Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications

Through Laplace transforms, we study the extremes of a continuous-time Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the extreme is ‘attained’. For this, we investigate discrete-time Markov-additive processes and use...

Full description

Saved in:

Bibliographic Details
Published in:	Methodology and computing in applied probability Vol. 13; no. 2; pp. 221 - 267
Main Authors:	Dieker, A. B., Mandjes, M.
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.06.2011 Springer Nature B.V
Subjects:	Buffers Business and Management Economics Electrical Engineering Laplace transforms Life Sciences Markov analysis Mathematical analysis Mathematical models Mathematics and Statistics Matrices Networks Nonlinearity Probability Queues Queuing Statistics Studies Secondary 90B05 Markov-additive processes Queueing networks Fluctuation theory 60G15 Primary 60K25
ISSN:	1387-5841, 1573-7713
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Through Laplace transforms, we study the extremes of a continuous-time Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the extreme is ‘attained’. For this, we investigate discrete-time Markov-additive processes and use an embedding to relate these to the continuous-time setting. The resulting Laplace transforms are given in terms of two matrices, which can be determined either through solving a nonlinear matrix equation or through a spectral method. Our results on extremes are first applied to determine the steady-state buffer-content distribution of several single-station queueing systems. We show that our framework comprises many models dealt with earlier, but, importantly, it also enables us to derive various new results. At the same time, our setup offers interesting insights into the connections between the approaches developed so far, including matrix-analytic techniques, martingale methods, the rate-conservation approach, and the occupation-measure method. We also study networks of fluid queues, and show how the results on single queues can be used to find the Laplace transform of the steady-state buffer-content vector; it has a matrix quasi-product form. Fluid-driven priority systems also have this property.
AbstractList	Through Laplace transforms, we study the extremes of a continuous-time Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the extreme is 'attained'. For this, we investigate discrete-time Markov-additive processes and use an embedding to relate these to the continuous-time setting. The resulting Laplace transforms are given in terms of two matrices, which can be determined either through solving a nonlinear matrix equation or through a spectral method. Our results on extremes are first applied to determine the steady-state buffer-content distribution of several single-station queueing systems. We show that our framework comprises many models dealt with earlier, but, importantly, it also enables us to derive various new results. At the same time, our setup offers interesting insights into the connections between the approaches developed so far, including matrix-analytic techniques, martingale methods, the rate-conservation approach, and the occupation-measure method. We also study networks of fluid queues, and show how the results on single queues can be used to find the Laplace transform of the steady-state buffer-content vector; it has a matrix quasi-product form. Fluid-driven priority systems also have this property.[PUBLICATION ABSTRACT] Through Laplace transforms, we study the extremes of a continuous-time Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the extreme is 'attained'. For this, we investigate discrete-time Markov-additive processes and use an embedding to relate these to the continuous-time setting. The resulting Laplace transforms are given in terms of two matrices, which can be determined either through solving a nonlinear matrix equation or through a spectral method. Our results on extremes are first applied to determine the steady-state buffer-content distribution of several single-station queueing systems. We show that our framework comprises many models dealt with earlier, but, importantly, it also enables us to derive various new results. At the same time, our setup offers interesting insights into the connections between the approaches developed so far, including matrix-analytic techniques, martingale methods, the rate-conservation approach, and the occupation-measure method. We also study networks of fluid queues, and show how the results on single queues can be used to find the Laplace transform of the steady-state buffer-content vector; it has a matrix quasi-product form. Fluid-driven priority systems also have this property.
Author	Dieker, A. B. Mandjes, M.
