Wide area telecommunication network design: application to the Alberta SuperNet
Summary (1 min read)
1. Introduction
- The NDP considered in this article is NP-hard because it subsumes several NP-hard problems like the STP.
- Wide area telecommunication network design 1461 due to the complexity of the resulting formulation.
- Instead, the authors opted for a decomposition approach in which they first solve the topological design problem (TDP) and then solve the loading problem (LP) on the TDP solution.
- The authors present models and algorithms for these problems in the next two sections, followed by computational results.
2. Model and heuristic for the TDP
- The objective minimizes the total edge and shelter costs.
- These two constraints lead to the correct cost calculation.
- The authors provide the above formulation for precision in problem definition.
2.1. Greedy heuristic
- It works on the directed graph in which each edge has been replaced by two opposite arcs.
- The SPPR determines the shortest origin-destination path and the relay locations on 1.
- When applied to a particular (o(k), d(k)) pair, the SPPR problem is denoted as SPPR(&).
3.2. Formulation
- If 16) ensure that sufficient fibre is installed on arc (i, j) to carry the flow passing on that arc; whereas constraints (17) guar antee that an appropriately sized cable is installed on (i, j) to accommodate the required number of fibre optical strands.
- This integer program is of large scale even for small net work examples, and is impractical for the Alberta SuperNet project.
3.3. TS algorithm
- The authors have also tested two stopping criteria with several parameter values: the total number of iterations spent in the search and the total number of iterations without improve ment in the value of the best known solution.
- The authors found that the second criterion with a value of 50 produced the best results.
4. Computational results
- As one can observe from Table 4 , the LP routines DBH, DBESH, SH, and SingleTS were very fast, usually per forming calculations in seconds even for the largest test set problems.
- TrunkTS and SingleTrunkTS were comparatively slower, with an average of 8.5 min and of over an hour in the worst case scenario.
- By comparing the gaps of Table 5 , one can see that neither the TrunkTS nor the SingleTrunkTS algorithms yielded solutions that were significantly better than the SingleTS algorithm.
- Figures 8 and 9 show that the SingleTS heuristic is the most promising.
- Each execution of the algorithm described in Figure 2 took, on average, 43 min, and the total gap between the best and the worst solution was 2.55%, corresponding to $3.25 million.
Did you find this useful? Give us your feedback
Citations
102 citations
76 citations
Cites background or methods from "Wide area telecommunication network..."
...Replenishment in various forms has been considered in other contexts, for example, in telecommunications network design involving the use of relays to regenerate signal [2, 3]; as a traveling salesman problem variant, in which the salesman cannot visit too many nodes in a row, or travel too far, without visiting a “replenishment” node [10]; and in aircraft routing, in which an aircraft cannot fly too many hours without having a maintenance opportunity [12]....
[...]
...[2, 3] use the same variant of WCSPP-R as a subproblem, but don’t describe methods for its solution....
[...]
61 citations
Cites background from "Wide area telecommunication network..."
...It has been introduced and studied in [4, 5], and applied to several contexts in [2, 7, 6]....
[...]
18 citations
16 citations
Cites background or methods from "Wide area telecommunication network..."
...[6] develop a two-step method for the design of a wide area broadband internet network in Alberta, CA....
[...]
..., connect a wireless network to an optical network [6, 15], or help to extend the coverage area in wireless networks [12]....
[...]
References
37 citations
37 citations
"Wide area telecommunication network..." refers background in this paper
...A large body of the research addresses pure topological problems like the Steiner tree problem (STP) (eg Koch and Martin, 1998; Lucena and Beasley, 1998; Patterson et al, 1999; Polzin and Vahdati Daneshmand, 2001a,b, 2003; Costa et al, 2006) or problems defined on particular topologies like trees (Randazzo and Luna, 2001; Gzara and Goffin, 2005), rings (eg Armony et al, 2000; Chamberland and Sansò, 2000), or meshes (Costa, 2005; Kerivin and Mahjoub, 2005; Magnanti and Raghavan, 2005)....
[...]
...…Patterson et al, 1999; Polzin and Vahdati Daneshmand, 2001a,b, 2003; Costa et al, 2006) or problems defined on particular topologies like trees (Randazzo and Luna, 2001; Gzara and Goffin, 2005), rings (eg Armony et al, 2000; Chamberland and Sansò, 2000), or meshes (Costa, 2005; Kerivin and…...
[...]
36 citations
"Wide area telecommunication network..." refers background in this paper
...Several papers address hierarchical problems that associate a particular technology with each level (eg Balakrishnan et al, 1998; Chamberland et al, 2000; Chamberland and Sansò, 2001; Chopra and Tsai, 2002; Labbé et al, 2004)....
[...]
...Thus the most cost-effective topology is a tree structure in which the digging and fibre installation costs are minimized, as suggested by Chamberland et al (2000)....
[...]
21 citations
"Wide area telecommunication network..." refers background in this paper
...Several papers address hierarchical problems that associate a particular technology with each level (eg Balakrishnan et al, 1998; Chamberland et al, 2000; Chamberland and Sansò, 2001; Chopra and Tsai, 2002; Labbé et al, 2004)....
[...]
...Several papers address hierarchical problems that associate a particular technology with each level (eg Balakrishnan et al, 1998; Chamberland et al, 2000; Chamberland and Sansò, 2001; Chopra and Tsai, 2002; Labbé et al, 2004)....
[...]
20 citations