The recently introduced “probability density approach” to modeling local control of CICR in cardiac myocytes [Williams et al. Biophys. J. 92(7):2311-28, 2007] and associated moment closure technique [95(4):1689-703, 2008] can reproduce whole cell voltage-clamp protocols high-gain Ca release that is graded with changes in membrane potential. This modeling formalism represents heterogeneous local Ca signals in a population of diadic subspaces and junctional sarcoplasmic reticulum (jSR) depletion domains using a system of differential-algebraic equations for the time-evolution of the zeroth, first, and second moments of probability density functions for jSR [Ca] jointly distributed with calcium release unit (CaRU) state. Here we show that a cardiac myocyte model that uses moment equations to represent heterogenous jSR Ca can exhibit Ca alternans when periodically stimulated by depolarizing voltage pulses, and makes predictions regarding the distribution of jSR [Ca] across a large population CaRUs as a function of stimulation frequency and cellular parameters such as the rate of diffusive transfer between network and junctional SR. Factors promoting alternating Ca responses in the moment closure model are analyzed and compared to analogous mechanism in a minimal “common pool” model with comparatively simple SR and PM fluxes. We derive load-release and release-reuptake curves for both models, and investigate how model parameters influence these relations and the existence and stability of steady-state periodic Ca responses during repetitive depolarizing voltage pulses. Specifically, we find that increasing SR Ca leak, RyR sensitivity, and maximum release flux decreases the steepness of load-release curves, shifts load-release curves to smaller SR loads, and increases the critical simulation frequency resulting in Ca alternans.