## 4 Proposed Algorithm
### Network Slicing Resource Allocation Algorithm Based on LSTM-D3 QN with DC
In the first part of Section 5, we first set the simulation parameters, including the system environment parameters and proposed algorithm parameters. In the second part, we first compare the performance of our proposed algorithm with two representative algorithms, including the baseline algorithm DQN and the algorithm LSTM-A2C in the reference [19]. The simulation results verify that our proposed algorithm outperforms other algorithms in terms of convergence and effectiveness. Then, we simulate the effects on various system optimization metrics with and without DC assistance. This also includes the following three cases: no service priority, eMBB service priority and URLLC service priority. The simulation results show that in either case, the system utility with DC assistance is better than that without DC assistance. For simulation parameters, we simulated the effects of different user numbers on the optimization indicators of the system. The simulation results show that the higher the number of users in the system, the lower the utility, and the approximate number of users that our scenario can accommodate under the condition of guaranteeing QoE is obtained. Finally, we also simulate the effect of different parameters on the algorithm and explain in detail the reasons for the change in performance of the algorithm due to different parameters. This section corresponds to the third part of our contribution. In summary, the contributions mentioned in our introductory section are presented in detail in the text. ## 7 Conclusions

In this paper, we propose a slice resource allocation algorithm based on LSTM-D3 QN to solve the problem of multi-service resource allocation in heterogeneous network scenarios. In order to meet the service requirements of users in small base stations, we use dual connectivity technology, so that users can obtain bandwidth resources from SBS and MBS at the same time, when the base station bandwidth resources are fixed. To address the non-convexity and dynamic nature of our research problem, an iterative LSTM-D3 QN algorithm is proposed. For the proposed algorithm, we first deduce the formulation of D3 QN, and then incorporate the LSTM neural network into the algorithm for better performance. Furthermore, we compare the proposed algorithm with other DRL algorithms to verify the excellent performance of our proposed algorithm. Finally, we compare our scheme with the slice resource allocation scheme without DC assistance from multiple perspectives, verifying the role of DC in resource allocation of heterogeneous network slices. The results show that the DC-assisted resource allocation scheme can achieve higher system utility, throughput and QoEs. **Author Contributions:** Conceptualization, G.C. ; Data curation, X.M. ; Formal analysis, G.C. and X.M. ; Methodology, Q.Z. ; Validation, F.S. ; Writing--original draft, G.C. ; Writing--review and editing, X.M. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the National Natural Science Foundation of China under Grant No. 61701284, 61871370, the Innovative Research Foundation of Qingdao under Grant No. 19-6-2-1-cg, the Elite Plan Project of Shandong University of Science and Technology under Grant No. skz21-3-B-048, the Application Research Project for Postdoctoral Researchers of Qingdao, the National Key R&D Program of China under Grant No. 2019 YFE0120700, 2019 YFB1803101, the Hundred Talent Program of Chinese Academy of Sciences under Grant No. E06 BRA1001, the Sci. & Tech. Development Fund of Shandong Province of China under Grant No. ZR202102230289, ZR202102250695 and ZR2019 LZH001, the Humanities and Social Science Research Project of the Ministry of Education under Grant No. 18 YJAZH017, the Taishan Scholar Program of Shandong Province, the Shandong Chongqing Science and technology cooperation project under Grant No. cstc2020 jscr ljsx20008, the Sci. & Tech. Development Fund of Qingdao under Grant No. 21-1-5-zlyj-1-zc, SDUST Research Fund under Grant No.