Online Call Admission in Optical Networks with Larger Demands

In the problem of Online Call Admission in Optical Networks, briefly called Oca, we are given a graph G = (V,E) together with a set of wavelengths W and a finite sequence σ = r1, r2, . . . of calls which arrive in an online fashion. Each call rj specifies a pair of nodes to be connected and an integral demand indicating the number of required lightpaths. A lightpath is a path in G together with a wavelength λ ∈ W . Upon arrival of a call, an online algorithm must decide immediately and irrevocably whether to accept or to reject the call without any knowledge of calls which appear later in the sequence. If the call is accepted, the algorithm must provide the requested number of lightpaths to connect the specified nodes. The essential restriction is the wavelength conflict constraint: each wavelength is available only once per edge, which implies that two lightpaths sharing an edge must have different wavelengths. Each accepted call contributes a benefit equal to its demand to the overall profit. The objective in Oca is to maximize the overall profit. Competitive algorithms for Oca have been known for the special case where every call requests just a single lightpath. In this paper we present the first competitive online algorithms for the more general case in which the demand of a call may be as large as |W |.