In-vehicle network architectures are evolving from a typical signal-based client-server paradigm to a service-oriented one, introducing flexibility for software updates and upgrades. While signal-based networks are static by nature, service-oriented ones can more easily evolve during and after the design phase. As a result, service-oriented protocols are becoming more prominent in automotive in-vehicle networks. While applications like infotainment are less sensitive to delays, others like sensing and control have more stringent timing and reliability requirements. Hence, wider adoption of service-oriented protocols requires addressing the timing analysis and predictability of such protocols, which is more challenging than in their signal-oriented counterparts. In service-oriented architectures, the discovery phase defines how clients find their required services. The time required to complete the discovery phase is an important parameter since it determines the readiness of a sub-system or even the vehicle. In this paper, we develop a formal timing analysis of the discovery phase of SOME/IP, which is an emerging service-oriented protocol being considered for adoption by several automotive Original Equipment Manufacturers (OEMs) and suppliers.