the following sources of literature may help to develop a mathematical model for fog computing latency.
Ashkan Yousefpour, Genya Ishigaki, and Jason P. Jue: „Fog Computing: Towards Minimizing Delay in the Internet of Things“, IEEE International Conference on Edge Computing (EDGE), June 2017; DOI: 10.1109/IEEE.EDGE.2017.12
https://ieeexplore.ieee.org/document/8029252/
Gilsoo Lee, Walid Saad, and Mehdi Bennis: An Online Secretary Framework for Fog Network Formation with Minimal Latency, arXiv:1702.05569v2, Apr 2017
https://arxiv.org/pdf/1702.05569.pdf
Haisheng Tan, Zhenhua Han, Xiang-Yang Li, and Francis C.M. Lau: Online Job Dispatching and Scheduling in Edge-Clouds, IEEE INFOCOM 2017 - IEEE Conference on Computer Communications, May 2017; DOI: 10.1109/INFOCOM.2017.8057116
https://ieeexplore.ieee.org/document/8057116/
Yong Xiao, and Marwan Krunz: QoE and Power Efficiency Tradeoff for Fog Computing Networks with Fog Node Cooperation, IEEE INFOCOM 2017 - IEEE Conference on Computer Communications, May 2017; DOI: 10.1109/INFOCOM.2017.8057196
https://ieeexplore.ieee.org/document/8057196/
Mohammed S. Elbamby, Mehdi Bennis, and Walid Saad: Proactive edge computing in latency-constrained fog networks, arXiv preprint arXiv:1704.06749, Apr. 2017.