A method, comprising: operating, at a particular node, a distributed routing protocol in a shared-media communication network ; determining a hop-distance, N, of the particular node from a root node of the shared-media communication network , wherein the particular node is a parent node, P; determining a pool of timeslots available to child nodes, C, of the particular node as timeslots that are multiples of an (N+2) th prime number; distributing timeslot allocations using the distributed routing protocol, where the particular node as the parent node, P, allocates the pool of timeslots available to the child nodes, C, of the parent node, P; and allocating particular timeslots from the pool to particular child nodes, C, of said particular node according to particular flows from a source to a target in the shared-media communication network in order to meet a defined time budget for a resultant time-synchronized path from the source to the target, wherein the allocating comprises: the particular node as the parent node, P, propagating a request for a time-synchronized path, the request carrying: an absolute time of cycle for a message from the source to reach the target; and a relative time, TC, initialized to the absolute time and decremented at each hop toward the source; and negotiating, with a particular child node, C, a particular corresponding timeslot to allocate from the parent node, P, to the particular child node, C, such that the particular corresponding timeslot, TPC, is earlier than TC. operating, at a particular node, a distributed routing protocol in a shared-media communication network ; determining a hop-distance, N, of the particular node from a root node of the shared-media communication network , wherein the particular node is a parent node, P; determining a pool of timeslots available to child nodes, C, of the particular node as timeslots that are multiples of an (N+2) th prime number; distributing timeslot allocations using the distributed routing protocol, where the particular node as the parent node, P, allocates the pool of timeslots available to the child nodes, C, of the parent node, P; and allocating particular timeslots from the pool to particular child nodes, C, of said particular node according to particular flows from a source to a target in the shared-media communication network in order to meet a defined time budget for a resultant time-synchronized path from the source to the target, wherein the allocating comprises: the particular node as the parent node, P, propagating a request for a time-synchronized path, the request carrying: an absolute time of cycle for a message from the source to reach the target; and a relative time, TC, initialized to the absolute time and decremented at each hop toward the source; and negotiating, with a particular child node, C, a particular corresponding timeslot to allocate from the parent node, P, to the particular child node, C, such that the particular corresponding timeslot, TPC, is earlier than TC. the particular node as the parent node, P, propagating a request for a time-synchronized path, the request carrying: an absolute time of cycle for a message from the source to reach the target; and a relative time, TC, initialized to the absolute time and decremented at each hop toward the source; and an absolute time of cycle for a message from the source to reach the target; and a relative time, TC, initialized to the absolute time and decremented at each hop toward the source; and negotiating, with a particular child node, C, a particular corresponding timeslot to allocate from the parent node, P, to the particular child node, C, such that the particular corresponding timeslot, TPC, is earlier than TC. <EOS>