  We consider a setup with Internet of Things (IoT), where a base station (BS)
collects data from nodes that use two different communication modes. The first
is pull-based, where the BS retrieves the data from specific nodes through
queries. In addition, the nodes that apply pull-based communication contain a
wake-up receiver: upon a query, the BS sends wake-up signal (WuS) to activate
the corresponding devices equipped with wake-up receiver (WuDs). The second one
is push-based communication, in which the nodes decide when to send to the BS.
Consider a time-slotted model, where the time slots in each frame are shared
for both pull-based and push-based communications. Therein, this coexistence
scenario gives rise to a new type of problem with fundamental trade-offs in
sharing communication resources: the objective to serve a maximum number of
queries, within a specified deadline, limits the transmission opportunities for
push sensors, and vice versa. This work develops a mathematical model that
characterizes these trade-offs, validates them through simulations, and
optimizes the frame design to meet the objectives of both the pull- and
push-based communications.
