Today's modern home-automation systems and services (HASS) frequently communicate over public telecommunications networks, such as the Internet. Unfortunately, these communication networks do not usually provide sufficient quality (i.e., a predictable delay), which is generally assured in fieldbus HASS networks. Consequently, the user-perceived quality of experience (QoE) cannot be maintained at a satisfactory level when using different HASS devices communicating over an IP-based network. The data transferred over the Internet can experience a non-negligible delay that can have a considerable influence on the QoE. For this reason, the main goal of our research was to measure the influence of the network delay on a subjective QoE assessment, while interacting with some frequently used HASS tasks. The results show that users are satisfied if the delay is kept below 0.8 s, and that they can tolerate delays of over 2 s (depending on the level of the HASS task interactivity). Since such a user-perceived subjective QoE assessment is both time-consuming and expensive we also propose objective QoE assessment models to represent the influence of network delay on a subjective QoE assessment for various HASS tasks.