— This paper considers scheduling divisible workloads from multiple sources in linear networks of processors. We propose a two phase scheduling strategy (TPSS) to minimize the overall processing time of these workloads by taking advantage of the processor equivalence technique. A case study with two sources of workloads is presented to illustrate the general approach for multiple sources of workloads. In the first phase, using processor equivalence, we derive recursive equations to obtain near-optimal workload distribution for all processors and the minimum processing time of the overall workloads. In the second phase, we propose an efficient algorithm to obtain near-optimal load distribution among processors represented by the equivalent processor. Experimental evaluation through simulations demonstrate performance improvement using our schemes compared to the equal partition scheme.