Author_xml	– sequence: 1 givenname: A. B. surname: Dieker fullname: Dieker, A. B. organization: H. Milton Stewart School of Industrial and Systems Engineering – sequence: 2 givenname: M. surname: Mandjes fullname: Mandjes, M. email: m.r.h.mandjes@uva.nl organization: Korteweg-de Vries Institute for Mathematics, University of Amsterdam
BookMark	eNp9kMtKxTAQhoMo6FEfwF1x48ZoLm2TLEWON5SjoG5DL1ONtk1N0qO-ve2pIAi6GGaY-b-Z4Z-h9da2gNAeJUeUEHHs6ZAUHkPRmGC5hrZoIjgWgvL1oeZS4ETGdBPNvH8hhNGEx1vocf4RHDTgI1tFN5l7tUuclaUJZgnRrbMFeD8M3014jhYtYG9KKKOrvun84dS966EH0z5FJ11XmyILxrZ-B21UWe1h9ztvo4ez-f3pBb5enF-enlzjgisSsKhIKvKMs5xRmVclBRUTgEooJhOVqjiGvGSQsrwkHBKqSpLHPAVWkYRIQvk2Opj2ds6-9eCDbowvoK6zFmzvtSJCcZmulPu_lC-2d-3wnJYpTZRgfBTRSVQ4672DSnfONJn71JTo0Wc9-azHGH3WcmDEL6YwYeVCcJmp_yXZRPrhSvsE7uelv6EvP4uS4A
CitedBy_id	crossref_primary_10_1016_j_orl_2009_10_014 crossref_primary_10_1080_15326349_2018_1513335 crossref_primary_10_1016_j_spa_2016_12_007 crossref_primary_10_1017_apr_2020_2 crossref_primary_10_1017_S0021900200012031 crossref_primary_10_1080_03461238_2019_1667424 crossref_primary_10_1016_j_spa_2010_05_007 crossref_primary_10_3390_risks7010017 crossref_primary_10_1239_jap_1421763333 crossref_primary_10_1017_apr_2025_2 crossref_primary_10_1080_03461238_2023_2280287 crossref_primary_10_1016_j_spa_2025_104771 crossref_primary_10_1016_j_spa_2019_05_015 crossref_primary_10_1007_s10959_012_0425_4 crossref_primary_10_1007_s10959_024_01322_8
Cites_doi	10.1017/S0269964801152046 10.2307/3215047 10.2307/1427915 10.1239/jap/1034082131 10.1016/j.spa.2005.04.002 10.2307/3215018 10.1023/A:1024125320911 10.1137/1.9780898719734 10.1214/aoap/1177005065 10.1016/0304-4149(74)90011-8 10.1080/15326349508807330 10.1239/jap/1118777186 10.1007/978-3-540-77913-1_5 10.1137/S00361445024180 10.1007/BF00533480 10.1142/9789812779311 10.1239/aap/1158685001 10.1239/jap/1143936254 10.1239/aap/1013540169 10.1016/j.spa.2003.07.005 10.1023/A:1011044217695 10.1287/opre.40.3.S257 10.1081/STM-120016443 10.1007/BF00532536 10.1080/15326349108807174 10.1081/STM-200046511 10.1214/aop/1176992159 10.1155/S1048953394000262 10.1017/S0269964802161031 10.1007/BF00531742 10.1023/A:1011096201765 10.1081/STM-200046459 10.1214/105051604000000206 10.1287/moor.1070.0259 10.15807/jorsj.44.344 10.1007/978-1-4612-1742-8 10.1017/S0269964807070064
ContentType	Journal Article
Copyright	The Author(s) 2009 Springer Science+Business Media, LLC 2011
Copyright_xml	– notice: The Author(s) 2009 – notice: Springer Science+Business Media, LLC 2011
DBID	C6C AAYXX CITATION 3V. 7WY 7WZ 7XB 87Z 88I 8AO 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V M0C M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYYUZ Q9U 7SC 8FD L7M L~C L~D
DOI	10.1007/s11009-009-9140-8
DatabaseName	Springer_OA刊 CrossRef ProQuest Central (Corporate) ProQuest ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) ProQuest Pharma Collection ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Business Premium Collection Technology collection ProQuest One Community College ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection ABI/INFORM Global Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Business (UW System Shared) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering collection ABI/INFORM Collection China ProQuest Central Basic Computer and Information Systems Abstracts Technology Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef ABI/INFORM Global (Corporate) ProQuest Business Collection (Alumni Edition) ProQuest One Business Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Pharma Collection ProQuest Central China ABI/INFORM Complete ProQuest Central ABI/INFORM Professional Advanced ProQuest One Applied & Life Sciences ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea ProQuest Central (New) ABI/INFORM Complete (Alumni Edition) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition ABI/INFORM China ProQuest Technology Collection ProQuest SciTech Collection ProQuest Business Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) Business Premium Collection (Alumni) Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	ABI/INFORM Global (Corporate) Computer and Information Systems Abstracts
