Stochastic networks and queues:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin, [u.a.]
Springer
[2003]
|
| Series: | Applications of mathematics
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 385 - 388 |
| Physical Description: | xvii, 398 Seiten Illustrationen |
| ISBN: | 3540006575 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV017372152 | ||
| 003 | DE-604 | ||
| 005 | 20241120 | ||
| 007 | t| | ||
| 008 | 030729s2003 gw a||| |||| 00||| eng d | ||
| 016 | 7 | |a 968060978 |2 DE-101 | |
| 020 | |a 3540006575 |9 3-540-00657-5 | ||
| 035 | |a (OCoLC)51755735 | ||
| 035 | |a (DE-599)BVBBV017372152 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 1 | |a eng |h fre | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-355 |a DE-824 |a DE-703 |a DE-91G |a DE-521 |a DE-20 |a DE-634 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA274.8.R6313 2003 | |
| 082 | 0 | |a 519.8/2 21 | |
| 082 | 0 | |a 519.8/2 |2 21 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a SK 970 |0 (DE-625)143276: |2 rvk | ||
| 084 | |a 60G55 |2 msc/2000 | ||
| 084 | |a MAT 608f |2 stub | ||
| 084 | |a 60K25 |2 msc/2000 | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 60H10 |2 msc/2000 | ||
| 084 | |a 28 |2 sdnb | ||
| 100 | 1 | |a Robert, Philippe |0 (DE-588)119807211 |4 aut | |
| 245 | 1 | 0 | |a Stochastic networks and queues |c Philippe Robert |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a xvii, 398 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 52 | |
| 500 | |a Literaturverzeichnis Seite 385 - 388 | ||
| 650 | 4 | |a Analyse stochastique | |
| 650 | 4 | |a Files d'attente, Théorie des | |
| 650 | 7 | |a Netwerken |2 gtt | |
| 650 | 7 | |a Puntprocessen |2 gtt | |
| 650 | 7 | |a Stochastische analyse |2 gtt | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 7 | |a Toepassingen |2 gtt | |
| 650 | 7 | |a Wachttijdproblemen |2 gtt | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Stochastic analysis | |
| 650 | 0 | 7 | |a Stochastisches Modell |0 (DE-588)4057633-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Warteschlangennetz |0 (DE-588)4225823-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Warteschlangennetz |0 (DE-588)4225823-6 |D s |
| 689 | 0 | 1 | |a Stochastisches Modell |0 (DE-588)4057633-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-662-13052-0 |
| 830 | 0 | |a Applications of mathematics |v 52 |w (DE-604)BV000895226 |9 52 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch Darmstadt |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010470110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010470110 | |
Record in the Search Index
| _version_ | 1816254057147269120 |
|---|---|
| adam_text |
PHILIPPE ROBERT STOCHASTIC NETWORKS AND QUEUES SPRINGER TABLE OF
CONTENTS 1. POINT PROCESSES 1 1.1 GENERAL DEFINITIONS 2 1.2 POISSON
PROCESSES 5 1.3 POISSON POINT PROCESSES ON THE REAL LINE 16 1.4 RENEWAL
POINT PROCESSES 22 2. GI/GI/1 FIFO QUEUES AND RANDOM WALKS 29 2.1
GENERAL RESULTS ON GI/GI/1 FIFO QUEUES 29 2.2 WIENER-HOPF FACTORIZATION
33 2.3 APPLICATIONS TO THE GI/GI/1 QUEUE 37 2.4 GI/M/1 AND M/GI/1 QUEUES
43 2.5 THE HI/G/1 QUEUE 50 2.6 A PROBABILISTIC PROOF 52 3. LIMIT
THEOREMS FOR GI/GI/1 QUEUES 57 3.1 INTRODUCTION 57 3.2 THE BIASED RANDOM
WALK 58 3.3 THE TAIL DISTRIBUTION OF W 63 3.4 THE MAXIMUM OF A BUSY
PERIOD 67 3.5 THE GI/GI/1 QUEUE NEAR SATURATION 69 3.6 THE RANDOM WALK
CONDITIONED TO HIT LEVEL A 74 4. STOCHASTIC NETWORKS AND REVERSIBILITY
79 4.1 INTRODUCTION 79 4.2 REVERSIBILITY OF MARKOV PROCESSES 80 4.3
LOCAL BALANCE EQUATIONS 90 4.4 QUEUEING NETWORKS WITH PRODUCT FORM 92 5.
