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We propose a quasi-dynamic network design algorithm considering traffic growth in multi-layered photonic networks that consist of electrical paths and optical paths. The quasi-dynamic network design proposed herein leaves existing paths unchanged in order to minimize service disruption due to path rerouting as well as human error. Simulations verify that the network cost strongly depends on the network design algorithms adopted and the holding terms of service traffic. We, then, introduce a new parameter that represents expected service holding terms. The parameter is shown to represent effectively the network cost trend versus the number of the incremental designs. Furthermore, lower network cost is obtained by taking advantage of the network design algorithms that consider service holding times. This study is the first to address the criteria in designing future multi-layered photonic networks that offer cost-effective expansion while accommodating different services.