## 4 Data Traffic Control Scheme for Periodic Data Collection  
In this section, we provide terminologies at first. Then, we present an outline of how our data traffic control scheme for periodic data collection works. We define two kinds of frames and Table 2 summarizes terminologies and notations. * **QueueFrame. ** The first kind is the **QueueFrame (QF)**, which consists of \(N_{all}\) slots whose length is \(\Delta t_{s}\) as shown in Figure 4. Let \(N_{i}\) be the number of nodes which belong to group \(i\) and Let \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
\begin{tabular}{c} No \\ consideration \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of related work in comparison with our work. be the number of multicycle polling groups in an IWSN. Some nodes may belong to multiple different groups. Then \(N_{all}\) in an IWSN is as bellows;  
\[N_{all}=\sum_{i=i}^{\tau_{g}}N_{i}. \tag{2}\]  
We assume that a central node collects data from all nodes at multiple periodic cycle as shown in Figure 2. The length of a QF is \(\Delta T_{QF}(=\Delta t_{s}\times N_{all})\). In our proposal, a central node generates at most \(N_{all}\) queries to all nodes in a QF, so that our data collection scheduler gives fair opportunities for all nodes even in a short time span (\(\Delta T_{QF}\)). We consider the bandwidth of downward traffic to define polling cycle \(\Delta t_{s}\). For example, a our preliminary experiment showed downward traffic for SmartMesh IP that is based on the 6 LoWPAN and IEEE802.15.4e standards is assigned every about 2 seconds by the default setting. \(\Delta t_{s}\) should be longer than the frequency for pre-assigned downlink traffic of IWSN protocols. In this paper, we set \(\Delta t_{s}\) to 3\(s\) for simulation setting. The order of queries to nodes are decided by a data collection scheduler. One of the simplest ways to do this is arranging nodes in ascending order of a unique id. \begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(N_{i}\) & \(N_{i}\) is the number of nodes in group \(i\). \\ \(\tau_{g}\) & \(\tau_{g}\) is the number of multicycle polling groups in an IWSN. \\ \(N_{all}\) & \(N_{all}\) is the number of total nodes which belong to all groups. \\ \(QF\) & QueueFrame (QF) is the minimum frame which consists of \(N_{all}\) slots. \\ \(\Delta T_{QF}\) & \(\Delta T_{QF}\) is The length of a \(QF\). A central node can transmit at most \(N_{all}\) polling requests in a QF. \\ \(\Delta t_{s}\) & \(\Delta t_{s}\) is the length of a slot. A central node can transmit a polling request in a slot. \\ \(T_{i}\) & \(T_{i}\) is a collection data interval of group \(i\). \\ \(SF\) & ScheduleFrame is the minimum unit of multicycle polling schedule. \\ \(T_{M}\) & \(T_{M}\) is a multicycle polling interval. \\ \(N_{QF}\) & \(N_{QF}\) is the number of QFs in a SF. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation and description. Figure 4: A composition of a QueueFrame (QF). * **ScheduleFrame. ** The second kind is the **ScheduleFrame (SF)**, which consists of QFs, as shown in Figure 5. Let \(T_{M}\) be the least common multiple of collection cycle of all groups as shown in Equation (3). In the interval \(T_{M}\), the SF consists of \(N_{QF}(=T_{M}\div\Delta T_{QF})\) QFs. Therefore, a SF is the minimum unit of multicycle polling schedule of \(N_{all}\) nodes. \[T_{M}=\text{lcm}(T_{i}),\text{for }i=1,2,...,\tau_{g}.\] (3) Our data collection scheduler decides all polling orders in order to make network traffic of all applications uniform during the \(T_{M}\) and our data traffic control scheme generates polling queries every \(\Delta t_{s}\) according to the schedule. Below, we give an outline of how our proposal works over any IWSN protocols that assign unequal bandwidth to upstream and downstream communication. In our scheme, we define two kinds of frames to decide all polling orders in both a short time span and a long time span.