Diversity of workload demands lays a critical impact on efficient resource allocation and management of cloud services. The existing literature has either weakly considered or overlooked the heterogeneous feature of job requests received from wide range of internet services users. To address this context, the proposed approach named Reliable and Energy Efficient Traffic Management (REE-TM) has exploited the diversity of internet traffic in terms of variation in resource demands and expected complexity. Specifically, REE-TM incorporates categorization of heterogeneous job requests and executes them by selecting the most admissible virtual node (a software-defined instance such as a virtual machine or container) and physical node (an actual hardware server or compute host) within the cloud infrastructure. To deal with resource-contention-based resource failures and performance degradation, a novel workload estimator ‘Toffoli Gate-based Quantum Neural Network’ (TG-QNN) is proposed, wherein learning process or interconnection weights optimization is achieved using Quantum version of BlackHole (QBHO) algorithm. The proactively estimated workload is used to compute entropy of the upcoming internet traffic with various traffic states analysis for detection of probable resource-congestion. REE-TM is extensively evaluated through simulations using a benchmark dataset and compared with optimal and without REE-TM versions. The performance evaluation and comparison of REE-TM with measured significant metrics reveal its effectiveness in assuring higher reliability by up to 30.25% and energy-efficiency by up to 23% as compared without REE-TM.