Transportation Planning and Traffic Engineering

Transport demand modelling

Transport demand modelling estimates how many trips are made in a study area, where they go, by which mode, and along which route. The classical process is the four-stage model of trip generation, trip distribution, modal split and trip assignment, and each stage takes the output of the previous one as its input. A forecast for a target year depends on the demand drivers of that year: the population and its socio-economic composition, the land use that locates trip origins and destinations, and the modal alternatives that the transport system offers in that year.

Trip generation predicts the number of trips produced by or attracted to each zone. In a regression based model the dependent variable is the number of trips, and the independent variables are zonal socio-economic characteristics such as population, number of households, number of employees and car ownership, so the model takes the form T = a_0 + a_1X_1 + a_2X_2 + \cdots + a_nX_n. In a cross-classification method, trip rates are read from a table indexed by household size and vehicle ownership. The total number of trips in a zone is the sum, over the cells that meet the stated condition, of the number of households multiplied by the trip rate of that cell.

The main models and their stages are as follows.

• Gravity model — a trip distribution model in which trips between two zones are proportional to the attractiveness of the destination and inversely related to the separation between zones.
• Fratar model — an iterative growth-factor method that adjusts a base-year origin-destination matrix to forecast totals.
• Growth factor model — a trip production forecast that multiplies base-year trip productions by growth factors.
• Logit model — a discrete choice model for modal split. The probability of mode i is P_i = e^{U_i} / \sum_j e^{U_j}, and when all utilities are equal each of n modes has probability 1/n.
• Greenshields model — the linear speed-density model used to describe traffic flow.
• Multiple regression model — the statistical tool used to estimate trip generation from zonal variables.
• MOVES — the US EPA model that estimates mobile source emissions from vehicle activity, a stage that follows assignment.

Freight demand is converted to vehicle demand with the payload factor, the average load carried by one truck, so the number of truck trips is N = \dfrac{\text{freight tonnage}}{\text{payload per truck}}. Shortest-path algorithms supply the travel costs for assignment: Dijkstra's algorithm finds single-source shortest paths when link costs are non-negative, and the Floyd-Warshall algorithm finds shortest paths between all pairs of nodes, whereas the logit and Huff models are choice and spatial interaction models and do not compute paths.

Assignment principles differ in how they treat congestion. User equilibrium, also called Wardrop's first principle, states that every used route between an origin-destination pair has equal and minimal travel time, and no unused route is faster. System equilibrium instead minimises the total travel time of the whole network. All-or-nothing assignment loads each trip onto a single shortest path without considering congestion, and incremental assignment loads the demand in successive fractions as a computational procedure.

Traffic analysis zones (TAZs) are the units of aggregation for these stages. Their boundaries are drawn along physical barriers such as rivers, mountains and forests, a TAZ may combine several wards, and its demographic data change as new residents move in, so they must be updated. The cordon line is the outer boundary that defines the study area within which the TAZs are located.

In a modal shift calculation, the total trips are obtained by dividing the ridership of the new mode by the shifted fraction of trips. The shifted trips are then allocated to the existing modes in the stated ratio, and the trips remaining for a mode are its original trips minus the trips shifted away from it.

The general aptitude part of this paper also tests botanical facts about Indian ornamental plants. Hibiscus rosa-sinensis is a flowering shrub with red, pink, white and yellow cultivars, frangipani and champa both name trees of the genus Plumeria, jacaranda, gulmohar and amaltas are recognised flowering trees, and the fruit of the kadam tree is globose and not poisonous to humans.

Spot speed statistics (time mean speed)

Spot speed is the instantaneous speed of a vehicle recorded at a single fixed point on the road, and a spot speed study is a set of such observations. Spot speeds are often measured with an enoscope, a periscope type observation instrument that allows an observer to record passing vehicles without being noticed by the drivers.

Two averages are computed from the same sample of spot speeds. The time mean speed is the arithmetic mean of the spot speeds of all vehicles passing a point, \bar{v}_t = \dfrac{1}{n}\sum_{i=1}^{n} v_i. The space mean speed is the harmonic mean, \bar{v}_s = \dfrac{n}{\sum_{i=1}^{n} (1/v_i)}, and it represents the mean speed over a length of road at an instant. The time mean speed is never smaller than the space mean speed, and the gap between them grows as the spread of speeds increases.

If the time mean speed and the other spot speeds are known, a missing spot speed can be recovered from v_{\text{missing}} = n\bar{v}_t - \sum v_{\text{others}}, and the space mean speed then follows from the sum of reciprocals.

Example: spot speeds of 30, 40, 50 and 60 km/h give a time mean speed of 45 km/h, while the space mean speed is 4/(1/30 + 1/40 + 1/50 + 1/60) \approx 42.1 km/h.

Cycle track design standards

A cycle track is a lane reserved for cyclists, and the Indian Road Congress guidelines fix its width and the conditions under which it is provided. A single-lane cycle track is at least 2 m wide, and where overtaking or two-way cycle movement must be accommodated the minimum width is 3 m.

A separate cycle track is warranted when peak-hour cycle traffic is large in relation to motor vehicle traffic. Under IRC 11:1962 the warrant is met when bicycle traffic is 400 or more per hour with motor vehicle volume of 100 to 200 per hour, or when bicycle traffic is 100 or more per hour with motor vehicle volume above 200 per hour. Low volumes of both modes satisfy neither warrant.

