Effective management of large-scale cellular data networks is critical to meet customer demands and expectations. Customer calls for technical support provide direct indication as to the problems customers encounter. In this paper, we study the customer tickets - free-text recordings and classifications by customer support agents - collected at a large cellular network provider, with two inter-related goals: i) to characterize and understand the major factors which lead to customers to call and seek support; and ii) to utilize such customer tickets to help identify potential network problems. For this purpose, we develop a novel statistical approach to model customer call rates which account for customer-side factors (e.g., user tenure and handset types) and geo-locations. We show that most calls are due to customer-side factors and can be well captured by the model. Furthermore, we also demonstrate that location-specific deviations from the model provide a good indicator of potential network-side issues.