Loosely Time-Triggered Architectures (LTTAs) are a proposal for constructing distributed embedded control systems. They build on the quasi-periodic architecture, where computing units executenearly periodically, by adding a thin layer of middleware that facilitates the implementation of synchronous applications.In this article, we show how the deployment of a synchronous application on a quasi-periodic architecture can be modeled using a synchronous formalism. Then we detail two protocols,Back-PressureLTTA, reminiscent of elastic circuits, andTime-BasedLTTA, based on waiting. Compared to previous work, we present controller models that can be compiled for execution, a simplified version of the Time-Based protocol and optimizations for systems using broadcast communication. We also compare the LTTA approach with architectures based on clock synchronization.