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LiTPiCs were proposed as a marriage of two innovative technologies - light-trails and photonic integrated circuits - as a solution to extend metro networks in regional domains and provide dynamism in bandwidth allocation for emerging services. Light-trails which are a generalized lightpath, essentially formed by an optical bus provide sub-wavelength optical grooming and facilitate dynamic bandwidth allocation amongst constituent nodes. Communication within a light-trail is all-optical thereby limiting their reach to a few node-spans. In parallel, photonic integrated circuits were developed that proposed the system on a chip concept enabling 3R regeneration of optical signal using embedded lasers and receivers on a single Indium Phosphide substrate. PIC technology has given rise to the concept of digital optical networks which have the capability to increase reach and commoditize metro networks. By conjoining the light-trail and PIC technologies we proposed LiTPiC which is essentially preserves light-trail properties while enhancing their reach. In this paper we study algorithms for scheduling traffic in a LiTPiC. We consider both the static case and the dynamic case - when traffic is known and not known apriori. Further we will establish a lower and upper bound that would facilitate an evaluation procedure of our algorithms.