This paper analyzes latency in a High-Speed Packet Access network appropriately resourced for emulated Machine-to-Machine and Online Gaming traffic. Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) are used for conveying application data and the measurement results from the end-user perspective are compared. In TCP case, traffic traces were recorded in two points of the core network as well (Gn interface and the firewall), and the overall delay is dissected to portions belonging to different parts of the network (access, core, backbone). The diversity of the traffic patterns used made it possible to draw conclusions concerning selectivity of certain parts of the network towards different traffic patterns, indicating the direction of future research on reducing latency for subject emerging application domains in legacy networks.