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We apply physical interpretations to construct algorithms for the key matrix G in discrete-time quasi-birth-and-death (dtQBD) and its z-transform G(z) , motivated by the work on stochastic fluid models (SFMs) in [13]. In this methodology, we first write a summation expression for G(z) by considering a physical interpretation similar to that of an algorithm in [13]. Next, we construct the corresponding iterative scheme, and prove its convergence to G(z). In particular, here we consider the physical interpretation of Algorithm 1 for Ψ(s) in [13], and use a similar physical interpretation for G(z) partitioned into three sections, each expressed in terms of matrices analogous to block matrices in the fluid generator Q(s) in stochastic fluid models.