The advent of cloud computing paradigms has significantly facilitated high-level infrastructure services to numerous dependable end-users. The performance of services depends on statistical accounts or the calibration of the arrival patterns of task-offloading requests at the cloud gateway. This paper brings a theoretical Markovian projection on the maximization of Shannon entropy subject to conventional Poisson-modulated probabilistic moment constraints. However, on considering the frequency of task arrival patterns or frequent dependent request demands from heterogeneous platforms, the performance modeling on the maximization of entropy or uncertainty workloads in conjunction with probabilistic shifted geometric moments along systems’ utility yields a probability distribution function, which characterizes the ubiquitous heavy-tail offloading traffic and power-law traffic phenomena. Numerous crucial metrics with respect to the proposed frameworks have been deduced to their closed forms for resilient systems’ performance analysis.