# Escalator: An Autonomous Scheduling Scheme for Convergecast in TSCH
## 4 Proposed Autonomous Scheduling Scheme for Convergecast
### Timeslot Allocation Mechanism  
The timeslot allocation mechanism of Escalator in a node generates a timeslot schedule for the convergecast slotframe that uses only the node ID and routing topology information without additional signaling with other nodes. The generated Escalator schedule of node \(v_{i}\) consists of the timeslots with the following four operations for the TSCH beacon and convergecast traffic transmission. * \(BT_{i}\): The operation in which \(v_{i}\) broadcasts a beacon
* \(BR_{ij}\): The operation in which \(v_{i}\) receives a beacon sent by \(v_{j}\)
* \(TX_{ij}\): The operation in which \(v_{i}\) transmits a unicast packet originated from \(v_{j}\) to the parent node \(p(v_{i})\)
* \(RX_{ij}\): The operation in which \(v_{i}\) receives a unicast packet, originated from \(v_{j}\), from one of the child nodes \(C(v_{i})\) \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Definition** \\ \hline \(G\) & The network consisting of nodes \(V\) and links \(E\) \\ \(N\) & The number of nodes in the network \\ \(V\) & The set of nodes in the network \\ \(E\) & The set of links in the network \\ \(DT\) & Duration of timeslot \\ \(Ch\) & The number of available orthogonal channel \\ CO & The channel offset that is used for multiple channel usage at a single timeslot \\ \(CO_{Op}\) & The channel offset used for \(Op\) \\ \(ASN\) & The total number of timeslots that have elapsed since the start of the network \\ \(S_{Conv}\) & The convergecast slotframe \\ \(S_{Base}\) & The baseline slotframe \\ \(L(S)\) & The size of slotframe \(S\) in timeslot unit \\ \(v_{i}\) & A node with ID \(i\) \\ \(p(v_{i})\) & The preferred parent of node \(v_{i}\) \\ \(C(v_{i})\) & The set of the direct child nodes of node \(v_{i}\) \\ \(SG(v_{i})\) & The set of nodes in the sub-graph of node \(v_{i}\), excluding \(v_{i}\) itself \\ \(l_{ij}\) & A link for which the sender is \(v_{i}\) and the receiver is \(v_{j}\) \\ \(H_{v_{i}}\) & Hop count of node \(v_{i}\), the number of hops from the sink to node \(v_{i}\) \\ \(Op(S,ts)\) & Operation at timeslot \(ts\) in slotframe \(S\), which is one of the following four operations \\ \(BT_{i}\) & The operation in which \(v_{i}\) broadcasts a beacon \\ \(BR_{ij}\) & The operation in which \(v_{i}\) receives a beacon sent by \(v_{j}\) \\ \(TX_{ij}\) & The operation in which \(v_{i}\) transmits a unicast packet originated from \(v_{j}\) \\  & to the parent node \(p(v_{i})\) \\ \(RX_{ij}\) & The operation in which \(v_{i}\) receives a unicast packet, originated from \(v_{j}\), \\  & from one of the child nodes \(C(v_{i})\) \\ \([ts_{1},ts_{2}]\) & The timeslot section from \(ts_{1}\) to \(ts_{2}\) \\ \(LCM(a,b)\) & Least common multiple of \(a\) and \(b\) \\ \(H_{max}(G)\) & Maximum hop counts of the packet-forwarding path in network \(G\) \\ \(D_{oE}(v_{i})\) & Average end-to-end delay of node \(v_{i}\) \\ \(B(G)\) & Average bandwidth of node in network \(G\) \\ \(Q(G)\) & Average required buffer capability of nodes in network \(G\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main notations. The timeslot allocation mechanism consists of the following five allocation rules that set operations to timeslots. * SET_BT(i): Node \(v_{i}\) sets \(BT_{i}\) to \(i\times 2-1\) timeslot (for example, \(BT_{1}=1\), \(BT_{2}=3\), \(BT_{3}=5\), \(BT_{4}=7\)). * SET_BR(i,j): Node \(v_{i}\), where \(v_{i}\
eq sink\), sets \(BR_{ij}\) to \(j\times 2\) timeslot to receive a broadcast beacon from \(v_{j}=p(v_{i})\) (for example, \(BR_{21}=2\), \(BR_{32}=4\), \(BR_{42}=4\)). * SET_TX(i,i): Node \(v_{i}\), where \(v_{i}\
eq sink\)), sets \(TX_{ii}\) to \(i\times 2\) timeslot to send its unicast packet to \(v_{i}\)'s parent \(v_{j}=p(v_{i})\) (for example, \(TX_{22}=4\), \(TX_{33}=6\), \(TX_{44}=8\)). * SET_RX(i,j): Node \(v_{i}\) sets \(RX_{ij}\) to the \(j\times 2-1\) timeslot to receive the unicast packet generated by the node \(v_{j}\in SG(v_{i})\) (for example, \(RX_{12}=3\), \(RX_{13}=5\), \(RX_{14}=7\), \(RX_{23}=5\), \(RX_{24}=7\)).