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The growing environmental concerns and increasing electricity prices have led to wider implementation of demand-side activities and created a new class of consumers, called demand response resources (DRRs). The DRRs actively participate in the electricity markets as buyers of electricity and sellers of load curtailment services. The demand profile modifications resulting from the DRR curtailments affect the market outcomes and impact the generation and transmission resource utilization. In this paper, we propose a computationally efficient simulation approach to quantify the impacts of DRRs on market performance, generation dispatch, transmission usage, environment and other system variable effects. We focus on the variable effects that are of interest in planning and policy analysis studies. We construct the proposed simulation approach by marrying the concepts of probabilistic simulation with snapshot-based analysis techniques. In this way, we effectively integrate the representation of the supply- and demand-side resources, electricity markets, transmission grid operations and constraints, and various sources of uncertainty in the simulation. We discuss the implementation aspects of the proposed approach to ensure computational tractability so as to allow its application to the simulation of large-scale systems over longer-term periods. We discuss representative simulation results to illustrate the application of the proposed approach to quantification of the variable effects of a large-scale test system. The reported results demonstrate the economic, environmental and reliability benefits the integration of DRRs can provide to the test system.