5G networks enable diverse services such as eMBB, URLLC, and mMTC through network slicing, necessitating intelligent admission control and resource allocation to meet stringent QoS requirements while maximizing Network Service Provider (NSP) profits. However, existing Deep Reinforcement Learning (DRL) frameworks focus primarily on profit optimization without explicitly accounting for service delay, potentially leading to QoS violations for latency-sensitive slices. Moreover, commonly used epsilon-greedy exploration of DRL often results in unstable convergence and suboptimal policy learning. To address these gaps, we propose DePSAC -- a Delay and Profit-aware Slice Admission Control scheme. Our DRL-based approach incorporates a delay-aware reward function, where penalties due to service delay incentivize the prioritization of latency-critical slices such as URLLC. Additionally, we employ Boltzmann exploration to achieve smoother and faster convergence. We implement and evaluate DePSAC on a simulated 5G core network substrate with realistic Network Slice Request (NSLR) arrival patterns. Experimental results demonstrate that our method outperforms the DSARA baseline in terms of overall profit, reduced URLLC slice delays, improved acceptance rates, and improved resource consumption. These findings validate the effectiveness of the proposed DePSAC in achieving better QoS-profit trade-offs for practical 5G network slicing scenarios.

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