Perfect periodic scheduling for binary tree routing in wireless networks

•An approach to scheduling data through a Wireless Mesh Network to the Internet.•An efficiency improvement of up to 50% relative to common cycle solutions.•An optimisation method for co-coordinating data transmission through a routing tree.•A polynomial time algorithm for a special case of an NP-hard combinatoric problem.•Perfect periodic solutions which accommodate multiple periodicities. In this paper we tackle the problem of co-ordinating transmission of data across a Wireless Mesh Network. The single task nature of mesh nodes imposes simultaneous activation of adjacent nodes during transmission. This makes the co-ordinated scheduling of local mesh node traffic with forwarded traffic across the access network to the Internet via the Gateway notoriously difficult. Moreover, with packet data the nature of the co-ordinated transmission schedule has a big impact upon both the data throughput and energy consumption. Perfect Periodic Scheduling, in which each demand is itself serviced periodically, provides a robust solution. In this paper we explore the properties of Perfect Periodic Schedules with modulo arithmetic using the Chinese Remainder Theorem. We provide a polynomial time, optimisation algorithm, when the access network routing tree has a chain or binary tree structure. Results demonstrate that energy savings and high throughput can be achieved simultaneously. The methodology is generalisable.