THE M/M/L QUEUE 103 5.1 INTRODUCTION 104 5.2 EXPONENTIAL MARTINGALES 106
5.3 HITTING TIMES : DOWNWARD 109 5.4 CONVERGENCE TO EQUILIBRIUM 113 5.5
HITTING TIMES : UPWARD 117 XVI TABLE OF CONTENTS 5.6 RARE EVENTS 120 5.7
FLUID LIMITS 124 5.8 LARGE DEVIATIONS 129 5.9 APPENDIX 139 6. THE M/M/OO
QUEUE 141 6.1 INTRODUCTION 141 6.2 POSITIVE MARTINGALES 146 6.3 HITTING
TIMES : DOWNWARD 150 6.4 HITTING TIMES : UPWARD 153 6.5 FLUID LIMITS 157
6.6 A FUNCTIONAL CENTRAL LIMIT THEOREM 160 6.7 THE M/M/N/N QUEUE 164 6.8
APPENDIX 174 7. QUEUES WITH POISSON ARRIVALS 177 7.1 FIFO M/G/L QUEUE
178 7.2 INFINITE SERVER QUEUE 180 7.3 PROCESSOR-SHARING M/G/L QUEUE 182
7.4 LIFO M/G/L QUEUE WITH PREEMPTIVE SERVICE 196 7.5 THE INSENSITIVITY
PROPERTY 202 7.6 THE DISTRIBUTION SEEN BY CUSTOMERS 202 7.7 APPENDIX:
FELLER-DYNKIN MARKOV PROCESSES 205 8. RECURRENCE AND TRANSIENCE OF
MARKOV CHAINS 207 8.1 RECURRENCE OF MARKOV CHAINS 209 8.2 ERGODICITY 211
8.3 TRANSIENCE 217 8.4 ERGODICITY OF MARKOV PROCESSES 222 8.5 SOME
APPLICATIONS 225 8.6 THE CLASSICAL VERSION OF LYAPUNOV'S THEOREM 229 9.
RESCALED MARKOV PROCESSES AND FLUID LIMITS 231 9.1 INTRODUCTION 231 9.2
RESCALED MARKOV PROCESSES 233 9.3 FLUID LIMITS OF A CLASS OF MARKOV
PROCESSES 241 9.4 RELATIONS WITH SKOROHOD PROBLEMS 249 9.5 CRITERIA FOR
ERGODICITY PROPERTIES 258 9.6 LOCAL EQUILIBRIUM OF A RESCALED MARKOV
PROCESS 271 9.7 BIBLIOGRAPHICAL NOTES 277 10. ERGODIC THEORY: BASIC
RESULTS 279 10.1 DISCRETE DYNAMICAL SYSTEMS 280 10.2 ERGODIC THEOREMS
284 10.3 CONTINUOUS TIME DYNAMICAL SYSTEMS 293 TABLE OF CONTENTS XVII
10.4 MARKOVIAN ENDOMORPHISMS 297 11. STATIONARY POINT PROCESSES 303 11.1
INTRODUCTION 303 11.2 THE PALM SPACE OF ARRIVAL PROCESS 304 11.3
CONSTRUCTION OF A STATIONARY POINT PROCESS 307 11.4 RELATIONS BETWEEN
THE PALM SPACE AND ITS EXTENSION 312 11.5 JOINT DISTRIBUTION OF THE
POINTS AROUND T = 0 316 11.6 SOME PROPERTIES OF STATIONARY POINT
PROCESSES 319 11.7 APPENDIX 326 12. THE G/G/L FIFO QUEUE 331 12.1
WAITING TIME 332 12.2 VIRTUAL WAITING TIME .' 336 12.3 NUMBER OF
CUSTOMERS 341 12.4 ASSOCIATED STATIONARY POINT PROCESSES 343 12.5 THE
UNSTABLE G/G/L QUEUE 346 12.6 A QUEUE WITH TWO SERVERS, THE G/G/2 QUEUE
347 A. MARTINGALES 351 A.I DISCRETE TIME PARAMETER MARTINGALES 351 A.2
CONTINUOUS TIME MARTINGALES 353 A.3 THE STOCHASTIC INTEGRAL FOR A
POISSON PROCESS 354 A.4 STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS 356
B. MARKOVIAN JUMP PROCESSES 359 B.I Q-MATRICES 360 B.2 GLOBAL BALANCE
EQUATIONS 362 B.3 THE ASSOCIATED MARTINGALES 364 C. CONVERGENCE IN
DISTRIBUTION 367 C.I TOTAL VARIATION NORM ON PROBABILITY DISTRIBUTIONS
367 C.2 CONVERGENCE OF STOCHASTIC PROCESSES 369 D. AN INTRODUCTION TO
SKOROHOD PROBLEMS 375 D.I DIMENSION 1 375 D.2 MULTI-DIMENSIONAL SKOROHOD
PROBLEMS 378 REFERENCES 385 RESEARCH PAPERS 389 INDEX 39;I |
| any_adam_object | 1 |
| author | Robert, Philippe |
| author_GND | (DE-588)119807211 |
| author_facet | Robert, Philippe |
| author_role | aut |
| author_sort | Robert, Philippe |
| author_variant | p r pr |
| building | Verbundindex |
| bvnumber | BV017372152 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.8.R6313 2003 |
| callnumber-search | QA274.8.R6313 2003 |
| callnumber-sort | QA 3274.8 R6313 42003 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 SK 970 |
| classification_tum | MAT 608f |
| ctrlnum | (OCoLC)51755735 (DE-599)BVBBV017372152 |
| dewey-full | 519.8/221 519.8/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.8/2 21 519.8/2 |
| dewey-search | 519.8/2 21 519.8/2 |
| dewey-sort | 3519.8 12 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV017372152</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241120</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">030729s2003 gw a||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">968060978</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540006575</subfield><subfield code="9">3-540-00657-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)51755735</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV017372152</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">fre</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.8.R6313 2003</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.8/2 21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.8/2</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 970</subfield><subfield code="0">(DE-625)143276:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60G55</subfield><subfield code="2">msc/2000</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 608f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60K25</subfield><subfield code="2">msc/2000</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H10</subfield><subfield