Nondeterministic Polling Systems
A nondeterministic polling system is considered in which a single server serves a number of stations. The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiex...
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| Veröffentlicht in: | Management science 1991-06, Vol.37 (6), p.667-681 |
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| creator | Srinivasan, Mandyam M |
| description | A nondeterministic polling system is considered in which a single server serves a number of stations. The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiexhaustive service discipline, then the next station polled is station j with probability p ij if there was service at station i . The service time at station i is a random variable which may depend on the station polled next. If no service is performed at station i , then the next station polled is station j with probability e ij . The time to switch between stations i and j is a random variable which may depend on whether service was performed at station i or not.
If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not.
Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained. |
| doi_str_mv | 10.1287/mnsc.37.6.667 |
| format | Article |
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If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not.
Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained.</description><identifier>ISSN: 0025-1909</identifier><identifier>EISSN: 1526-5501</identifier><identifier>DOI: 10.1287/mnsc.37.6.667</identifier><identifier>CODEN: MSCIAM</identifier><language>eng</language><publisher>Linthicum, MD: INFORMS</publisher><subject>Applied sciences ; Computer systems ; Conservation Laws ; Determinism ; Exact sciences and technology ; Gas stations ; Management science ; Mathematical expressions ; Mathematical models ; Mathematical moments ; mean waiting times ; Network servers ; Operational research and scientific management ; Operational research. Management science ; polling systems ; Polls ; queueing theory ; Queuing theory. Traffic theory ; Random variables ; Service stations ; Studies ; Vehicles</subject><ispartof>Management science, 1991-06, Vol.37 (6), p.667-681</ispartof><rights>Copyright 1991 The Institute of Management Sciences</rights><rights>1992 INIST-CNRS</rights><rights>Copyright Institute for Operations Research and the Management Sciences Jun 1991</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c509t-82f9b8cc42247af2f8200af4b8f1160c514e2274b0a2be31b116c2344135ab673</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2632524$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/mnsc.37.6.667$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,780,784,803,3692,4008,27869,27924,27925,58017,58250,62616</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5002879$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/inmormnsc/v_3a37_3ay_3a1991_3ai_3a6_3ap_3a667-681.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Srinivasan, Mandyam M</creatorcontrib><title>Nondeterministic Polling Systems</title><title>Management science</title><description>A nondeterministic polling system is considered in which a single server serves a number of stations. The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiexhaustive service discipline, then the next station polled is station j with probability p ij if there was service at station i . The service time at station i is a random variable which may depend on the station polled next. If no service is performed at station i , then the next station polled is station j with probability e ij . The time to switch between stations i and j is a random variable which may depend on whether service was performed at station i or not.
If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not.
Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained.</description><subject>Applied sciences</subject><subject>Computer systems</subject><subject>Conservation Laws</subject><subject>Determinism</subject><subject>Exact sciences and technology</subject><subject>Gas stations</subject><subject>Management science</subject><subject>Mathematical expressions</subject><subject>Mathematical models</subject><subject>Mathematical moments</subject><subject>mean waiting times</subject><subject>Network servers</subject><subject>Operational research and scientific management</subject><subject>Operational research. 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The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiexhaustive service discipline, then the next station polled is station j with probability p ij if there was service at station i . The service time at station i is a random variable which may depend on the station polled next. If no service is performed at station i , then the next station polled is station j with probability e ij . The time to switch between stations i and j is a random variable which may depend on whether service was performed at station i or not.
If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not.
Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained.</abstract><cop>Linthicum, MD</cop><pub>INFORMS</pub><doi>10.1287/mnsc.37.6.667</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Management science, 1991-06, Vol.37 (6), p.667-681 |
| issn | 0025-1909 1526-5501 |
| language | eng |
| recordid | cdi_highwire_informs_mansci_37_6_667 |
| source | RePEc; INFORMS PubsOnLine; Periodicals Index Online; EBSCOhost Business Source Complete; JSTOR Archive Collection A-Z Listing |
| subjects | Applied sciences Computer systems Conservation Laws Determinism Exact sciences and technology Gas stations Management science Mathematical expressions Mathematical models Mathematical moments mean waiting times Network servers Operational research and scientific management Operational research. Management science polling systems Polls queueing theory Queuing theory. Traffic theory Random variables Service stations Studies Vehicles |
| title | Nondeterministic Polling Systems |
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