{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T11:51:41Z","timestamp":1773143501364,"version":"3.50.1"},"reference-count":20,"publisher":"Elsevier BV","issue":"14","license":[{"start":{"date-parts":[[2004,12,1]],"date-time":"2004-12-01T00:00:00Z","timestamp":1101859200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers & Operations Research"],"published-print":{"date-parts":[[2004,12]]},"DOI":"10.1016\/s0305-0548(03)00190-4","type":"journal-article","created":{"date-parts":[[2003,7,16]],"date-time":"2003-07-16T13:35:31Z","timestamp":1058362531000},"page":"2333-2347","source":"Crossref","is-referenced-by-count":4,"title":["Policy iteration type algorithms for recurrent state Markov decision processes"],"prefix":"10.1016","volume":"31","author":[{"given":"Stephen D.","family":"Patek","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0305-0548(03)00190-4_BIB1","series-title":"Dynamic programming and Markov decision processes","author":"Howard","year":"1960"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB2","doi-asserted-by":"crossref","unstructured":"Campos-N\u00e1\u00f1ez E, Patek SD. On-line tuning of prices for network services. In: Proceedings of IEEE INFOCOM, San Francisco 2003, to appear.","DOI":"10.1109\/INFCOM.2003.1208959"},{"issue":"2","key":"10.1016\/S0305-0548(03)00190-4_BIB3","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/90.842140","article-title":"Congestion-dependent pricing of network services","volume":"8","author":"Paschalidis","year":"2000","journal-title":"IEEE\/ACM Transactions on Networking"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB4","doi-asserted-by":"crossref","unstructured":"Patek SD, Campos-N\u00e1\u00f1ez E. Pricing of dialup services: an example of congestion-dependent pricing in the internet. In: Proceedings of the 39th IEEE Conference on Decision and Control (CDC 2000), 2000. pp. 2296\u2013301.","DOI":"10.1109\/CDC.2000.914140"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB5","unstructured":"Bertsekas DP. Dynamic programming and optimal control, vol. 1. Belmont, MA: Athena Scientific, 1995."},{"issue":"2","key":"10.1016\/S0305-0548(03)00190-4_BIB6","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1137\/S0363012995291609","article-title":"A new value iteration method for the average cost dynamic programming problem","volume":"36","author":"Bertsekas","year":"1998","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"3","key":"10.1016\/S0305-0548(03)00190-4_BIB7","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1287\/moor.16.3.580","article-title":"Analysis of stochastic shortest path problems","volume":"16","author":"Bertsekas","year":"1991","journal-title":"Mathematics of Operations Research"},{"issue":"2","key":"10.1016\/S0305-0548(03)00190-4_BIB8","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1137\/0331018","article-title":"Discrete-time controlled Markov processes with average cost criterion","volume":"31","author":"Arapostathis","year":"1993","journal-title":"SIAM Journal on Control and Optimization"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB9","series-title":"Markov decision processes: discrete stochastic dynamic programming","author":"Puterman","year":"1994"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB10","doi-asserted-by":"crossref","first-page":"521","DOI":"10.2307\/1425832","article-title":"Optimal decision procedures for finite Markov chains. Part II","volume":"5","author":"Bather","year":"1973","journal-title":"Advances in Applied Probability"},{"issue":"2","key":"10.1016\/S0305-0548(03)00190-4_BIB11","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1287\/moor.8.2.298","article-title":"Denumerable undiscounted semi-Markov decision processes with unbounded rewards","volume":"8","author":"Federgruen","year":"1983","journal-title":"Mathematics of Operations Research"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB12","doi-asserted-by":"crossref","first-page":"356","DOI":"10.2307\/3213407","article-title":"The optimality equation in average cost denumerable state semi-Markov decision problems, recurrency conditions and algorithms","volume":"15","author":"Federgruen","year":"1978","journal-title":"Journal of Applied Probability"},{"issue":"4","key":"10.1016\/S0305-0548(03)00190-4_BIB13","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/1120093","article-title":"On controlled finite state Markov processes with compact control sets","volume":"20","author":"Feinberg","year":"1975","journal-title":"Theory of Probability and its Applications"},{"issue":"2","key":"10.1016\/S0305-0548(03)00190-4_BIB14","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1137\/1123033","article-title":"The existence of a stationary \u03b5-optimal policy for a fintie Markov chain","volume":"23","author":"Feinberg","year":"1978","journal-title":"Theory of Probability and its Applications"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB15","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1287\/opre.15.5.866","article-title":"Existence of a stationary control for the Markov chain maximizing the average reward","volume":"15","author":"Martin-L\u00f6f","year":"1967","journal-title":"Operations Research"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB16","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0022-247X(83)90023-9","article-title":"On the solvability of Bellman's functional equations for Markov renewal programming","volume":"96","author":"Schweitzer","year":"1983","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"1","key":"10.1016\/S0305-0548(03)00190-4_BIB17","first-page":"71","article-title":"On undiscounted Markovian decision processes with compact action spaces","volume":"19","author":"Schweitzer","year":"1985","journal-title":"RAIRO Recherche Op\u00e9rationnelle"},{"key":"10.1016\/S0305-0548(03)00190-4_BIB18","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0022-247X(87)90297-6","article-title":"A Brouwer fixed-point mapping approach to communicating Markov decision processes","volume":"123","author":"Schweitzer","year":"1987","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"1","key":"10.1016\/S0305-0548(03)00190-4_BIB19","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1287\/moor.12.1.163","article-title":"On the convergence of policy iteration in finite state undiscounted Markov decision processes","volume":"12","author":"Hordijk","year":"1969","journal-title":"Mathematics of Operations Research"},{"issue":"3","key":"10.1016\/S0305-0548(03)00190-4_BIB20","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1080\/15326348708807061","article-title":"Counter examples for compact action Markov decision chains with average reward criteria","volume":"3","author":"Dekker","year":"1987","journal-title":"Communications in Statistics: Stochastic Models"}],"container-title":["Computers & Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054803001904?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054803001904?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,17]],"date-time":"2019-03-17T13:52:58Z","timestamp":1552830778000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0305054803001904"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":20,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2004,12]]}},"alternative-id":["S0305054803001904"],"URL":"https:\/\/doi.org\/10.1016\/s0305-0548(03)00190-4","relation":{},"ISSN":["0305-0548"],"issn-type":[{"value":"0305-0548","type":"print"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}