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This paper proposes an integrated method for the accurate and fair cost allocation of the transmission system among the users (generators and loads) of the network. It mitigates the existing research gaps and implementation issues in the marginal participation approach for network cost allocation. Major challenges in the marginal participation approach are 1) fair selection of economic slack busses 2) inaccuracy due to use of DC power flow 3) treatment of the counter flows and 4) enforcement of cost-causality. While the prior art has addressed the sub-problems individually, an integrated approach has been missing. This work fills this research gap. Besides, it for the first time introduces the use of linearized AC power flow for calculating the marginal flows. This provides a major improvement over the DC power flow model as nominal voltage and reactive power variables can be modeled without compromising linearity. Economic slack bus selection by min-max fairness approach, modelling of counter flows without resulting in negative cost-shares (payoffs), enhancement of cost-causality by segregating usage cost, reliability cost, and residual costs are other salient contributions of the proposed work. These features result in a rigorously fair, accurate, and yet tractable method computationally. Case-studies on many systems including the IEEE-118 bus system demonstrate the claims made. [ABSTRACT FROM AUTHOR]