A PH<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>i</a:mi> </a:mrow> </a:mfenced> </a:math>/PH<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mi>i</f:mi> <f:mo>,</f:mo> <f:mi>n</f:mi> </f:mrow> </f:mfenced> <f:mo>/</f:mo> <f:mrow> <f:mrow> <f:mi>C</f:mi> <f:mo>/</f:mo> <f:mi>C</f:mi> </f:mrow> </f:mrow> </f:math> Queuing Model in Randomly Changing Environments for Traffic Circulation Systems
Bibliographic record
Abstract
Robust optimal design of circulation systems (e.g., roads for vehicles or corridors for pedestrians) relies on an accurate steady-state traffic flow model that considers the effect of randomly changing environmental factors (e.g., daily periodicity and weather). Most analytical models assume that the customer interarrival time and service time of circulation facilities follow the exponential distribution with fixed rate parameters, which is unrealistic in most cases. In this paper, we develop a stationary PH i /PH i , n / C / C state-dependent queuing model in a randomly changing environment (RE), which is represented by a Markov chain. The model simultaneously considers the general randomness of arrival and service, the randomly varying rate parameters, and the state-dependent service (the travel time increases with the number of customers). The existing matrix analytic scheme (MAS) algorithm is extended to solve the proposed model because it avoids the explicit calculation of probability distributions. The space complexity of the algorithm is only linear in the number of RE states and is independent of the enormous (four-dimensional) state space of the Markov process. Its time complexity is a linear function of the product of the queue capacity and the number of RE states. Our model is validated versus simulation estimates. The obtained conditional performance measures can accurately capture the queue accumulation and dissipation and reveal the effect of randomly changing environments. Numerical experiments provide some interesting findings. (1) The proposed stationary model coincides with the transient M( t )/G x / C / C fluid queuing model under special conditions. (2) Under high traffic intensities, increasing the randomness in the duration time of the RE state leads to an obvious growth in the conditional queue length. (3) An increase in the facility length leads to an increase or a decrease in the average output rate, depending on whether the congestion dissipates effectively in one cycle. (4) A larger width is required to obtain the maximum average output rate for traffic demand with a greater nonuniformity.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.008 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.601 | 0.615 |
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".