Erlang analysis of cellular networks using stochastic Petri nets and user-in-the-loop extension for demand control
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Bibliographic record
Abstract
Cellular networks face severe challenges due to the expected growth of application data rate demand with an increase rate of 100% per year. Over-provisioning capacity has been the standard approach to reduce the risk of overload situations. Traditionally in telephony networks, call blocking and overload probability have been analyzed using the Erlang-B and Erlang-C formulas, which model limited capacity communication systems without or with session request buffers, respectively. While a closed-form expression exists for the blocking probability for constant load and service, a steady-state Markov chain (MC) analysis can always provide more detailed data, as long as the Markov property of the arrival and service processes hold. However, there is a significant modeling advantage by using the stochastic Petri net (SPN) paradigm to model the details of such a system. In addition, software tool support allows getting numeric analysis results quickly by solving the state probabilities in the background and without the need to run any simulation. Because of this efficiency, the equivalent SPN model of the Engset, Erlang-B and Erlang-C situation is introduced as novelty in this paper. Going beyond the original Erlang scenario, the user-in-the-loop (UIL) approach of demand shaping by closed-loop control is studied as an extension. In UIL, demand control is implemented by a dynamic usage-based tariff which motivates users to reduce or postpone the use of applications on their smart phone in times of light to severe congestion. In this paper, the effect of load on the price and demand reduction is modeled with an SPN based on the classical Erlang Markov chain structure. Numeric results are easily obtained and presented in this paper, including probability density functions (PDF) of the load situation, and a parameter analysis showing the effectiveness of UIL to reduce the overload probability.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it