On the Queueing Time Analysis for State-Dependent Fixed-Cycle Traffic Light Queues
Bibliographic record
Abstract
We analyze a Fixed-Cycle Traffic Light (FCTL) intersection model. Vehicles arrive according to a Poisson process and must wait for a green signal. Each signal period (red or green) consists of a number of phases. Exactly one waiting vehicle is released (passes through the intersection) per green signal period phase, while vehicles remain waiting during red signal periods phases. The lengths of red and green signal periods are not constants, rather they depend on the number of vehicles in the queue. That is, we propose a state-dependent scheduling mechanism for green and red signal periods in an FCTL intersection. The number of green phases increases if the number of vehicles waiting in the intersection is greater than or equal to a threshold N(> 0). The number of green phases increases from g(> 0) to g1(≥ g) and the number of red phases decreases from r(> 0) to r1(≤ r) in such a way that the total length of a cycle period, c = g + r = g1 + r1, is fixed. This mechanism allows one to control the waiting time of vehicles through the FCTL intersection. We analyze the distributions of queue length and vehicle waiting time during each phase of the green signal period. We provide several numerical examples to gain insight into the performance of our proposed FCTL scheduling mechanism. The proposed state-dependent FCTL queueing model dynamically adjusts green and red light durations based on the volume of traffic in queues. This FCTL model with state-dependent scheduling is ideal for smart city traffic optimization, improves traffic flow, reduces delays, and minimizes fuel consumption in busy urban areas.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".