# Multi-Connectivity for Multicast Video Streaming in Cellular Networks
## 3 Resource Allocation in MC Multicast  
Consider a system of \(C\) cells, each with one base station serving it. There are \(M\) multi-connected multicast UEs in the system that can receive multicast content from any subset of the \(C\) base stations. The set \([C]=\{1,2,\ldots,C\}\) denotes the set of all cells/base stations, and the set of all users is denoted by \([M]=\{1,2,\ldots,M\}\). Resource allocation decisions are made at every time slot \(t\). In each time slot, there are \(N\) PRBs available for allocation in each cell. The set of all PRBs is denoted by \([N]=\{1,2,\ldots,N\}\). We assume that there is multicast content available in all the cells, which is being streamed by all the UEs. The multicast content is streamed at a rate of \(R\) bits per second. The UEs can potentially receive the multicast streaming content from any number of neighboring base stations in addition to their respective primary base stations. The multicast stream is allocated to one PRB in each cell, in each time slot. Resource allocation decisions are either made independently by each base station or by a central entity such as the MCE that manages the base stations within a region. The channel states of UEs vary as a function of time \(t\) as well as the PRB \(j\in[N]\). In the PRB \(j\) of cell \(c\) at time \(t\), UE \(k\) can decode a maximum rate of \(r_{jk}^{c}[t]\) bits per second, which is a function of the channel state of the UE. That is, the better the channel experienced by UE \(k\), the higher the rate \(r_{jk}^{c}[t]\). Since the multicast content is transmitted at a rate of \(R\) bits per second, a UE may not successfully receive the multicast content from the base station that it is connected to. For instance, consider that the PRB \(j\) is allocated to the multicast stream in cell \(c\) at time \(t\). UE \(k\) will be able to decode the content sent by \(c\) only if \(R\leq r_{jk}^{c}[t]\). On the other hand, if \(R>r_{jk}^{c}[t]\), UE \(k\) will not be able to successfully decode the content sent from cell \(c\). Thus, in the absence of multi-connectivity, a UE can successfully receive data only if it can decode the content from its primary cell, whereas a multi-connected UE successfully receives data if it can decode the content from any one of the base stations that it receives content from. **Remark 1**: _Note that, even though we assume a constant bit rate \(R\), video streaming traffic typically uses a variable bit rate (VBR) encoding, which means that the amount of data to be transmitted for the video varies over time. We employed a constant rate model for the sake of simplicity in defining the resource allocation problem. However, our problem, as well as the proposed resource allocation policies, can be easily adapted to the VBR model by considering the proposed setup as a snapshot of a longer VBR video stream. More specifically, to adapt to the VBR model, the transmission rate \(R\) can be made a function of time \(t\) (denoted by \(R(t)\)). Then, the system model discussed above essentially represents a small enough block of time during which the rate \(R(t)\) is constant. Similarly,the resource allocation problem can be defined with the time dependent rate \(R(t)\). As we will see in the following sections, the proposed policies make allocation decisions in every time slot. Thus, the proposed policies can be used as is with the relevant rate \(R(t)\) in each time slot._  
In the following, we define the resource allocation problem for this system. Problem DefinitionThe resource allocation problem within the MC multicast system aims to maximize the number of UEs served in each time slot. We chose the _number of UEs served_ as the optimization metric for this problem to capture the unique requirements of the MC multicast problem. The primary objective of the MC multicast system is to ensure that the multicast video stream is delivered to a large audience without causing network congestion.