{"id":"W1997322796","doi":"10.1239/jap/1014843080","title":"Sharp results on convergence rates for the distribution of <i>GI</i>/<i>M</i>/1/<i>K</i> queues as <i>K</i> tends to infinity","year":2000,"lang":"en","type":"article","venue":"Journal of Applied Probability","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Markov chain; Infinity; Distribution (mathematics); Stationary distribution; Combinatorics; Limit (mathematics); Queue; Chain (unit); Convergence (economics); Mathematical analysis; Discrete mathematics; Statistics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01226448,0.002154097,0.001618346,0.004154122,0.002267256,0.00383749,0.004061067,0.002615308,0.00876887],"category_scores_gemma":[0.1054975,0.001386246,0.002656626,0.001729148,0.00507286,0.01142386,0.005060097,0.007470706,0.00141728],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003698071,"about_ca_system_score_gemma":0.001652194,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002130972,"about_ca_topic_score_gemma":0.001442075,"domain_scores_codex":[0.9968149,0.0009151601,0.0001913383,0.0006690336,0.0007789406,0.0006306742],"domain_scores_gemma":[0.9340054,0.05029101,0.004950318,0.002876402,0.00533854,0.002538375],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003856356,0.0001459833,0.00552803,0.0006803309,0.0001530645,0.0006467672,0.002374798,0.05767463,0.008860148,0.898959,0.002971175,0.0216206],"study_design_scores_gemma":[0.0001015145,0.0002471029,0.006011348,0.000614333,0.0002012814,0.001372167,0.0008909395,0.5080482,0.01128311,0.463793,0.007157634,0.0002793374],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1801687,0.008666643,0.7636578,0.003986257,0.0004600052,0.0003159175,0.0004857298,0.001061106,0.04119774],"genre_scores_gemma":[0.8822086,0.007196216,0.08858569,0.001786481,0.0006525965,0.0009387071,0.0005684958,0.000921106,0.01714204],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01226448,"threshold_uncertainty_score":0.06486154,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04237952015029214,"score_gpt":0.3250445251434332,"score_spread":0.2826650049931411,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}