## 1 Introduction
In decision-making in stochastic systems with access points (APs) operating on multiple channels, an AP is assigned to each user upon arrival to minimize the long-term total average holding cost [15]. In contrast to those previous studies that do not consider multi-band multi-connectivity in mobile communication networks, we propose a transmission point selection algorithm, which selects one or more connectivities by considering the multi-band radio environment of FR1, FR2, and FR3. We also perform simulations in practical network environments exploiting the channel model and beamforming model identified by the 3 rd Generation Partnership Project (3 GPP). Our simulation results show that selecting and serving multiple transmission points regardless of frequency band performs better than services through single-band single-connectivity operation. It is clearly helpful for research and development of multi-band multi-connectivity operation technology. The major contributions of this paper are as follows:  
* We propose TPS algorithms that select multiple transmission points regardless of frequency band in multi-band radio environments, e.g., with FR1, FR2, and FR3: (a) a general TPS algorithm and (b) a sequential TPS algorithm. The proposed TPS algorithms select TPs with the most allowed number of connections for each user, disregarding other users' situations, e.g., received signal strength. * The general algorithm first selects the TP with the maximum expected service time among the available TPs. Then, it selects the maximum expected service time among the TPs, excluding the previously selected TP(s), until the number of connections reaches the total number of allowed connections for each user. * The sequential TPS algorithm selects TPs for each user based on maintaining the candidate set of TPs, by comparing the maximum expected service time in the candidate set with that for prospective TP. In other words, the TP with the maximum expected service time is sequentially eliminated from the TPs in the candidate set, including the prospective TP, until no more TPs are available to compare. * The computational complexity of the general TPS algorithm, which selects connection by connection, depends on the number of connections and transmission points. In contrast, the sequentially selected algorithm attains low complexity compared to the general TPS algorithm. It is due to the fact that the sequential algorithm for a user maintains the candidate set of TPs, by determining whether a TP is included in the set or not. We also show the computational complexity of the proposed TPS algorithms as well as the performance bounds by proving approximation ratios in terms of service time. In particular, the sequential TPS algorithm is a 2-approximation algorithm and it decreases the computational complexity compared to the general TPS algorithm. * Via extensive simulation settings with realistic parameters in the UMi-Street Canyon scenario, we have expressly observed the following: _transmission with multiple connections and an increasing number of connections achieve high system performance regarding the rate of received data, compared to transmission with a single connection, relatively._  
The rest of this paper is organized as follows. We begin with the system model in Section 2. Next, we propose a transmission point selection algorithm in a multi-connectivity operation in multi-band networks in Section 3. We evaluate the proposed algorithm via simulations in Section 4. Finally, we conclude this paper in Section 5.