{"paper":{"title":"Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic","arxiv_id":"math/0602526","primary_cat":"math.PR","submitted_at":"2006-02-23T11:59:03+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.98,"id":"s0","own":false,"role":"background","text":"A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.13,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.98,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":1,"p":0.39,"id":"s1","own":true,"role":"contribution","text":"An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the system's state.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.79,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.26,"result":0.0,"background":0.35,"limitation":0.0,"future_work":0.0,"contribution":0.39,"interpretation":0.0}},{"i":2,"p":0.43,"id":"s2","own":false,"role":"background","text":"We examine two versions of the problem: ``nonpreemptive,'' where service is uninterruptible, and ``preemptive,'' where service to a customer can be interrupted and then resumed, possibly at a different station.","hedge":{"p":0.9,"label":"asserted"},"own_p":0.35,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.16,"result":0.0,"background":0.43,"limitation":0.0,"future_work":0.0,"contribution":0.41,"interpretation":0.0}},{"i":3,"p":0.46,"id":"s3","own":false,"role":"method","text":"We study the problem in the asymptotic heavy traffic regime proposed by Halfin and Whitt, in which the arrival rates and the number of servers at each station grow without bound.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.28,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.19,"role_probabilities":{"gap":0.0,"method":0.46,"result":0.0,"background":0.34,"limitation":0.0,"future_work":0.0,"contribution":0.2,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":true,"role":"result","text":"The two versions of the problem are not, in general, asymptotically equivalent in this regime, with the preemptive version showing an asymptotic behavior that is, in a sense, much simpler.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.74,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.03}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"result","text":"Under appropriate assumptions on the structure of the system we show: (i) The value function for the preemptive problem converges to $V$, the value of a related diffusion control problem.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":6,"p":0.99,"id":"s6","own":true,"role":"result","text":"(ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.65,"quantitative":false,"quantitative_p":0.32,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":7,"p":0.98,"id":"s7","own":true,"role":"method","text":"The construction of these policies is based on a Hamilton--Jacobi--Bellman equation associated with $V$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.89,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"(ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$.","location":"abstract s6","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":6395,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.03,"states_limitation":0.68,"human_participants":0.02,"controlled_comparison":0.11,"randomized_assignment":0.01,"states_quantitative_result":0.08,"compares_with_prior_results":0.31,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.81,"text":"(ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$.","location":"abstract s6"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":8,"sentences_in_abstract":8},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}