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Economics Statistics Mathematics
EISSN	1573-7713
EndPage	267
ExternalDocumentID	2318313261 10_1007_s11009_009_9140_8
GroupedDBID	-5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 1SB 203 29M 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5VS 67Z 6NX 7WY 88I 8AO 8FE 8FG 8FL 8FW 8TC 8UJ 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBO EBS EBU EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV L6V LAK LLZTM M0C M2P M4Y M7S MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOS QWB R89 R9I RIG RNI ROL RPX RSV RZC RZE RZK S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TH9 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z81 Z88 ZL0 ZMTXR ~8M AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7XB 8FK JQ2 L.- L.0 PKEHL PQEST PQUKI PRINS Q9U 7SC 8FD L7M L~C L~D
ID	FETCH-LOGICAL-c390t-7f067ba32b218bfd1e940eef7928596944ebd2e62bd03e519d0b436e2f0508013
IEDL.DBID	7WY
ISICitedReferencesCount	12
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000289483900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1387-5841
IngestDate	Fri Jul 11 11:11:19 EDT 2025 Tue Nov 04 17:13:22 EST 2025 Tue Nov 18 22:28:07 EST 2025 Sat Nov 29 02:52:17 EST 2025 Fri Feb 21 02:25:56 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Secondary 90B05 Markov-additive processes Queueing networks Fluctuation theory 60G15 Primary 60K25
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c390t-7f067ba32b218bfd1e940eef7928596944ebd2e62bd03e519d0b436e2f0508013
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
OpenAccessLink	https://link.springer.com/10.1007/s11009-009-9140-8
PQID	861597231
PQPubID	26119
PageCount	47
ParticipantIDs	proquest_miscellaneous_907938601 proquest_journals_861597231 crossref_primary_10_1007_s11009_009_9140_8 crossref_citationtrail_10_1007_s11009_009_9140_8 springer_journals_10_1007_s11009_009_9140_8
PublicationCentury	2000
PublicationDate	2011-06-01
PublicationDateYYYYMMDD	2011-06-01
PublicationDate_xml	– month: 06 year: 2011 text: 2011-06-01 day: 01
PublicationDecade	2010
PublicationPlace	Boston
PublicationPlace_xml	– name: Boston – name: New York
PublicationTitle	Methodology and computing in applied probability
PublicationTitleAbbrev	Methodol Comput Appl Probab
PublicationYear	2011
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Asmussen (CR3) 1994; 7 Moler, Van Loan (CR34) 2003; 45 Asmussen (CR4) 1995; 11 Tzenova, Adan, Kulkarni (CR44) 2005; 21 Beneš (CR11) 1963 Asmussen (CR5) 2000 Preater (CR39) 1997; 34 Miyazawa (CR32) 2004; 14 Neuts (CR35) 1989 Boxma, Kella, Perry (CR13) 2001; 15 Asmussen, Avram, Pistorius (CR7) 2004; 109 Prabhu (CR38) 1998 Bertoin (CR12) 1996 Dȩbicki, Dieker, Rolski (CR17) 2007; 32 Gail, Hantler, Taylor (CR21) 1996; 28 Kennedy (CR26) 1994; 31 Kulkarni (CR28) 1997 Scheinhardt, Zwart (CR41) 2002; 16 Ney, Nummelin (CR36) 1987; 15 Pistorius (CR37) 2006; 43 Kella, Whitt (CR25) 1992 Arjas, Speed (CR2) 1973; 26 Çinlar (CR15) 1972; 24 Asmussen, Kella (CR8) 2000; 32 Kaspi (CR22) 1982; 59 Kella, Whitt (CR24) 1992; 40 Zhao, Li, Braun (CR46) 2003; 5 Lucantoni (CR31) 1991; 7 Kyprianou, Palmowski (CR29) 2008 Asmussen (CR6) 2003 Bean, O’Reilly, Taylor (CR10) 2005; 115 Takada (CR42) 2001; 44 Dȩbicki, Mandjes, van Uitert (CR18) 2007; 21 CR45 Dieker (CR19) 2006; 38 Kella (CR23) 2001; 37 Kroese, Scheinhardt (CR27) 2001; 37 Latouche, Ramaswami (CR30) 1999 Ahn, Ramaswami (CR1) 2005; 42 Rogers (CR40) 1994; 4 Takada, Miyazawa (CR43) 2002; 18 Bean, O’Reilly, Taylor (CR9) 2005; 21 Miyazawa, Takada (CR33) 2002; 39 Cohen (CR16) 1974; 2 Feller (CR20) 1971 Chung (CR14) 2001 O Kella (9140_CR23) 2001; 37 J Bertoin (9140_CR12) 1996 NG Bean (9140_CR10) 2005; 115 WRW Scheinhardt (9140_CR41) 2002; 16 H Takada (9140_CR42) 2001; 44 S Asmussen (9140_CR3) 1994; 7 S Asmussen (9140_CR5) 