Scheduling linear network for space and time efficiency

We consider scheduling resources on linear networks where each request is for a set of contiguous resources and for a different amount of time. Allocating spectrum to satisfy variable size data communication requests, utilizing linear resource on a light-trail network for higher efficiency, scheduling communication path for a segmented light-trails network or a multi-hop network with no intermediate storage (receive and forward paradigm), or allocating resources on any linear pipeline, would benefit from such a resource allocation scheme which is proposed here. The problem is similar to a two-dimensional bin packing problem, which is known to be NP-hard, but with an additional constraint that one coordinate location for an object is already fixed. That makes the problem different and interesting to solve. We develop an efficient algorithm and show that it find minimal length schedule with very high probability and demonstrate that a minimum length schedule is not determined by the usage durations of individual resources.