Traffic flow of a movement at an unsignalized intersection is guided by the hierarchical position of the movement specified either tacitly (by rules of driving) or decreed (through static signs, such as ``STOP'' or ``YIELD''). At any unsignalized intersection there are various types of movements, like (i) through movement on major street, (ii) right turn movement from major street, (iii) left turn movement from major street, (iv) through movement on minor street, etc. Each of these movements have a place in the hierarchy specifying their claim on the right-of-way at the common intersecting space. For example, in general, first in the hierarchy is the through movement on the major street and slightly lower down is the right turn from major street. Now if in a situation there is a vehicle on the right turn movement and another on the conflicting through movement then the latter will use the intersection and the former has to wait till the latter clears the intersection. If some movement is still lower down the hierarchy (like the right turn from minor street) then vehicles on that movement has to wait till vehicles on movements higher up in the hierarchy has cleared the intersection. As can be seen, the departure process is purely stochastic and extremely complex to model. A detailed discussion on the arrival and departure processes is provided next.
However, before going into the discussion on arrival and departure processes it must be understood that unsignalized intersections work very efficiently if the total conflicting volume is not very high. For example, if at a major street - minor street intersection the traffic to and from the minor street is low then the intersection works quite well irrespective of the volume on the major street. If, however, conflicting movements have reasonable volumes then unsignalized intersections become inefficient and tend to cause large delays to the low priority (i.e., lower in the hierarchy) movements. This is when signalization becomes imperative. In the next chapter, some conditions which justify or warrant signalization are described.
Arrival process
Arrival process of vehicles obviously do not depend on the type of intersection at which they arrive. Hence they are like at signalized intersections and no separate discussion is provided here.
Departure process
Departure process from unsignalized intersections are quite different from that at signalized intersections. The departure process of a movement is determined by the hierarchical position of the movement and the type of control (``STOP'' or ``YIELD'') on the movement. If a movement is at the top of the hierarchy and is not controlled (or ``YIELD'' controlled) then vehicles on the movement always have right of way at the intersection and their flow is not interrupted. However, for the majority of the movements, their position is not at the top of the hierarchy and are often ``STOP'' controlled. For these movements the departure process is complex and is explained through an example here.
Consider the situation shown in Figure 14. In this situation, two through vehicles (marked T1 and T2) and two right turning vehicles (marked R1 and R2) on the left-to-right stream are shown. Numerous vehicles on the right-to-left stream are also shown. Further consider the arrival and departure processes for the left-to-right stream at a proper location on the road (say the Stop Line). Vehicles arrive at this point as has been described earlier. The departure process for the two types of vehicles shown, however, are different. The through vehicles represent those vehicles which always have the right of way. Hence for these vehicles the arrival time at the stop line is always equal to the departure time from the stop line. The right turning vehicles represent those vehicles which are lower in the hierarchy and have to wait for gaps in the opposing stream to complete their maneuver. For example, vehicle R1 waits at the stop line and evaluates each of the gaps in the opposing stream. Only when a gap is greater than some value (at which the driver is comfortable) does the driver of the vehicle accept the gap and makes the right turn. In the figure shown this could be Gap III. Hence, vehicles which have to look for gaps in the opposing stream (or streams), sometimes have to wait at the stop line before departing. Since the arrival of gaps is a stochastic process, the departure process of vehicles (or the waiting time at the stop line), is also a stochastic process.
Once the vehicle at the stop line departs, all those vehicles waiting behind it moves up. In case it is a single lane (in each direction) road, the vehicles waiting behind could be of any kind (T or R in this case). If it is a through vehicle then as soon as it reaches the stop line, it departs. If, on the other hand, it is a right turning vehicle (or any other kind lower in the hierarchy) then the vehicle again may have to wait at the stop line for an adequate gap.
Before leaving this section, a brief discussion on this concept of adequate gap is necessary. The minimum value of the adequate gap is referred to as the critical gap. In the deterministic view of things, a driver accepts a gap whenever the gap is greater than the critical gap and rejects it whenever the gap is less than the critical value. In reality, however, this is not true and the critical gap is only an idealization of the observation that drivers tend not to choose gaps which are ``small'' and choose gaps which are ``large.'' The analysis of unsignalized intersections, nonetheless, assume that a critical gap exists.