2000 J Preater (9140_CR39) 1997; 34 P Ney (9140_CR36) 1987; 15 S Asmussen (9140_CR7) 2004; 109 W Feller (9140_CR20) 1971 MF Neuts (9140_CR35) 1989 E Çinlar (9140_CR15) 1972; 24 J Kennedy (9140_CR26) 1994; 31 O Kella (9140_CR24) 1992; 40 NU Prabhu (9140_CR38) 1998 AE Kyprianou (9140_CR29) 2008 OJ Boxma (9140_CR13) 2001; 15 DM Lucantoni (9140_CR31) 1991; 7 S Ahn (9140_CR1) 2005; 42 H Kaspi (9140_CR22) 1982; 59 S Asmussen (9140_CR4) 1995; 11 S Asmussen (9140_CR8) 2000; 32 JW Cohen (9140_CR16) 1974; 2 V Kulkarni (9140_CR28) 1997 KL Chung (9140_CR14) 2001 9140_CR45 S Asmussen (9140_CR6) 2003 K Dȩbicki (9140_CR17) 2007; 32 AB Dieker (9140_CR19) 2006; 38 C Moler (9140_CR34) 2003; 45 E Arjas (9140_CR2) 1973; 26 O Kella (9140_CR25) 1992 VE Beneš (9140_CR11) 1963 H Takada (9140_CR43) 2002; 18 G Latouche (9140_CR30) 1999 E Tzenova (9140_CR44) 2005; 21 NG Bean (9140_CR9) 2005; 21 DP Kroese (9140_CR27) 2001; 37 M Miyazawa (9140_CR33) 2002; 39 M Miyazawa (9140_CR32) 2004; 14 YQ Zhao (9140_CR46) 2003; 5 K Dȩbicki (9140_CR18) 2007; 21 HR Gail (9140_CR21) 1996; 28 M Pistorius (9140_CR37) 2006; 43 LCG Rogers (9140_CR40) 1994; 4
References_xml	– ident: CR45 – year: 2001 ident: CR14 publication-title: A course in probability theory – volume: 15 start-page: 189 year: 2001 end-page: 198 ident: CR13 article-title: An intermittent fluid system with exponential on-times and semi-Markov input rates publication-title: Probab Eng Inf Sci doi: 10.1017/S0269964801152046 – volume: 31 start-page: 561 year: 1994 end-page: 563 ident: CR26 article-title: Understanding the Wiener-Hopf factorization for the simple random walk publication-title: J Appl Probab doi: 10.2307/3215047 – volume: 28 start-page: 114 year: 1996 end-page: 165 ident: CR21 article-title: Spectral analysis of M/G/1 and G/M/1 type Markov chains publication-title: Adv Appl Probab doi: 10.2307/1427915 – volume: 21 start-page: 83 year: 2007 end-page: 107 ident: CR18 article-title: A tandem queue with Lévy input: a new representation of the downstream queue length publication-title: Probab Eng Inf Sci – volume: 39 start-page: 604 year: 2002 end-page: 618 ident: CR33 article-title: A matrix exponential form for hitting probabilities and its application to a Markov-modulated fluid queue with downward jumps publication-title: J Appl Probab doi: 10.1239/jap/1034082131 – volume: 115 start-page: 1530 year: 2005 end-page: 1556 ident: CR10 article-title: Hitting probabilities and hitting times for stochastic fluid flows publication-title: Stoch Process their Appl doi: 10.1016/j.spa.2005.04.002 – year: 1996 ident: CR12 publication-title: Lévy processes – volume: 34 start-page: 1061 year: 1997 end-page: 1067 ident: CR39 article-title: M/M/∞ transience revisited publication-title: J Appl Probab doi: 10.2307/3215018 – volume: 5 start-page: 35 year: 2003 end-page: 58 ident: CR46 article-title: Censoring, factorizations, and spectral analysis for transition matrices with block-repeating entries publication-title: Methodol Comput Appl Probab doi: 10.1023/A:1024125320911 – year: 1999 ident: CR30 publication-title: Introduction to matrix analytic methods in stochastic modeling doi: 10.1137/1.9780898719734 – year: 1989 ident: CR35 publication-title: Structured stochastic matrices of / /1 type and their applications – volume: 4 start-page: 390 year: 1994 end-page: 413 ident: CR40 article-title: Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains publication-title: Ann Appl Probab doi: 10.1214/aoap/1177005065 – volume: 2 start-page: 31 year: 1974 end-page: 57 ident: CR16 article-title: Superimposed renewal processes and storage with gradual input publication-title: Stoch Process their Appl doi: 10.1016/0304-4149(74)90011-8 – volume: 11 start-page: 21 year: 1995 end-page: 49 ident: CR4 article-title: Stationary distributions for fluid flow models with or without Brownian noise publication-title: Stoch Models doi: 10.1080/15326349508807330 – start-page: 321 year: 1997 end-page: 338 ident: CR28 article-title: Fluid models