--- title: "Parking terms; speed-density and flow relations" subject: "Transportation Engineering II" chapter: 1 key: "semester_7/transportation_engineering_ii:parking-terms-speed-density-relation" source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/parking-terms-speed-density-relation site: BCT Engineering --- # Parking terms; speed-density and flow relations Transportation Engineering II · Chapter 1: Traffic Engineering - Asked in: 2081 Baisakh, 4+4 marks - Video: [Relation between fundamental traffic flow parameters, Flow, Speed and Density, A simple explanation](https://www.youtube.com/watch?v=MOxya1UVxgc) — Transportation Engg Talks | Satish IITR - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/parking-terms-speed-density-relation - Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-1 ## Question Define parking accumulation, parking turnover, parking load and parking index. Explain speed-density relation and speed-flow relation with required graphs. ## Short answer Parking accumulation is number of vehicles parked at a given time; turnover is rate of use per bay; load is total vehicle-hours; index is percentage occupancy relative to capacity. Speed-density relation is linear v=vf(1−k/kj); speed-flow relation is parabolic with maximum flow qmax=vf kj/4 at speed vf/2 and density kj/2. ## Answer #### Parking terms - **Parking accumulation:** the number of vehicles parked in a study area at a given instant. Plotting it against time gives the accumulation curve; its peak gives the demand. - **Parking volume:** total number of vehicles parked in an area during a given period (usually a day); it counts each vehicle once. - **Parking load:** the area under the accumulation curve, in vehicle-hours (or vehicle-minutes) in a given period; it shows the total parking demand in time. - **Parking duration:** the length of time a vehicle stays parked. - **Parking turnover:** the rate of use of a parking space, the number of vehicles parked per bay in a given time. $$ \text{Turnover} = \frac{\text{Number of vehicles parked in the period}}{\text{Number of parking bays available}} $$ - **Parking index (occupancy):** the ratio of the number of bays occupied to the number of bays available, as a percentage. It measures how well the supply is used. $$ \text{Parking index} = \frac{\text{Parking load (vehicle-hours)}}{\text{Parking capacity (bay-hours)}} \times 100 $$ where parking capacity = number of bays x hours of study. An index near 100 percent means the supply is exhausted; a very low value means over-supply. #### Speed-density relation Speed falls as density rises. The simplest (Greenshields) model is linear: $$ v = v_f\left(1 - \frac{k}{k_j}\right) $$ where $v_f$ is the free-flow speed (at $k \to 0$) and $k_j$ is the jam density (where $v = 0$). ```text v ^ vf |* | * | * | * | * +---------------*--> k 0 kj ``` #### Speed-flow relation Since $q = vk$, eliminating $k$ gives $q = k_j\left(v - v^2/v_f\right)$, a parabola with maximum flow $q_{max} = v_f k_j/4$ at $v = v_f/2$. ```text v ^ vf |* | * | * uncongested vm |- - - -*----- (v = vf/2) | * congested | * +-----|----> q 0 qmax ``` The upper branch is stable (uncongested) flow, and the lower branch is forced (congested) flow. Flow rises with density up to $k_m = k_j/2$ (capacity) and then falls to zero at jam density. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is parking load? A. Number of vehicles parked at an instant B. The area under the accumulation curve, in vehicle-hours C. Vehicles per bay D. Time one vehicle stays Answer: B. Parking load is the area under the accumulation curve in vehicle-hours. (Key point: Parking load) 2. How is parking turnover calculated? A. Number of vehicles parked in the period / number of bays available B. Bays occupied x hours C. Load / duration D. Accumulation x bays Answer: A. Turnover is vehicles parked per bay in a given period. (Key point: Parking turnover) 3. What does a parking index near 100 percent mean? A. Over-supply of bays B. The parking supply is exhausted C. Zero demand D. Turnover is low Answer: B. Index = load / capacity x 100; near 100 percent means the bays are fully used. (Key point: Parking index) 4. What is the maximum flow in the Greenshields model and where does it occur? A. vf kj at v = vf B. vf kj/4 at v = vf/2 C. vf kj/2 at v = vf/4 D. kj/4 at v = vf Answer: B. q = kj(v - v^2/vf) peaks at v = vf/2 with qmax = vf kj/4; the upper branch is uncongested. 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