## 6 Conclusions  
Due to the rapid growth of mobile data traffic, limited network capacity has become a bottleneck that affects the ability of service providers to satisfy customers' data demands. When the network handles too much data traffic at the same time, network congestion occurs. In turn, the customers feel unsatisfied and may leave the network. Once a customer leaves the network, it is difficult to induce her/him to re-join the network, which induces a revenue loss to the service provider and influences the performance of this service supply chain. The pricing scheme used for mobile data plans has evolved in recent decades. Under connection-speed-restriction pricing, the service provider imposes a restriction on data speed rather than data usage. A customer is allowed to buy the supplementary data package to keep using data service at full speed, which also brings more data traffic to the network. The aim of this paper is to manage demand and to maximize the mobile service provider's revenue under connection-speed-restriction pricing. First, we propose a dynamic plan control method, which allows the service provider to dynamically set the data plans' availability for new subscriptions in each period. With this method, the service provider can balance the benefit of satisfying the increase in data demand and the cost of network congestion caused by too much data traffic. In other words, while attracting new customers to join the network, the service provider also manages to avoid network congestion. Second, we provide a framework to model the behaviors of the service provider and customers, which involves a high-dimensional stochastic dynamic programming problem. Third, to find the optimal control policy, we adapt it to an equivalent mixed linear integer programming, where the market is featured with a near-infinite number of customers. Fourth, we validate our model and framework based on the empirical data from a large European mobile service provider. We conclude our findings as follows: (1) After introducing the realistic mechanism of dynamic plan control, we are able to formulate a stochastic dynamic programming problem based on mild and reasonable assumptions about data plan settings and customers' decision-making procedures. (2) According to Theorem 1 and 2, the dynamic programming problem can be transformed to an equivalent mixed integer linear programming problem, so that the dimension is significantly reduced for efficient computation. (3) The result of numerical evaluation shows that the dynamic plan control method helps a large European mobile service provider manage demand considering congestion and increase its revenue by 31.44%. (4) Compared with the \"all plans always open\" policy, the proposed dynamic  
Figure 7: Relationship between revenue and potential customers’ willingness to join the network. plan control method is able to provide more robust revenue for the service provider when network capacity or the potential customers' willingness to join the network changes. If a mobile service provider has a small network capacity or its potential customers have a high level of willingness, then it can benefit more from the dynamic plan control method. Although we summarized three important contributions of this study in Section 1, we suggest the following directions for future research based on current limitations. First, this paper only assumes the connection-speed-restriction pricing scheme, so it would be interesting to implement the dynamic plan control under other types of pricing schemes. Second, our model considers only one mobile service provider. Based on our research, a model with competing mobile service providers would be an interesting extension, especially if these service providers employ different pricing schemes. Finally, since our approach succeeds in the context of wireless telecommunication management, we consider exploring its applications in other similar systems. **Author Contributions**: Formal analysis, X.M., J.Z. and Z.H. ; investigation, J.N. ; data curation, Y.C.