Transient Analysis for Multihop Wireless Networks Under Static Routing

In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network under static routing. Our work is motivated by novel applications from the domain of process automation, MachineType Communication (MTC) and cyber- physical systems, where short messages are communicated and statistical guarantees need to be provided on a per-message level. In order to optimize such a network, apart from understanding the stationary system dynamics, an understanding of the short-term dynamics (i.e. transient behavior) is also required. To this end, we derive novel Wireless Transient Bounds (WTB) for end-to-end delay and backlog in a multi-hop wireless network using stochastic network calculus approach. We start by analyzing a single end-toend path, i. e. a line topology, and then we show how the obtained results can be applied to a mesh network with static routing using a concept called 'leftover service'. WTB depends on the initial backlog at each node as well as the instantaneous channel states. We numerically compare WTB with Kernel-Based-Transient Bound ( KBTB), which can be obtained by adapting existing stationary bound, as well as simulated end-to- end delay of the investigated network. While KBTB and stationary bounds are not able to capture the short-term system dynamics well, WTB provides relatively tight upper bound and has a decay rate that closely matches the simulation. This is achieved by WTB only with a slight increase in the computational complexity, by a factor of O(T + N), where T is the duration of the arriving sequence and N is the number of hops in the network. We believe that the presented analysis and the bounds are necessary tools for future work on transient network optimization for many important emerging applications, e.g., massive MTC, critical MTC, edge computing and autonomous vehicle.