The network services present diversity as the continuous evolution of communication scenarios, which brings a great challenge to the efficient utilization of resources. The ALOHA access mechanism is considered as an effective solution to deal with multi services for its feature of shared bandwidth. However, the collision problem of ALOHA degrades the quality of service (QoS) seriously. The multi packet reception (MPR) technology could mitigate collision and improve network performance. Considering ALOHA mechanism with MPR capability, we propose a novel random access scheme for aggregate traffic based on deep fusion of supermartingale and improved sparrow search algorithm (SSA) to provide delay QoS guarantee. Firstly, we construct a complicated queuing model with heterogeneous arrivals and ALOHA-type service. Secondly, we derive the tighter delay-violation probability bound relying on supermartingale theory, and the optimization problem is constructed with the goal of minimizing the service rate and the constraint of supermartingale bound. Finally, we improve the SSA by combining Circle chaotic map, nonlinear inertia weight and Lévy flight strategy, then the scheme is designed by applying the improved SSA and supermartingale constraint. Simulation results show that the proposed algorithm has faster convergence speed and the scheme is more bandwidth-saving.