**3.1 Latency measure**

The proposed system utilizes the Optical-Fog layer that reduces the delay and improves QoE. The latency measured in the context of delay is the most concerning issue. The communication between ONU and OLT is supported by the multi-point control protocol (MPCP) which is a frame-based protocol [15]. Here, only GATE and REPORT messages are exchanged between OLT and ONU. So, in the Optical-Fog network, the delay is measured as the time between the arrival of its last bit at ONU and the arrival of its last bit at OLT. The delay *tD*(*fi*) is the computation of adding three basic components shown as:

$$tD\left(f\_i\right) = \Gamma\_i + t\_p + T\_R \tag{4}$$

Alternatively, it is the time during which the respective REPORT message reaches at the OLT completely, where Γ*i* represents the one-way propagation time of *ONUi*, *tp* represents the time between the request arriving at *ONUi* and the start of the next REPORT message, and *TR* represents the time duration of REPORT message [16]. Thus, the Optical-Fog layer processes more smart applications which require ultralow delay as well as efficient QoS requirements.
