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| DC Field | Value | Language |
|---|---|---|
| dc.creator | Jones, Lee K. | - |
| dc.creator | Larson, Richard C., 1943- | - |
| dc.date | 2004-05-28T19:24:34Z | - |
| dc.date | 2004-05-28T19:24:34Z | - |
| dc.date | 1994-03 | - |
| dc.date.accessioned | 2013-10-09T02:37:53Z | - |
| dc.date.available | 2013-10-09T02:37:53Z | - |
| dc.date.issued | 2013-10-09 | - |
| dc.identifier | http://hdl.handle.net/1721.1/5131 | - |
| dc.identifier.uri | http://koha.mediu.edu.my:8181/xmlui/handle/1721 | - |
| dc.description | This paper derives recursive algorithms for efficiently computing event probabilities related to order statistics and applies the results in a queue inferencing setting. Consider a set of N i.i.d. random variables in [0, 1]. When the experimental values of the random variables are arranged in ascending order from smallest to largest, one has the order statistics of the set of random variables. Both a forward and a backward recursive O(N3 ) algorithm are developed for computing the probability that the order statistics vector lies in a given N-rectangle. The new algorithms have applicability in inferring the statistical behavior of Poisson arrival queues, given only the start and stop times of service of all N customers served in a period of continuous congestion. The queue inference results extend the theory of the "Queue Inference Engine" (QIE), originally developed by Larson in 1990 [8]. The methodology is extended to a third O(N 3 ) algorithm, employing both forward and backward recursion, that computes the conditional probability that a random customer of the N served waited in queue less than r minutes, given the observed customer departure times and assuming first come, first served service. To our knowledge, this result is the first O(N3 ) exact algorithm for computing points on the in-queue waiting time distribution function,conditioned on the start and stop time data. The paper concludes with an extension to the computation of certain correlations of in-queue waiting times. Illustrative computational results are included throughout. | - |
| dc.format | 1762904 bytes | - |
| dc.format | application/pdf | - |
| dc.language | en_US | - |
| dc.publisher | Massachusetts Institute of Technology, Operations Research Center | - |
| dc.relation | Operations Research Center Working Paper;OR 289-94 | - |
| dc.subject | order statistics, queues, inference, computational probability. | - |
| dc.title | Efficient Computation of Probabilities of Events Described by Order Statistics and Applications to Queue Inference | - |
| dc.type | Working Paper | - |
| Appears in Collections: | MIT Items | |
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