Two fundamental elements of the lane-based traffic network model used in SIDRA INTERSECTION are (i) determination of the ** backward spread of congestion** as queues on downstream lanes block upstream lanes, and (ii) application of

**to oversaturated upstream lanes for determining exit flow rates, thus limiting the flows entering downstream lanes. These two elements are highly interactive with opposing effects. A network-wide iterative process is used to find a solution that balances these opposing effects.**

*capacity constraint*Backward spread of congestion is based on queue blockage probability calculations using the SIDRA percentile queue model. In this context, percentile queue is a "probabilistic measure" representing a queue length that would be observed if there was enough storage space before reaching an upstream intersection (or if there was no upstream intersection). According to the model, when the queue length exceeds the storage space, the vehicles will queue in the upstream lanes (*queue spillback*). They will then be mixed with other movements in upstream lanes (e.g. they could be sharing lanes with turning vehicles not moving to the downstream lanes) and they will be subject to the conditions of the upstream intersection including intersection geometry (e.g. they could be queuing in a short lane), lane use, demand volumes, gap acceptance, signal timing and so on as relevant. Therefore, those vehicles are modelled at the upstream intersection.

Modelling the traffic interactions between upstream and downstream intersection conditions allowing for capacity reductions in upstream lanes resulting from blockage by downstream queues (as well as the capacity constraint effects that may result) presents a complex mathematical problem. SIDRA uses an *iterative approximation method* to find an equilibrium solution to this network modelling problem.

By default, the SIDRA Network Model shows *average back of queue* values in output reports and displays, in contrast to individual Site analysis where percentile back of queue values are reported. In Network analysis, the average back of queue distance will never exceed the available storage length. Estimated percentile queue length may exceed the storage distance but this is not meaningful in the context of Network analysis as the spillback is accounted for in modelling the blockage of upstream intersection lanes as explained above.

The solutions should not be expected to be "precise" under high degrees of saturation (near-capacity and oversaturated conditions) and high levels of queue spillback. These conditions indicate "unstable and chaotic" behaviour of traffic as discussed by Lay (Measuring traffic congestion. Road & Transport Research 20(1), pp 42-53, 2011). The Network Model Variability results given in the Network Summary, Route Summary and Diagnostics output reports indicate how settled the model solution is. A large value of *Number of Iterations *and a *Percentage Stopping Condition* which is not satisfied indicate a higher uncertainty in network analysis results.

A model calibration issue for oversaturated conditions exists in the use of input traffic volumes based on stop-line counts rather than demand volumes counted at the back of queue which are difficult to obtain in closely-spaced intersection networks. In this case, the estimation of performance statistics (delay, queue length, and so on) is problematic. A simple method recommended for model calibration in oversaturated cases with unknown demand volumes is given in the SIDRA User Guide Section 2.6.1.

It should be noted that a small amount of lane blockage could have a high impact on the upstream intersection performance when upstream lanes are operating at high degrees of saturation, and in contrast, a large amount of blockage could have a minor impact on the upstream intersection performance when upstream lanes are operating at low degrees of saturation.