for single buffer systems publication-title: Frontiers in queueing – start-page: 112 year: 1992 end-page: 128 ident: CR25 article-title: A tandem fluid network with Lévy input publication-title: Queueing and related models – volume: 42 start-page: 531 year: 2005 end-page: 549 ident: CR1 article-title: Efficient algorithms for transient analysis of stochastic fluid flow models publication-title: J Appl Probab doi: 10.1239/jap/1118777186 – start-page: 121 year: 2008 end-page: 135 ident: CR29 article-title: Fluctuations of spectrally negative Markov additive processes publication-title: Séminaire de probabilités vol XLI doi: 10.1007/978-3-540-77913-1_5 – year: 1998 ident: CR38 publication-title: Stochastic storage processes – volume: 45 start-page: 3 year: 2003 end-page: 49 ident: CR34 article-title: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later publication-title: SIAM Rev doi: 10.1137/S00361445024180 – year: 1963 ident: CR11 publication-title: General stochastic processes in the theory of queues – volume: 44 start-page: 344 year: 2001 end-page: 365 ident: CR42 article-title: Markov modulated fluid queues with batch fluid arrivals publication-title: J Oper Res Soc Jpn – volume: 26 start-page: 105 year: 1973 end-page: 118 ident: CR2 article-title: Symmetric Wiener-Hopf factorisations in Markov additive processes publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00533480 – year: 2000 ident: CR5 publication-title: Ruin probabilities doi: 10.1142/9789812779311 – volume: 38 start-page: 768 year: 2006 end-page: 791 ident: CR19 article-title: Applications of factorization embeddings for Lévy processes publication-title: Adv Appl Probab doi: 10.1239/aap/1158685001 – volume: 43 start-page: 208 year: 2006 end-page: 220 ident: CR37 article-title: On maxima and ladder processes for a dense class of Lévy processes publication-title: J Appl Probab doi: 10.1239/jap/1143936254 – volume: 32 start-page: 376 year: 2000 end-page: 393 ident: CR8 article-title: A multi-dimensional martingale for Markov additive processes and its applications publication-title: Adv Appl Probab doi: 10.1239/aap/1013540169 – volume: 109 start-page: 79 year: 2004 end-page: 111 ident: CR7 article-title: Russian and American put options under exponential phase-type Lévy models publication-title: Stoch Process their Appl doi: 10.1016/j.spa.2003.07.005 – volume: 37 start-page: 99 year: 2001 end-page: 139 ident: CR27 article-title: Joint distributions for interacting fluid queues publication-title: Queueing Syst doi: 10.1023/A:1011044217695 – volume: 40 start-page: 257 year: 1992 end-page: 262 ident: CR24 article-title: A storage model with a two-state random environment publication-title: Oper Res doi: 10.1287/opre.40.3.S257 – volume: 18 start-page: 529 year: 2002 end-page: 552 ident: CR43 article-title: A Markov modulated fluid queue with batch arrivals and preemptions publication-title: Stoch Models doi: 10.1081/STM-120016443 – volume: 24 start-page: 85 year: 1972 end-page: 93 ident: CR15 article-title: Markov additive processes. I, II publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00532536 – volume: 7 start-page: 1 year: 1991 end-page: 46 ident: CR31 article-title: New results on the single server queue with a batch Markovian arrival process publication-title: Stoch Models doi: 10.1080/15326349108807174 – year: 1971 ident: CR20 publication-title: An introduction to probability theory and its applications, vol II – volume: 21 start-page: 149 year: 2005 end-page: 184 ident: CR9 article-title: Algorithms for return probabilities for stochastic fluid flows publication-title: Stoch Models doi: 10.1081/STM-200046511 – volume: 15 start-page: 561 year: 1987 end-page: 592 ident: CR36 article-title: Markov additive processes. I. Eigenvalue properties and limit theorems publication-title: Ann Probab doi: 10.1214/aop/1176992159 – volume: 7 start-page: 269 year: 1994 end-page: 299 ident: CR3 article-title: Busy period analysis, rare events and transient behavior