Splittable traffic partition in WDM/SONET rings to minimize SONET ADMs

Abstract

SONET ADMs are the dominant cost factor in the WDM/SONET rings. Recently several articles (Belvaux et al., European J. Oper. Res. 108 (1) (1998) 26–35; Călinescu and Wan, Traffic partition in WDM/SONET rings to minimize SONET ADMs, submitted for publication; Gerstel et al., Proc. IEEE INFOCOM’98, vol. 1, pp. 94–101; Liu et al., Proc. INFOCOM, vol. 2, 2000, pp.~1020–1025; Sutter et al., Oper. Res. 46 (5) (1998) 719–728) proposed a number of heuristics for traffic partition so as to use as few SONET ADMs as possible. Most of these heuristics assumes wavelength-continuity, i.e., the same wavelength is allocated on all of the links in the path established for a traffic stream. It was first observed and argued by Gerstel et al. that the number of ADMs can be potentially reduced by allowing a traffic stream to be locally transferred from one ADM in a wavelength to another ADM in a different wavelength at any intermediate node, in other words, the traffic streams are splittable. In this paper, we study two variations of this minimum ADM problem with splittable traffic streams: all traffic streams have prespecified routings, and all traffic streams have no prespecified routings respectively. Both variations are shown to be NP-hard. For the former variation, a heuristic with approximation ratio at most 5/4 is proposed. For the latter variation, a similar heuristic with approximation ratio 3/2 is proposed.