code="2">msc/2000</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">28</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Robert, Philippe</subfield><subfield code="0">(DE-588)119807211</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stochastic networks and queues</subfield><subfield code="c">Philippe Robert</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">[2003]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvii, 398 Seiten</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applications of mathematics</subfield><subfield code="v">52</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverzeichnis Seite 385 - 388</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse stochastique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Files d'attente, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Netwerken</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Puntprocessen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastische analyse</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastische processen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Toepassingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Wachttijdproblemen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Queuing theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastisches Modell</subfield><subfield code="0">(DE-588)4057633-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Warteschlangennetz</subfield><subfield code="0">(DE-588)4225823-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Warteschlangennetz</subfield><subfield code="0">(DE-588)4225823-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stochastisches Modell</subfield><subfield code="0">(DE-588)4057633-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-662-13052-0</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applications of mathematics</subfield><subfield code="v">52</subfield><subfield code="w">(DE-604)BV000895226</subfield><subfield code="9">52</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010470110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010470110</subfield></datafield></record></collection> |
| id | DE-604.BV017372152 |
| illustrated | Illustrated |
| indexdate | 2024-11-20T15:00:46Z |
| institution | BVB |
| isbn | 3540006575 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010470110 |
| oclc_num | 51755735 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-703 DE-91G DE-BY-TUM DE-521 DE-20 DE-634 DE-83 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-703 DE-91G DE-BY-TUM DE-521 DE-20 DE-634 DE-83 DE-11 |
| physical | xvii, 398 Seiten Illustrationen |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Robert, Philippe (DE-588)119807211 aut Stochastic networks and queues Philippe Robert Berlin, [u.a.] Springer [2003] © 2003 xvii, 398 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 52 Literaturverzeichnis Seite 385 - 388 Analyse stochastique Files d'attente, Théorie des Netwerken gtt Puntprocessen gtt Stochastische analyse gtt Stochastische processen gtt Toepassingen gtt Wachttijdproblemen gtt Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-662-13052-0 Applications of mathematics 52 (DE-604)BV000895226 52 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010470110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robert, Philippe Stochastic networks and queues Applications of mathematics Analyse stochastique Files d'attente, Théorie des Netwerken gtt Puntprocessen gtt Stochastische analyse gtt Stochastische processen gtt Toepassingen gtt Wachttijdproblemen gtt Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4225823-6 |
| title | Stochastic networks and queues |
| title_auth | Stochastic networks and queues |
| title_exact_search | Stochastic networks and queues |
| title_full | Stochastic networks and queues Philippe Robert |
| title_fullStr | Stochastic networks and queues Philippe Robert |
| title_full_unstemmed | Stochastic networks and queues Philippe Robert |
| title_short | Stochastic networks and queues |
| title_sort | stochastic networks and queues |
| topic | Analyse stochastique Files d'attente, Théorie des Netwerken gtt Puntprocessen gtt Stochastische analyse gtt Stochastische processen gtt Toepassingen gtt Wachttijdproblemen gtt Queuing theory Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| topic_facet | Analyse stochastique Files d'attente, Théorie des Netwerken Puntprocessen Stochastische analyse Stochastische processen Toepassingen Wachttijdproblemen Queuing theory Stochastic analysis Stochastisches Modell Warteschlangennetz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010470110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT robertphilippe stochasticnetworksandqueues |