in fluid flow models publication-title: J Appl Math Stoch Anal doi: 10.1155/S1048953394000262 – volume: 16 start-page: 29 year: 2002 end-page: 45 ident: CR41 article-title: A tandem fluid queue with gradual input publication-title: Probab Eng Inf Sci doi: 10.1017/S0269964802161031 – year: 2003 ident: CR6 publication-title: Applied probability and queues – volume: 59 start-page: 179 year: 1982 end-page: 196 ident: CR22 article-title: On the symmetric Wiener-Hopf factorization for Markov additive processes publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00531742 – volume: 37 start-page: 141 year: 2001 end-page: 161 ident: CR23 article-title: Markov-modulated feedforward fluid networks publication-title: Queueing Syst doi: 10.1023/A:1011096201765 – volume: 21 start-page: 37 year: 2005 end-page: 55 ident: CR44 article-title: Fluid models with jumps publication-title: Stoch Models doi: 10.1081/STM-200046459 – volume: 14 start-page: 1029 year: 2004 end-page: 1054 ident: CR32 article-title: Hitting probabilities in a Markov additive process with linear movements and upward jumps: applications to risk and queueing processes publication-title: Ann Appl Probab doi: 10.1214/105051604000000206 – volume: 32 start-page: 629 year: 2007 end-page: 647 ident: CR17 article-title: Quasi-product forms for Lévy-driven fluid networks publication-title: Math Oper Res doi: 10.1287/moor.1070.0259 – volume: 32 start-page: 629 year: 2007 ident: 9140_CR17 publication-title: Math Oper Res doi: 10.1287/moor.1070.0259 – volume: 43 start-page: 208 year: 2006 ident: 9140_CR37 publication-title: J Appl Probab doi: 10.1239/jap/1143936254 – start-page: 112 volume-title: Queueing and related models year: 1992 ident: 9140_CR25 – volume: 44 start-page: 344 year: 2001 ident: 9140_CR42 publication-title: J Oper Res Soc Jpn doi: 10.15807/jorsj.44.344 – volume: 109 start-page: 79 year: 2004 ident: 9140_CR7 publication-title: Stoch Process their Appl doi: 10.1016/j.spa.2003.07.005 – volume: 15 start-page: 189 year: 2001 ident: 9140_CR13 publication-title: Probab Eng Inf Sci doi: 10.1017/S0269964801152046 – volume: 18 start-page: 529 year: 2002 ident: 9140_CR43 publication-title: Stoch Models doi: 10.1081/STM-120016443 – volume: 31 start-page: 561 year: 1994 ident: 9140_CR26 publication-title: J Appl Probab doi: 10.2307/3215047 – volume: 32 start-page: 376 year: 2000 ident: 9140_CR8 publication-title: Adv Appl Probab doi: 10.1239/aap/1013540169 – volume: 21 start-page: 149 year: 2005 ident: 9140_CR9 publication-title: Stoch Models doi: 10.1081/STM-200046511 – volume-title: Stochastic storage processes year: 1998 ident: 9140_CR38 doi: 10.1007/978-1-4612-1742-8 – volume: 2 start-page: 31 year: 1974 ident: 9140_CR16 publication-title: Stoch Process their Appl doi: 10.1016/0304-4149(74)90011-8 – volume: 5 start-page: 35 year: 2003 ident: 9140_CR46 publication-title: Methodol Comput Appl Probab doi: 10.1023/A:1024125320911 – volume-title: Applied probability and queues year: 2003 ident: 9140_CR6 – volume: 26 start-page: 105 year: 1973 ident: 9140_CR2 publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00533480 – volume: 15 start-page: 561 year: 1987 ident: 9140_CR36 publication-title: Ann Probab doi: 10.1214/aop/1176992159 – volume-title: Lévy processes year: 1996 ident: 9140_CR12 – volume: 59 start-page: 179 year: 1982 ident: 9140_CR22 publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00531742 – ident: 9140_CR45 – volume: 115 start-page: 1530 year: 2005 ident: 9140_CR10 publication-title: Stoch Process their Appl doi: 10.1016/j.spa.2005.04.002 – volume-title: Introduction to matrix analytic methods in stochastic modeling year: 1999 ident: 9140_CR30 doi: 10.1137/1.9780898719734 – volume: 34 start-page: 1061 year: 1997 ident: 9140_CR39 publication-title: J Appl Probab doi: 10.2307/3215018 – volume-title: An introduction to probability theory and its applications, vol II year: 1971 ident: 9140_CR20 – volume: 28 start-page: 114 year: 1996 ident: 9140_CR21 publication-title: