# Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data
## 3 Traffic Information Estimation and Forecasting Methods
### Traffic Information Estimation Methods
#### 3.1.1 Traffic Flow Estimation  
This study considers the amount of HOs (\(h_{i}\)) and the amount of NLUs (\(q_{i,n}\)) to estimate traffic flow (\(Q_{i}\)) on the road segment covered by Cell\({}_{i}\).  
Traffic Flow Estimation by Using HO Events  
When a call arrives within the coverage area of a cell, the destination (or the originating) MS will be connected if a channel is available. While a communicating MS moves from the coverage area of one cell to the coverage area of another cell, the channel in the old cell is released, and the new cell will provide a channel to the MS if there is a free channel. This process is called a handover.  
Figure 1a illustrates the space diagram for vehicle movement and the handover on a road. Figure 1b depicts the timing diagram for the handover on the road segment covered by Cell\({}_{i}\). The MS in a car performs the call set-up at time \(t_{0}\) (in Figure 1a,b); then, the MS goes into the handover area of the coverage of Cell\({}_{i-1}\) and Cell\({}_{i}\) at time \(t_{1}\) (in Figure 1a,b), and the base station controller (BSC) or radio network controller (RNC) will allocate an available channel for the communicating MS. At this moment, if Cell\({}_{i}\) has a free channel, the connection between the MS and Cell\({}_{i}\) will be established successfully. The process is called a handover from Cell\({}_{i-1}\) to Cell\({}_{i}\).  
This study assumes that the call holding time (\(t\)) is exponentially distributed with the mean \(1/\mu\) to generate handovers [25]. The average speed of cars is \(U_{i}\), and the traffic flow is \(Q_{i}\). Furthermore, the length of road segment covered by Celli is \(l_{i}\). Let the variable \(x\) be the time difference between \(t_{0}\) and \(t_{1}\), and \(l_{i}/U_{i}\) denotes the time difference between \(t_{1}\) and \(t_{2}\). The handover procedure will be performed when the call holding time (\(t\)) is larger than \(x\). Thereby, the amount of handover (\(h_{i}\)) on the road segment covered by Cell\({}_{i}\) can be expressed as Equation (2), and this study can estimate traffic flow (\(q_{i,h}\)) by using Equation (3), which is the traffic flow multiplied by the number of HO events.  
Figure 1: **(a)** The scenario diagram for vehicle movement and the handover on the road; **(b)** the timing diagram for the handover on the road segment covered by Cell\(i\). BSC, base station controller; RNC, radio network controller.  
\[h_{i} =Q_{i}\times\int_{x=0}^{\infty}\Pr\left(t>x\right)dx\] \[=Q_{i}\times\int_{x=0}^{\infty}\int_{t=x}^{\infty}u\mathrm{e}^{-u \mu}dtdx\] \[=Q_{i}\times\int_{x=0}^{\infty}\left(-e^{-u\mu}\big{|}_{t=x}^{ \infty}\right)dx=Q_{i}\times\int_{x=0}^{\infty}e^{-u\mu x}dx \tag{2}\] \[=Q_{i}\times\left(\frac{-e^{-u\mu}}{\mu}\bigg{|}_{x=0}^{\infty} \right)=\frac{Q_{i}}{\mu}\] \[q_{i,h}=h_{i}\times\mu \tag{3}\]  
Traffic Flow Estimation by Using NLU Events  
In cellular networks, the NLU event is generated when an MS moves from a location area (LA) to another LA. Therefore, traffic flow can be estimated by using the number of NLU events. This study assumes that the actual traffic flow on the road segment covered by Cell\({}_{i}\) is \(Q_{i}\) and one MS is in each car (shown in Figure 2) [24]. Therefore, the estimated traffic flow \(q_{i,n}\) (_i.e._, the number of NLU events) on the road segment covered by Cell\({}_{i}\) can be calculated as Equation (4), which is the traffic flow multiplied by the number of NLU events.  
\[q_{i,n}=Q_{i} \tag{4}\]