Energy consumption has become dominant issue for wireless internet of things (IoT) networks with battery-powered nodes. The prevailing mechanism allowing to reduce energy consumption is duty-cycling. In this technique the node sleeps most of the time and wakes up only at selected moments to extend the lifespan of nodes up to 5-10 years. Unfortunately, the scheduled duty-cycling technique is always a trade-off between energy consumption and delay in delivering data to the target node. The delay problem can be alleviated with an additional wake-up radio (WuR) channel. In the paper we present original power consumption models for various duty-cycling schemes. They are the basis for checking whether WuR approach is competitive with scheduled duty-cycling techniques. We determine the maximum energy level that an additional wake-up radio can consume to become a reasonable alternative of widely used duty-cycling techniques for typical IoT networks.