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In this paper, we propose a compositional approach for the construction offinite abstractions (a.k.a. finite Markov decision processes (MDPs)) fornetworks of discrete-time stochastic control subsystems that are notnecessarily stabilizable. The proposed approach leverages the interconnectiontopology and a notion of finite-step stochastic storage functions, thatdescribes joint dissipativity-type properties of subsystems and theirabstractions, and establishes a finite-step stochastic simulation function as arelation between the network and its abstraction. To this end, we first developa new type of compositionality conditions which is less conservative than theexisting ones. In particular, using a relaxation via a finite-step stochasticsimulation function, it is possible to construct finite abstractions such thatstabilizability of each subsystem is not necessarily required. We then proposean approach to construct finite MDPs together with their correspondingfinite-step storage functions for general discrete-time stochastic controlsystems satisfying an incremental passivablity property. We also constructfinite MDPs for a particular class of nonlinear stochastic control systems. Todemonstrate the effectiveness of the proposed results, we apply our results onthree different case studies.

Compositional Abstraction of Large-Scale Stochastic Systems: A Relaxed Dissipativity Approach