The method of moments for higher moments and the usefulness of formula manipulation systems
Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been ob...
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creator | Paterok, Martin Dauphin, Peter Herzog, Ulrich |
description | Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been obtained in the last decades. This paper investigates the suitability of the method of moments to derive higher moments. Starting from general considerations, the problems in dealing with higher moments are insulated, and solutions are presented. These results give a deep insight into the nature of the method of moments.
It is difficult to handle the complex formulae for higher moments without the help of a formula manipulation system such as SCRATCHPAD II The tool was particularly useful to make first steps to find hypothetical formulae, then start proof (e.g. by induction) and to perform complex derivations, e.g. for comparison. The use of the tool gives deep insight into the potential use of computer algebra systems for queueing analysis. |
doi_str_mv | 10.1007/BFb0024307 |
format | Book Chapter |
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It is difficult to handle the complex formulae for higher moments without the help of a formula manipulation system such as SCRATCHPAD II The tool was particularly useful to make first steps to find hypothetical formulae, then start proof (e.g. by induction) and to perform complex derivations, e.g. for comparison. The use of the tool gives deep insight into the potential use of computer algebra systems for queueing analysis.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540603009</identifier><identifier>ISBN: 354060300X</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540447894</identifier><identifier>EISBN: 354044789X</identifier><identifier>DOI: 10.1007/BFb0024307</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>computer algebra ; method of moments ; queueing theory</subject><ispartof>Quantitative Evaluation of Computing and Communication Systems, 2005, p.56-70</ispartof><rights>Springer-Verlag Berlin Heidelberg 1995</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/BFb0024307$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/BFb0024307$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>775,776,780,789,27902,38232,41418,42487</link.rule.ids></links><search><contributor>Bause, Falko</contributor><contributor>Beilner, Heinz</contributor><creatorcontrib>Paterok, Martin</creatorcontrib><creatorcontrib>Dauphin, Peter</creatorcontrib><creatorcontrib>Herzog, Ulrich</creatorcontrib><title>The method of moments for higher moments and the usefulness of formula manipulation systems</title><title>Quantitative Evaluation of Computing and Communication Systems</title><description>Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been obtained in the last decades. This paper investigates the suitability of the method of moments to derive higher moments. Starting from general considerations, the problems in dealing with higher moments are insulated, and solutions are presented. These results give a deep insight into the nature of the method of moments.
It is difficult to handle the complex formulae for higher moments without the help of a formula manipulation system such as SCRATCHPAD II The tool was particularly useful to make first steps to find hypothetical formulae, then start proof (e.g. by induction) and to perform complex derivations, e.g. for comparison. The use of the tool gives deep insight into the potential use of computer algebra systems for queueing analysis.</description><subject>computer algebra</subject><subject>method of moments</subject><subject>queueing theory</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540603009</isbn><isbn>354060300X</isbn><isbn>9783540447894</isbn><isbn>354044789X</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2005</creationdate><recordtype>book_chapter</recordtype><sourceid/><recordid>eNpFUMtOwzAQNC-JqvTCF_jIJbD2unZ8hIoWpEpcyolD5MTrJtAkVZwe-HtcgcpeZjU7OxoNY7cC7gWAeXhalgBSIZgzNrMmx7kCpUxu1TmbCC1EhqjsxemmAQHsJZsklJk1Cq_ZLMZPSINSg9QT9rGpibc01r3nfeBt31I3Rh76gdfNtqbhRLnO8zGJD5HCYddRjMeHJGwPO8db1zX7tIxN3_H4HUdq4w27Cm4XafaHU_a-fN4sXrL12-p18bjOogA0mfW-zKsKg1PkMXdSCemsq0iHkIIq70qiPGhlUmRwOK-kn9sSFGnMdUCcsrtf37gfmm5LQ1H2_VcsBBTH3or_3vAHLb9b-w</recordid><startdate>20050609</startdate><enddate>20050609</enddate><creator>Paterok, Martin</creator><creator>Dauphin, Peter</creator><creator>Herzog, Ulrich</creator><general>Springer Berlin Heidelberg</general><scope/></search><sort><creationdate>20050609</creationdate><title>The method of moments for higher moments and the usefulness of formula manipulation systems</title><author>Paterok, Martin ; Dauphin, Peter ; Herzog, Ulrich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-s1037-9ddb8cc3fa4ed38a2412a9ace6ff0034dabee8f6476020a35c2d59b04e6386f33</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2005</creationdate><topic>computer algebra</topic><topic>method of moments</topic><topic>queueing theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Paterok, Martin</creatorcontrib><creatorcontrib>Dauphin, Peter</creatorcontrib><creatorcontrib>Herzog, Ulrich</creatorcontrib></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Paterok, Martin</au><au>Dauphin, Peter</au><au>Herzog, Ulrich</au><au>Bause, Falko</au><au>Beilner, Heinz</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>The method of moments for higher moments and the usefulness of formula manipulation systems</atitle><btitle>Quantitative Evaluation of Computing and Communication Systems</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2005-06-09</date><risdate>2005</risdate><spage>56</spage><epage>70</epage><pages>56-70</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540603009</isbn><isbn>354060300X</isbn><eisbn>9783540447894</eisbn><eisbn>354044789X</eisbn><abstract>Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been obtained in the last decades. This paper investigates the suitability of the method of moments to derive higher moments. Starting from general considerations, the problems in dealing with higher moments are insulated, and solutions are presented. These results give a deep insight into the nature of the method of moments.
It is difficult to handle the complex formulae for higher moments without the help of a formula manipulation system such as SCRATCHPAD II The tool was particularly useful to make first steps to find hypothetical formulae, then start proof (e.g. by induction) and to perform complex derivations, e.g. for comparison. The use of the tool gives deep insight into the potential use of computer algebra systems for queueing analysis.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/BFb0024307</doi><tpages>15</tpages></addata></record> |
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source | Springer Books |
subjects | computer algebra method of moments queueing theory |
title | The method of moments for higher moments and the usefulness of formula manipulation systems |
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