Adv Appl Probab doi: 10.2307/1427915 – start-page: 321 volume-title: Frontiers in queueing year: 1997 ident: 9140_CR28 – volume-title: General stochastic processes in the theory of queues year: 1963 ident: 9140_CR11 – volume: 14 start-page: 1029 year: 2004 ident: 9140_CR32 publication-title: Ann Appl Probab doi: 10.1214/105051604000000206 – volume-title: Structured stochastic matrices of M/G/1 type and their applications year: 1989 ident: 9140_CR35 – volume-title: Ruin probabilities year: 2000 ident: 9140_CR5 doi: 10.1142/9789812779311 – volume: 21 start-page: 83 year: 2007 ident: 9140_CR18 publication-title: Probab Eng Inf Sci doi: 10.1017/S0269964807070064 – volume: 45 start-page: 3 year: 2003 ident: 9140_CR34 publication-title: SIAM Rev doi: 10.1137/S00361445024180 – volume: 37 start-page: 141 year: 2001 ident: 9140_CR23 publication-title: Queueing Syst doi: 10.1023/A:1011096201765 – volume: 37 start-page: 99 year: 2001 ident: 9140_CR27 publication-title: Queueing Syst doi: 10.1023/A:1011044217695 – volume: 7 start-page: 269 year: 1994 ident: 9140_CR3 publication-title: J Appl Math Stoch Anal doi: 10.1155/S1048953394000262 – volume: 24 start-page: 85 year: 1972 ident: 9140_CR15 publication-title: Z Wahrscheinlichkeitstheor Verw Geb doi: 10.1007/BF00532536 – volume: 21 start-page: 37 year: 2005 ident: 9140_CR44 publication-title: Stoch Models doi: 10.1081/STM-200046459 – volume: 4 start-page: 390 year: 1994 ident: 9140_CR40 publication-title: Ann Appl Probab doi: 10.1214/aoap/1177005065 – start-page: 121 volume-title: Séminaire de probabilités vol XLI year: 2008 ident: 9140_CR29 doi: 10.1007/978-3-540-77913-1_5 – volume: 11 start-page: 21 year: 1995 ident: 9140_CR4 publication-title: Stoch Models doi: 10.1080/15326349508807330 – volume-title: A course in probability theory year: 2001 ident: 9140_CR14 – volume: 38 start-page: 768 year: 2006 ident: 9140_CR19 publication-title: Adv Appl Probab doi: 10.1239/aap/1158685001 – volume: 42 start-page: 531 year: 2005 ident: 9140_CR1 publication-title: J Appl Probab doi: 10.1239/jap/1118777186 – volume: 7 start-page: 1 year: 1991 ident: 9140_CR31 publication-title: Stoch Models doi: 10.1080/15326349108807174 – volume: 16 start-page: 29 year: 2002 ident: 9140_CR41 publication-title: Probab Eng Inf Sci doi: 10.1017/S0269964802161031 – volume: 40 start-page: 257 year: 1992 ident: 9140_CR24 publication-title: Oper Res doi: 10.1287/opre.40.3.S257 – volume: 39 start-page: 604 year: 2002 ident: 9140_CR33 publication-title: J Appl Probab doi: 10.1239/jap/1034082131
SSID	ssj0021534
Score	1.9596673
Snippet	Through Laplace transforms, we study the extremes of a continuous-time Markov-additive process with one-sided jumps and a finite-state background Markovian...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	221
SubjectTerms	Buffers Business and Management Economics Electrical Engineering Laplace transforms Life Sciences Markov analysis Mathematical analysis Mathematical models Mathematics and Statistics Matrices Networks Nonlinearity Probability Queues Queuing Statistics Studies
SummonAdditionalLinks	– databaseName: Springer Journals dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB60CtaDb7G-2IMnNZBkkyZ7LFIRwar4oLeQZGdPkkrTFH--M3m0KiroIYdkd7PLvubbmZ1vAE5kbPyU4JCl_di1SEJIK0YCcpj6XuxKP7FdXQabCAaDcDhUd7Ufd97cdm9MkuVOPXd2c0pFPj2K7ySGi7DkM9kMH9EfnmenLKquimRLq4ekq9OYMr_7xWdhNEeYX4yipay5XP9XKzdgrYaWolfNhU1YwGwLVhrP43wLVm9mHK301macWdE0b8Nz_23CmsJcjIxg_53R1OKrRrwZitqZgBJZaytuM7Q4yKcW1zQX8vPq632BBVJLRe-DSXwHni77jxdXVh1ywUqlsidWYEh6JbF0ExL9idEOKs9GNIFioruu8jxMtItdN9G2REJ_2k482UXX2IT0CE7uQisbZbgHwvPR8fyAAIfRnjSpMk7QpWKhlkpTiQ7YTd9Hac1HzmExXqI5kzL3ZcQP92UUduB0VuS1IuP4LfNBM6BRvS7zKCQAx3HWnA6IWSotKLaSxBmOijxSTBkY0jm1A2fNEM9_8GN1-3_KfQDtSjnN6pxDaE3GBR7BcjqlcR8flxP6HYHb7iA priority: 102 providerName: Springer Nature
Title	Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications
URI	https://link.springer.com/article/10.1007/s11009-009-9140-8 https://www.proquest.com/docview/861597231 https://www.proquest.com/docview/907938601
