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The "switchless" all-optical network is an alternative networking approach being developed in the framework of the ACTS project named SONATA, which aims to provide a future single layer, advanced transport architecture on a national scale. The single hop, shared access network employs time and wavelength agility (a WDMA/TDMA scheme), using fast tunable transmitters and receivers, to set up individual customer connections through a single wavelength router (suitably replicated for resilience). The dimensioning of this type of network is one of the main tasks for the design of networks serving a certain number of customers, connected together by means of passive optical networks (PONs). This paper reports an analytical model which allows the network dimensioning according to some relevant design parameters: the number of customers per PON, the number of PONs, the offered traffic per single user (either considering residential or business user), and the required system performance expressed in terms of blocking probability. Furthermore, relevant issues related to the dimensioning of switchless networks are discussed and some results achieved for relevant network scenarios are reported, to assess the feasibility of the system concept.