Channel Sensitivity of LIFO-Backpressure: Quirks and Improvements

We study the delay performance of backpressure routing algorithms using last-in first-out (LIFO) schedulers (LIFO-backpressure). We uncover a surprising behavior in which, under certain channel conditions, the average delay of packets is high at low traffic load and decreases as the load in the network increases. We propose and analyze a queueing-theoretic model under which the scheduler can transmit packets only if the queue length meets or exceeds a threshold, and we show that the model analytically bears out the observed phenomenon. Using matrix geometric methods, we derive a numerical solution for the average packet delay in the general case, and, using $z$- transform techniques, we further provide closed-form solutions for a special case. Our analysis indicates that when the threshold is fixed (as may happen under lossless channel conditions), the average delay is small at low traffic load and increases with increasing load, as expected. On the other hand, when the threshold fluctuates (as may happen under changing, lossy channel conditions), the average delay may be high at low load and decrease, sometimes substantially, with the traffic load. We corroborate these findings with TOSSIM simulations on different types of networks, using measured channel traces. Further, we propose a replication-based LIFO-backpressure algorithm (RBL) to improve the delay performance of LIFO-backpressure. Analytical and simulation results show that RBL dramatically reduces the delay of LIFO-backpressure at low load, while maintaining high throughput performance at high load.