Volume	13
WOSCitedRecordID	wos000289483900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: 7WY dateStart: 19990701 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global (OCUL) customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: M0C dateStart: 19990701 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: M7S dateStart: 19990701 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest advanced technologies & aerospace journals customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: P5Z dateStart: 19990701 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: BENPR dateStart: 19990701 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Computer Science Database (NC LIVE) customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: K7- dateStart: 19990701 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1573-7713 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: M2P dateStart: 19990701 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: Springer Journals customDbUrl: eissn: 1573-7713 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0021534 issn: 1387-5841 databaseCode: RSV dateStart: 19990701 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB6Vx6E9lFdRtzzkQ0-ARRInm_hUUbQItWJZ3o9LlMRjCalKKNlF_fmdyWsBCS4cMlLiOLYytmc8M54P4LtKbJCROiRNkHiSJISSCZIih1ngJ54KUsczFdhEOBxG19d61MTmlE1YZbsmVgu1KTK2ke9GJHoZIcv9cf9XMmgUO1cbBI0ZmCM5HTCAQXh10-23qOEa05bmEclZt3VqVifn3MorQJfmAMfouVia6pov3KOV1DlYeGd_F-Fzo26KvXp8LMEHzJfh01GXq7VcgcvBvzEbCUtRWMFHd4pHyVFGvA6K5hwBFbLBVhznKBnf04hfNAzKnfrpyQQnSN0Xe0-84V_g4mBwvn8oG7QFmSntjGVoSXClifJSkvqpNS5q30G0oeYcd33t-5gaD_teahyFpPgZJ_VVHz3rkJJHmuQqzOZFjl9B-AG6fhCSrmGNr2ymrRv2qVpklDZUowdO-7PjrElFzogYf-JpEmXmT8wX8yeOerDVVbmv83C89fJay5O4mZJl3DGkB6IrpbnEDpIkx2JSxpqzBUa0Re3Bdsv36Qdebe7bm82twcfaDs2Wm3WYHT9McAPms8fxXfmwWY3YTZj7ORiOTunudyiJHjn7TL0R0_CM6Ci4JXp6dvkfft33ng
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LTxUxFD5BMFEW4DNeAe1CN2rjTNt5LQghCAEvXDVBw26cmZ4mJmYGmHtRfxT_kXPmddVEdixcdDOdtmn79TzbcwBe6MwFBYlD0gaZksQhtMyQBDksApMpHeSesk2yiWgyiU9Oko8LcNm_heFrlT1NbAi1rQq2kb-NifVyhix_6_RMctIodq72GTRaVIzx1w_S2OrNg3e0vS-V2ts93tmXXVIBWZB6P5WRI_qcZ1rlxNxyZ31MjIfoooRDuYWJMZhbhaHKraeR5Bvr5UaHqJxHsgwJTNTvLVgyOg75QI0jOeh3NNE2hy6dW-Lrfu9EbV7q-Y0XgkrCFyrjP9ngXLb9yx3bcLm91f9sfe7BSidOi-0W__dhAcsHsHw0xKKtH8KX3Z9TNoLWonKCnyZVF5JvUTGdF907Capkg7T4UKLk_KVWvCeY12_ar59mOENaLrH9m7f_EXy-kYk9hsWyKvEJCBOgb4KIZClnjXZF4vwopGax1YmlFiPw-s1Niy7UOmf8-J7Og0QzHlIujIc0HsGroclpG2fkup_XegykHcmp0wEAIxBDLdEKdgBlJVazOk04GmJMKvgIXvc4m3fwz-GeXjvcc7izf3x0mB4eTMZrcLe1ubOVah0Wp-cz3IDbxcX0W33-rDktAr7eNPyuAPQCS2o
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1R1NT9RA9AUXY_SgiBpXFOYgF3RCO9Nu24MhKLsRkXUlaLjVtvMmMTEt0l3An-a_471-rZLAjQOHuXQ6M5mZN-_7A-C1TqyfETskjZ8oSRRCywSJkcPM9xKl_dRRpio2EYzH4dFRNFmAv20sDLtVtjixQtSmyFhHvhkS6eUKWe6mbbwiJjujrePfkgtIsaG1raZRQ8ge_jkj6a18t7tDV72u1Gh4-OGjbAoMyIxE_akMLOHqNNEqJUKXWuNi5DmINog4rdsg8jxMjcKBSo2jkXgd46SeHqCyDvE1xDzRvHdgMdAk8_Rg8f1wPDnopD3adl1Rl14xUXm3NalWcXtuZZOgFrF7Zfg_UZxzupeMsxXNGz26xae1BA8bRlts1y_jMSxgvgwP9rssteUT-D48n7J6tBSFFRy0VJxK9q9iCiCaCArqZFW1-JKj5MqmRnyiB1C-rb9-neEM6ejE9j9-AE_h241s7Bn08iLH5yA8H13PD4jLssbTNousGwxoWGh0ZGhEH5z2ouOsScLOtUB-xfP00QwbMTeGjTjsw0Y35LjOQHLdzystPMQNMirjDhj6ILpewiJsGkpyLGZlHHGexJCE8z68aWFuPsGVy724drk1uEdQF3_eHe-twP1aGc_qq5fQm57M8BXczU6nP8uT1ebpCPhx0_B3AfDcVbw
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Extremes+of+Markov-additive+Processes+with+One-sided+Jumps%2C+with+Queueing+Applications&rft.jtitle=Methodology+and+computing+in+applied+probability&rft.au=Dieker%2C+A.+B.&rft.au=Mandjes%2C+M.&rft.date=2011-06-01&rft.issn=1387-5841&rft.eissn=1573-7713&rft.volume=13&rft.issue=2&rft.spage=221&rft.epage=267&rft_id=info:doi/10.1007%2Fs11009-009-9140-8&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11009_009_9140_8
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1387-5841&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1387-5841&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1387-5841&client=summon