The maximum gradient for cycle tracks is not 1 in 15, and the sight distance that a cyclist needs is not 80 m. These figures must be checked against the code itself, not memorised as general rules.

Road hierarchy functional classification

Functional classification arranges roads into a hierarchy according to how they balance mobility, the movement of through traffic over long distances, against access, the ability to reach adjacent property.

• Expressway — a road with fully controlled access and no direct frontage access, carrying long-distance through traffic.
• Arterial road — carries major through traffic and has limited access points.
• Collector road — gathers traffic from local streets and connects them to the arterial system.
• Local street — gives direct access to abutting property and carries short trips.

Accessibility and hierarchy are inversely related. As the functional class rises, mobility increases and accessibility falls, so the accessibility of the road classes in descending order is local street, collector road, arterial road and expressway. A graph of accessibility against hierarchy therefore slopes downward, and a line that rises with accessibility, or stays horizontal, does not represent this relationship.

Minimum spanning tree network

A spanning tree of a network connects all nodes with exactly n-1 links and contains no cycle. The minimum spanning tree (MST) is the spanning tree whose total link weight, such as travel time, is the least. Kruskal's algorithm sorts the links by weight and adds each link in turn unless it closes a cycle, while Prim's algorithm grows the tree from one node by repeatedly adding the cheapest link that reaches a new node. When two links have equal weight, more than one MST may exist, but the minimum total weight is the same for all of them.

An MST must not be confused with a shortest path. An MST minimises the total length of a network that connects all nodes, so the path between two nodes inside the MST need not be the shortest. A shortest path problem minimises the cost between a specified origin and destination. Dijkstra's algorithm solves it for a single source when all link costs are non-negative: each node receives a tentative label, and the node with the smallest label is made permanent at each step. The minimum travel time from a node to the destination is the permanent label of the destination once it has been fixed.

Peak hour factor

The peak hour factor (PHF) measures how evenly traffic is spread within the peak hour. It is defined as \text{PHF} = \dfrac{V_{PH}}{4 \times V_{15}}, where V_{PH} is the peak hour volume and V_{15} is the highest 15-minute volume within that hour. The peak hour is the consecutive four-interval window with the largest total volume, which is found by sliding the window across the whole survey period. A PHF close to 1.0 indicates a flat flow, and a smaller value indicates stronger peaking within the hour.

Example: four consecutive 15-minute counts of 200, 260, 240 and 220 PCU give V_{PH} = 920 and V_{15} = 260, so \text{PHF} = 920/1040 \approx 0.88.

The volume to capacity ratio compares the peak flow with the capacity of the road section, and both must be in the same unit, PCU per hour. Each vehicle count is multiplied by its PCU factor before the totals are added. The capacity of a one-way road is the design capacity per lane multiplied by the number of lanes. Example: two lanes at 1200 PCU/hr per lane and a peak volume of 1800 PCU/hr give V/C = 1800/2400 = 0.75.

Car parking norms and area estimation

Parking norms specify how many car spaces a building must provide. A common Indian norm is one car space for each fixed amount of built-up area, for example one space per 100 m^2. Commercial parking standards are often expressed in equivalent car spaces (ECS) per 100 m^2 of floor area, and the number of ECS required for a use equals its floor area divided by 100 and multiplied by the standard rate.

The parking requirement is computed from the built-up area counted for FAR, and car parking areas are usually exempted from that FAR calculation. The area needed in a parking level equals the number of cars multiplied by the area per car, and that area differs between a ground floor and a basement. When the same parking area is provided at two levels, the car numbers satisfy a_1 N_1 = a_2 N_2, where a is the area per car. Together with a known total N_1 + N_2, these two equations give the number of cars at each level.

Example: a plot of 0.5 ha with FAR 1.5 gives 7500 m^2 of built-up area, which needs 75 car spaces at one per 100 m^2. If each car needs 25 m^2, the 75 cars require 75 \times 25 = 1875 m^2 of parking.

Speed-flow-density relationships

The speed-flow-density relationships describe a traffic stream through three variables linked by q = kv, where q is the flow in vehicles per hour, k is the density in vehicles per km and v is the speed in km/h. The Greenshields model assumes a linear speed-density relationship, v = v_f\left(1 - \dfrac{k}{k_j}\right), where v_f is the free-flow speed and k_j is the jam density.

The two ends of a linear speed-density graph have definite meanings. The speed at zero density is the free-flow speed, at which vehicles travel unhindered. The density at zero speed is the jam density, at which vehicles are stopped bumper to bumper. Flow is zero at both ends, and the maximum flow occurs at half the jam density and half the free-flow speed, so q_{\max} = v_f k_j / 4.

For a linear equation v = a - bk, the free-flow speed is a and the jam density is a/b. For example, v = 60 - 0.2k gives v_f = 60 km/h and k_j = 60/0.2 = 300 vehicles/km, so the capacity is 60 \times 300 / 4 = 4500 vehicles/hr.

Parking turnover rate

Parking turnover is the number of vehicles that use a parking facility during an observation period, divided by the number of bays. Expressed per hour per bay, the turnover is \dfrac{N}{B \times T}, where N is the number of vehicles served, B is the number of bays and T is the observation period in hours.