Loosely Time-Triggered Architectures (LTTAs) are a proposal for constructing distributed embedded control systems. They build on the quasi-periodic architecture, where computing units execute 'almost periodically', by adding a thin layer of middleware that facilitates the implementation of synchronous applications. In this paper, 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-Pressure LTTA, reminiscent of elastic circuits, and Time-Based LTTA, based on waiting. Compared to previous work, we present controller models that can be compiled for execution and a simplified version of the Time-Based protocol. We also compare the LTTA approach with architectures based on clock synchronization.