## Dynamic Matching Strategies in Two-Sided Markets
### Dynamic Tuning Strategy
This waiting will thicken the market for finding neighbors; therefore, \(S_{i}\) will flag its voting state to \(v_{p}\) when invoking DTS-based matching, which means that it expects every other node to wait for matching patiently. If \(S_{i}\) has neighbors, there are other service inquiries in the market whose matching conditions comply with that of \(S_{i}\). Since \(S_{i}\) has neighbors, it prefers completing the match as soon as possible. Therefore, the \(S_{i}\) will flag its voting state to \(v_{g}\), which means that \(S_{i}\) embraces the greedy market strategy more. Figure 11 depicts the block diagram of the proposed DTS for matching, and its detailed processing flow is shown in Figure 12.  
Figure 11: The block diagram of the proposed DTS-based matching mechanism. After voting, if the number of \(S_{i}\)'s neighbors is greater than zero, then \(S_{i}\) investigates the voting states of other service inquiries in the blockchain and calculates its value as \(\alpha\). In this work, \(\alpha\) is defined as the ratio of the number of \(v_{p}\) to the current market size. That is,  
\[\alpha\ =\ \frac{num(Vp)}{num(Vp)+num(Vg)}. \tag{10}\]  
First, let us consider two extreme cases for further discussion:  
* If all nodes in the market do not have any neighbors, all inquiries will change their voting states to \(v_{p}\). At this time, \(\alpha=1\), and our DTS-based matching is equivalent to that of a patient algorithm. All nodes in the market have a consistent choice: to wait patiently. * If all nodes in the market do have neighbors, all inquiries will change their voting states to \(v_{g}\). At this time, \(\alpha=0\), and our DTS-based matching effect is equivalent to a greedy algorithm, and all nodes in the market have a consistent choice: to match as soon as possible. Second, from Equation (1), the value of \(\alpha\) will be dynamically tuned according to the ratio of the number of \(v_{p}\) to the market's total votes. As the system members' voting states are changing, the strategy for matching should also be altered dynamically. (2) Decision Function: The realization of the proposed DTS depends on the following Match Decision Function:  
\[T\ H=m-\lfloor m*\alpha\rfloor, \tag{11}\]  
\[D=\ \begin{cases}Wait&NOAI>TH\\ Match&NOAI\leq TH.\end{cases}  \tag{12}\]  
In Equation (3), NOAI denotes the number of available times remained in the lifecycle interval for the service inquiry, m is the maximum time of the service inquiry when invoking a matching process in its lifecycle. For example, if \(m=10\) and the service inquiry \(S_{i}\) have failed to get match four times in the current pairing procedure, then \(NOAI=6\). Assuming \(\alpha=0.5\), then \(TH=5\). Now (\(NOAI-TH\)) = \(6-5=1\), \(D=Wait\), and \(S_{i}\) will continue to wait until the next call for the matching function. As one more matching period passed, \(S_{i}\) in the new matching process will have \(NOAI=5\). Assuming \(\alpha=0.5\) again, then  
Figure 12: The detailed processing flow of the proposed DTS-based matching algorithm. \(D=Match\), and the corresponding \(S_{i}\) will try its best to match one of its neighbors and leave the market. Furthermore, the longer a node remains on the market, the easier it finds a match. Therefore, all nodes in the market will operate according to the remaining feasible time and have the characteristics mentioned above.