We present a tandem network of queues 0 , ⋯ , s- 1. Customers arrive at queue 0 according to a Poisson process with rate λ. There are s independent batch service processes at exponential rates μ₀, ⋯ , μ_{s - 1}. Service process i, i= 0 , ⋯ , s- 1 , at rate μ_i is such that all customers of all queues 0 , ⋯ , i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of μ_i appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.

In this paper, we consider communication on a two-hop channel, in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper and there is a cooperative node which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code and the other one is based on a lattice chain code. It is proved that in the high Signal-to-Noise-Ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.