Abstract:  Timely use of an automated external defibrillator (AED) is critical for survival after out-of-hospital cardiac arrest, yet AED deployment creates value only if devices reach patients within a clinical window. We study how a city should allocate an AED budget between fixed locations and mobile fleets to maximize timely deliveries. In the fixed-location (static system), a responder retrieves an AED before reaching the patient; in the mobile system, on-demand fleet vehicles carry AEDs for direct delivery. We develop a stochastic spatial model capturing two-leg static retrieval and mobile fleet idleness. We first characterize both pure systems. Static performance depends jointly on AED and responder density: increasing either resource eventually yields a ceiling determined by the other. Mobile deployment avoids this retrieval-geometry bottleneck, but fleet idleness and driver responsiveness discount each AED-equipped vehicle’s value. Across otherwise comparable cities, a larger population increases responder density but reduces mobile fleet idleness, producing a unique switch in the preferred pure system from mobile to static. Under identifiable conditions, small budgets can make static deployment inferior even with arbitrarily dense responders. We then solve the joint allocation problem. A log-miss reformulation reveals a scale effect of static deployment, whereas each mobile AED contributes a constant log-miss reduction. Optimal policies therefore concentrate AEDs in one channel until a channel-specific limit makes hybrid deployment relevant. Computable thresholds characterize these regimes. Using real-world data, we find that, at observed AED stocks, the calibrated model favors pure static deployment in New York City and pure mobile deployment in Singapore.