	Number of Constraints
Flow conservation constraints in Eq. (4)	$L \times N \times Z$
Wavelength conversion constraints in Eq. (5)	$L \times N \times Z$
Exclusive WC usage constraints in Eq. (6)	$E \times W \times Z$
Converter quantity constraints in Eq. (7)	$N \times Z$
Lightpath persistency constraints in Eq. (8)	$L \times E \times Z \times (Z - 1)$

Solution Methods	References
Branch and bound	In [3], $O ({(K_{MAX})}^{L})$ for the lightpath routing subproblem, where $K_{MAX}$ denotes the maximum number of alternative paths between a given node pair. Note that its complexity is exponential with respect to the number of SSLDs.
Heuristic algorithms	In [10], $O (N^{3} + L \log (L) + L^{2} N^{2})$ for its constructive heuristics (which end deterministically); in [18], $O (L^{2} (E W + N \log N))$ .

Parameters					Results
W	$y_{s d n}$	$r_{s d n}$	$d_{i j}$	F	q	J	Number of Rejected SSLDs
12	49	24	4	4	9122	9256	2
12	49	24	4	0	9146	9414	5
8	49	24	4	4	10165	11178	31
8	49	24	4	0	10174	11762	37
10	49	24	4	4	9263	10005	14
10	49	24	4	0	9287	10330	19
10	49	24	8	4	17820	17862	30
10	49	24	8	0	17829	17922	37
12	20	20	4	4	9278	9781	9
12	20	20	4	0	9288	10145	15
12	20	20	8	4	17723	17882	35
12	20	20	8	0	17726	17942	41

Network Settings				Total Number of SSLDs in Traffic Matrix	J	q	Duality Gap (%)
Network Name	Number of Nodes $(N)$	Number of Links $(E)$	Number of Wavelength Channels $(W)$	Total Number of SSLDs in Traffic Matrix	J	q	Duality Gap (%)
NSFNET	14	21	12	231	11653	11344	2.72
	14	21	4	105	5379	5081	5.86
	14	21	7	165	8198	8035	2.03
Random Network	22	35	10	352	18278	17641	3.61
	22	35	6	211	11015	10715	2.80
	22	35	8	263	13708	13346	2.72
European Network	28	61	8	403	19421	19162	1.35
	28	61	10	605	28180	27222	3.52
	28	61	4	201	9673	9217	4.95
	28	61	12	807	37837	35434	5.43
Average Duality Gap (%)							3.50

Lightpath Scheduling and Routing for Traffic Adaptation in WDM Networks

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Journal of Optical Communications and Networking