Exchange of crucial and confidential information leads to the unprecedented attention on the security problem in wireless networks. Even though the security has been studied in a number of works, the joint optimization of the physical layer security and the end-to-end delay management, which requires a meticulous cross-layer design, has seldom been evaluated. In this paper, by combining the tools from stochastic geometry and queueing theory, we analyze the tradeoff between the delay and the security performance in large wireless networks. We further propose a simple transmission mechanism which splits a message into two packets and evaluate its effect on the mean delay and the secrecy outage probability. Our numerical results reveal that the security performance is better for larger path loss exponent when the density of legitimate nodes is large, and it is reverse when the density is small. Moreover, it is observed that by introducing the simple mechanism of message split, the security performance is greatly improved in the backlogged scenario and slightly improved in the dynamic scenario when the density of legitimate transmitters is large. In summary, this paper provides an understanding and a rule-of-thumb for the practical design of wireless networks where both the delay and the security are key concerns.
 Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver 1 rate R_ 1 and common messages to both receivers at rate R_ o , while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R_ 1 ,R_ e ,R_ o ) where R_ e is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Korner-Marton on the broadcast Channel. Wyner's results for discrete memoryless wire-tap channels are extended to the Gaussian wire-tap channel. It is shown that the secrecy capacity Cs is the difference between the capacities of the main and wire.tap channels. It is further shown that Rd= Cs is the upper boundary of the achievable rate-equivocation region.