Coverability in Wait-Only Networks with non-blocking bounded sendings

Let us assume a distributed system with an unknown number of participants. They all execute the same program given as a finite-state machine called a protocol and can communicate by sending messages. In the protocol, transitions among two states are either reception transitions (labeled by a message), broadcast transitions (labeled by a message), or sending transitions (labeled by a message and an integer). When a process takes a broadcast transition labeled by a message $a$, all other agents on a state with an outgoing reception transition labeled by message $a$ take it. When a process takes a sending transition labeled by a message $a$ and an integer $k$, we distinguish between two cases: (1) either there exist $k$ processes who are on a state with an outgoing reception transition labeled by message $a$, and they take this transition; (2) or there exist $j < k$ such processes and only those $j$ agents take the corresponding reception transition. The problem asking, given a protocol and a state of this protocol, if there exists a number of agents with which we can find a run leading to a configuration in which at least one agent is on this state is called the coverability problem and is EXPSPACE-complete. We consider a restriction on protocols namely Wait-Only protocol: in a Wait-Only protocol, each state is either an action state (all its outgoing transitions are broadcast transitions or sending transitions) or a waiting state (all its outgoing transitions are reception transitions). The complexity of the coverability problem is unknown in that case.