What is good about analytical traffic modelling?

An analytical model is

• an engineering approach
• algorithmic
• combines theoretical and empirical approaches
  e.g. performance estimation based on queuing theory with formulations calibrated using established (well specified) survey techniques
• auditable (allows in-depth questioning of model assumptions).

An analytical model can

• calculate
• find solutions
• estimate capacity as a basic parameter that determines traffic performance (see Section 3.1)
• optimise traffic performance
• optimise traffic signal phasings and timings
• quantify the effect of pedestrians on signal timings and vehicle movement capacity
• contribute to traffic modelling as part of a Movement and Place approach
  (SIDRA with extensive pedestrian modelling and detailed modelling of vehicle movement classes including cyclist, bus, tram / light rail and large truck is ideal in relation to the "Movement" aspect of this, even where "Place" is more important than "Movement")
• model CO2 emissions for environmental assessments
  (the SIDRA power-based fuel and emissions models can estimate emissions of traffic movements, in particularly CO2, with great accuracy)
• provide consistent modelling of different intersection types by using algorithms that employ consistent methods
  (SIDRA capacity and performance models provide a unique consistent approach for different types of signalised and unsignalised traffic facilities)
• predict and assess conditions that cannot be seen in "animation",
  e.g. delay to vehicles departing from the queue after the modelling period under oversaturated conditions (see Section 3.2).

Powerful concepts and model parameters used by analytical models

• are well-established
• are understood by the profession
• provide a common language for communication
• are useful in assessing traffic conditions
• are useful for signal timing analysis including analysis for actuated signal control
• can be used for verification and calibration of various aspects of microsimulation models (Yoshii 1999).

These concepts and model parameters include

• capacity (see Section 3.1)
• degree of saturation (demand flow / capacity ratio)
• saturation flow (queue discharge flow rate)
• critical gap and follow-up headway for gap acceptance processes
• percentile queue length and probability of blockage by downstream queues
• fundamental relations among flow, speed, density and spacing
• parameters used by traffic signal control systems such as SCATS MF and detector occupancy
• bunching (random moving queues in an uninterrupted stream)
• platoons of vehicles departing from signalised intersections.

These concepts and parameters have been developed and used in traffic modelling and control for a long time.  These include key parameters used in analytical model calibration.

The concepts and parameters listed above are for "traffic streams" or "traffic movements" which is a modelling approach that converts "individual vehicle" movement characteristics such as car following, lane change, acceleration and deceleration to more aggregate and measurable "traffic" characteristics.  This provides the capabilities listed above.  For information about the level of detail in analytical models, see Section 3.4.

Analytical models are less costly than microsimulation to use, providing workflow efficiencies as they

• are easier to set up (low model specification time due to clarity of concepts)
• are quicker to run (quicker solutions)
• reduce modelling times by helping the modeller to spend less time on setting of key parameters
• help modellers to analyse large number of scenarios (alternative solutions, existing and development conditions, design life analysis for future traffic conditions) and make decisions about recommended solutions with less effort
• can be reviewed (audited) to assess whether calibration of key model parameters has produced realistic results (as listed above).

Analytical models offer a more stable answer compared with microsimulation model results which vary due to randomness and depend on the number of simulation runs.  Understanding and dealing with uncertainty and sensitivity of solutions to model parameters is important. 

Uncertainty:

• Finding a reliable solution representing average and percentile values of performance variables would require a large number of simulation runs with long simulation periods for convergent solutions.
• Analytical models are not "deterministic" as is claimed sometimes. They use queuing theory for random overflow and persistent oversaturation (congestion)
  See Section 3.1.
• For oversaturated conditions, simulation cannot be run for longer periods for convergence since queues build up persistently with longer periods because of demand exceeding capacity. An increased number of simulations is needed rather than longer simulations for this reason.
• For near-saturated conditions when the average demand is less than but close to capacity, significant overflow queues occur due to randomness of arrival flows. Therefore, average results require a large number of simulations.  Figure 1 shows the difference between average values of two simulation points for low and high degrees of saturation.  This is important since the effect of randomness in arrival flow rates is highest near capacity conditions, and furthermore, the capacity values can also change cycle-by cycle.  This shows the difficulty of obtaining performance estimates representing average conditions from microsimulation modelling. 
  See the discussions in Sections 3.1 and 3.2.
• For convergent solutions, downstream queue blockage effects resulting in capacity losses by upstream movements need an increased number of iterations for analytical models and an increased number of simulations by microsimulation models (especially if downstream queue blockage causes oversaturation).

Sensitivity:

The sensitivity of performance variables (delay, queue, stop, etc.) is much higher at high degrees of saturation due to the nonlinearity of the performance function as seen in Figure 1.

Figure 1 - Non-linear characteristic of traffic performance

Existing analytical models get improved and models are developed for new areas of transport practice as traffic science discovers laws applicable to traffic movements. 

Better knowledge and understanding of the laws that rule traffic movements

Analytical models for traffic design, operations and planning practice facilitate better knowledge and understanding of the laws that rule traffic movements (as distinct from, but based on, the behaviour of individual vehicles and their relationships) and the interactions of those movements in a complex traffic system.  Watching an animation, even if it is a perfect replication of the real-life conditions, does not reveal those laws to a modeller who does not have adequate knowledge based on concepts developed by decades of traffic science.

It is also uncertain whether an animation based on a single simulation run would represent the traffic conditions of a scenario given the variations among many simulation runs necessary for oversaturated and near-saturated traffic conditions (refer to Figure 1).

No model is perfect

It is important to understand the model and know its limitations.  An analytical model user with knowledge and expertise can question the model assumptions and address areas of concern more readily because of the conceptual strength of the model.

Expert use of traffic models with high levels of knowledge and understanding will be even more important as Artificial Intelligence (AI) threatens to take over the decision-making process in the traffic planning, design and operations processes as in other professions.