## 3 Simulation-Based System Architecture
### Requests Queue Scheduler
#### 3.4.4 Prioritised Classification of Requests and Their Dispatching Policies
Then, the set of LL requests, \(N_{LL}^{VR}\), that will need a relocation request to be triggered will be given by \[N_{LL}^{VR}\overset{\Delta}{=}\left\{i\in N_{LL}^{-}\mid\zeta_{i}\leq\theta^{ \prime\prime}min\ \vee\ \xi_{i}-\tau_{ji}\leq\theta^{\prime\prime}min,\ \forall j\in J\right\}\] (3) *
where the \(\theta\) parameters have been adopted as \(\theta^{\prime\prime}=20\) min, \(\theta^{\prime\prime\prime}=5\) min. * **LL requests to reject. ** LL requests are maintained in the system until its time window is no longer feasible. As they are the longest trips and their time windows are also very long, this will imply that they will be in the system for a very long time. To avoid keeping them in the system for an unnecessary amount of time, it would be convenient to identify the instant at which it is no longer viable to serve them. The set \(N_{LL}^{rej}\) of LL requests to reject in a cycle will be: \[N_{LL}^{rej}\stackrel{{\Delta}}{{=}}\left\{i\in N_{LL}^{-}\mid t_{ 0}+\bar{\mu}_{i}\geq\hat{t}_{i}\right\}\] (4) where \(t_{0}\) is the current time and \(\hat{t}_{i}\) the latest arrival time at its destination for a request \(i\). \(\bar{\mu}_{i}\) is the minimum estimated travel time of the trip that the nearest vehicle would need to go to pick up the client at its current location (the stop) and drop him off at its destination (vehicle's tour or future detours are not taken into account). * **Booking requests to reject. ** Given that each B request starts to be considered some time in advance, the total time window that these types of requests are maintained in the system is very large, and the system identifies the time instants when a B request is impossible to be satisfied. Those that will be rejected define the following set: \[N_{B}^{rej}\stackrel{{\Delta}}{{=}}\left\{i\in B\mid t_{0}\geq \hat{d}_{i}\;\vee\;t_{0}+\bar{\mu}_{i}\geq\hat{t}_{i}\right\}\] (5) where \(t_{0}\) is the current time, \(\hat{d}_{i}\) the desired departure time at the origin of the client and \(\hat{t}_{i}\) is the maximum arrival time at its destination. \(\bar{\mu}_{i}\) refers to the minimum estimated travel time of the trip that the nearest vehicle would need to go to pick up the client at its origin and drop him off at its destination (vehicle's tour or future detours are not taken into account). A summary of the actions taken on each of the previously defined sets in a given cycle is given in Table 2 below. The table also shows, for each of the sets, the previous priority of their requests (for waiting requests only), their priority and the action to be applied after a failed attempt has occurred for resolving them. The last column specifies the subsets considering the intermodal preference of the requests (a, b and =). The configuration of the proposed dispatching methodology is related to the quality of service provided by the system. A value of \(\theta=25\) min has been set so that the last-leg dispatchings are delayed in order not to overload the system with too early requests and, on the other hand, the complete tour plan is elaborated around 25 min before leaving the PT system. \(\theta^{\prime}=30\) min enforces Booking requests received in advance, prioritising them above regular requests, and at the same time, it makes it easier for the system to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Main** & **Previous** & **Prio** & **Action after** & **Subset from User’s** \\
**Subset** & **Priority** & **(*)** & **2 Failed Ass.** & & **Preference** \\ \hline \(N_{W}\) & \(N_{W}^{LL}\) & 4 & retry & & \\  & \(N_{W}^{B}\) & 4 & retry & \(N_{W}^{Ba}\) & \(N_{W}^{Bb}\) & \(N_{W}^{B=}\) \\  & \(N_{W}^{HN}\) & 2 & reject & \(N_{W}^{HNa}\) & \(N_{W}^{HNb}\) & \(N_{W}^{HN=}\) \\ \hline \(N_{LL}\) & 3 & move to & \(N_{W}^{LL}\) & & \\ \hline \(N_{B}\) & 3 & move to & \(N_{W}^{B}\) & \(N_{B}^{a}\) & \(N_{B}^{b}\) & \(N_{B}^{=}\) \\ \hline \(N_{HN}\) & 1 & move to & \(N_{W}^{HN}\) & \(N_{HN}^{a}\) & \(N_{HN}^{b}\) & \(N_{HN}^{=}\) \\ \hline \hline \end{tabular} (*) = 1 less prioritised.  
\end{table}