## 3 Challenges in Monitoring Traffic Conditions in Real-time Using Loop Detector Data  
### Monitoring Traffic Conditions  
Monitoring the changes over extended segments of freeway is important in evaluating the effect of changes in capacity of toll plaza and travel times, and can be properly conducted if loop detectors span the entire segment [16; 17]. However, if there is only one detector, attempting to monitor the changes in traffic conditions over extended segments solely based on localized data can result in erroneous conclusions and should be avoided in practice. This is illustrated in the following section. Figure 2a,b shows the flow-occupancy relationship observed 2.5 miles upstream of the RSRB toll plaza. Only two out of seven investigated days displayed the relationship shown on Figure 2b, while, on the other days, the relationship remained within the free flow state, as shown in Figure 2a [15]. Investigation of the traffic data collected at the loop detector located 2.5 miles upstream of toll plaza can be used to monitor whether or not the tail of the queue reached the detector station. However, changes in traffic conditions over the 2.5-mile segment cannot be properly quantified based on the localized information from a loop detector or the toll booth discharge rate (_i.e._, observed flow departing the toll plaza); the toll booth will operate at its capacity while there is a queue at its upstream and downstream remains freely flowing [15]. This is further explained with the aid of Figure 2c,d. Figure 2c,d show two hypothetical situations in which the queue began at the toll plaza (TP) and how their tail grew upstream. The traffic condition within the grey triangle is congested, while other sections of the time-space region remain freely flowing. In both figures, \(D\) indicates the location of loop detectors with respect to the tail of queue, while \(L\) is the length of the segment encompassing the entire queue that grew from the TP, and the travel times along this segment need to be compared to quantify the effect of the changes made at the TP. Suppose that travel times were estimated solely based on the speed data reported from a loop detector location at \(D\). When the tail of the queue does not reach \(D\), the data collected at location \(D\) will exhibit the flow-occupancy relationship shown in Figure 2a. Utilizing the information from location \(D\) will assume that the traffic condition between \(D\) and the TP remains freely flowing, while the traffic travels at a reduced speed \(v_{i}<V_{f}\) within the congested region and underestimates travel times by \(t_{i}\) (see Figure 2c). When the tail of the queue reaches location \(D\) as shown in Figure 2d, the flow-occupancy relationship may display the pattern shown in Figure 2b. However, travel times still cannot be accurately estimated based on data collected at \(D\). Figure 2d shows the trajectories of three vehicles that entered the congested region at times \(T_{a}\), \(T_{b}\) and \(T_{c}\). When the first vehicle enters the congested region at time \(T_{a}\), the traffic condition at \(D\) is still freely flowing, and travel times estimated based on loop detector data from \(D\) at time \(T_{a}\) can underestimate the travel time by \(t_{j}\). The estimated travel time of the second vehicle, which entered the congested region when the tail of the queue reached \(D\) at time \(T_{b}\), can be more accurately estimated. However, the estimated travel times of vehicles arriving after \(T_{b}\) will be biased due to the unknown time spent in the queue upstream of \(D\). The bias will be function of \(l\), the length of queue upstream of \(D\). The magnitude of this bias can also be exacerbated depending on the speed of vehicles while they travel within the queue. The traffic state in the congested region can reside anywhere between \(S_{1}\) and \(S_{2}\) along the dotted straight line shown in Figure 2b. Based on the flow-occupancy relationship observed at \(D\), the speed within the queue can range from \(V_{2}\) to \(V_{1}\) (see Figure 2e).