The problem of security against packet timing based traffic analysis in wireless networks is considered in this work. An analytical measure of anonymity of routes in eavesdropped networks is proposed using the information-theoretic equivocation. For a physical layer with orthogonal transmitter directed signaling, scheduling and relaying techniques are designed to maximize achievable network performance for any desired level of anonymity. The network performance is measured by the total rate of packets delivered from the sources to destinations under strict latency and medium access constraints. In particular, analytical results are presented for two scenarios: For a single relay that forwards packets from m users, relaying strategies are provided that minimize the packet drops when the source nodes and the relay generate independent transmission schedules. A relay using such an independent scheduling strategy is undetectable by an eavesdropper and is referred to as a covert relay. Achievable rate regions are characterized under strict and average delay constraints on the traffic, when schedules are independent Poisson processes. For a multihop network with an arbitrary anonymity requirement, the problem of maximizing the sum-rate of flows (network throughput) is considered. A randomized selection strategy to choose covert relays as a function of the routes is designed for this purpose. Using the analytical results for a single covert relay, the strategy is optimized to obtain the maximum achievable throughput as a function of the desired level of anonymity. In particular, the throughput-anonymity relation for the proposed strategy is shown to be equivalent to an information-theoretic rate-distortion function.