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This work proposes a method to divide the vector of optimal usage of facilities in the grid on account of the transmission of a number of transactions flowing simultaneously into multiple vectors of flows on individual transactions basis. This work focusses on levying charges varying linearly with the power transmitted along various lines. The proposed method is based on the `proportionality assumption`, which is equivalent to compliance of probability laws in the process of flow in the grid, when flows are normalised. A Markov matrix is generated with demand nodes treated as absorbing states. Various powers of the transient sub-matrix allow tracing the fraction of flow from different generation nodes to the demand nodes for any grid flow problem. In this work, various demand nodes are billed for the linearly varying wheeling charges of the grid for the lines actually used. Results for test problems are presented.