{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T23:14:55Z","timestamp":1712445295875},"reference-count":0,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[1976,11]]},"abstract":" Consider a storage process X = {X(t), t \u2265 0} with compound Poisson input and a (state-dependent) release rule r(\u00b7) which is arbitrary except for the requirement that state zero be reachable in finite time from any positive starting state. We show that there exists a stationary distribution for X if and only if there is a limiting distribution independent of the initial state, in which case the stationary distribution is unique and coincides with the limiting distribution. A necessary and sufficient condition for the existence of a stationary distribution, as well as a general solution for the distribution when it exists, is given. We also give a general formula for U(x), the probability that level b is exceeded before level a is reached, starting from state x \u2208 (a, b]. Both the stationary distribution and U(x) are expressed in terms of a certain positive kernel. <\/jats:p>","DOI":"10.1287\/moor.1.4.347","type":"journal-article","created":{"date-parts":[[2008,10,31]],"date-time":"2008-10-31T22:43:38Z","timestamp":1225493018000},"page":"347-358","source":"Crossref","is-referenced-by-count":98,"title":["The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule"],"prefix":"10.1287","volume":"1","author":[{"given":"J. Michael","family":"Harrison","sequence":"first","affiliation":[{"name":"Graduate School of Business, Stanford University, Stanford, California 94305"}]},{"given":"Sidney I.","family":"Resnick","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University, Stanford, California 94305"}]}],"member":"109","container-title":["Mathematics of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/moor.1.4.347","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T13:29:09Z","timestamp":1680442149000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/moor.1.4.347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1976,11]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1976,11]]}},"alternative-id":["10.1287\/moor.1.4.347"],"URL":"https:\/\/doi.org\/10.1287\/moor.1.4.347","relation":{},"ISSN":["0364-765X","1526-5471"],"issn-type":[{"value":"0364-765X","type":"print"},{"value":"1526-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[1976,11]]}}}