1124:
36:
where jobs arrive in and/or are served in groups of random size. Batch arrivals have been used to describe large deliveries and batch services to model a hospital out-patient department holding a clinic once a week, a transport link with fixed capacity and an elevator.
88:
and form a single queue, from the front of which batches of customers (typically with a fixed maximum size) are served at a rate with independent distribution. The equilibrium distribution, mean and variance of queue length are known for this model.
495:
1203:
1738:
556:
266:
1562:
2165:
1158:
1695:
1675:
60:
for single queueing nodes, the random variable denoting bulk arrivals or service is denoted with a superscript, for example M/M/1 denotes an
2079:
222:
Berg, Menachem; van der Duyn
Schouten, Frank; Jansen, Jorg (1998). "Optimal Batch Provisioning to Customers Subject to a Delay-Limit".
1996:
675:
1680:
2006:
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2048:
1945:
964:
2235:
2225:
2071:
1763:
1748:
2135:
2099:
530:
41:
2403:
2140:
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1250:
1151:
203:
178:
2205:
2250:
2056:
2040:
1955:
1783:
1753:
1175:
881:
409:
Henderson, W.; Taylor, P. G. (1990). "Product form in networks of queues with batch arrivals and batch services".
2155:
2120:
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1520:
1437:
740:
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2094:
1723:
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1525:
1422:
366:
2408:
2185:
2021:
1920:
1905:
1444:
1317:
1233:
1144:
952:
668:
2180:
2060:
622:
Medhi, Jyotiprasad (1975). "Waiting Time
Distribution in a Poisson Queue with a General Bulk Service Rule".
2190:
1033:
922:
295:
224:
134:
2195:
1831:
1793:
1377:
1322:
1238:
995:
2125:
2130:
2115:
1758:
1728:
1295:
1193:
330:
Glazer, A.; Hassin, R. (1987). "Equilibrium
Arrivals in Queues with Bulk Service at Scheduled Times".
2210:
2011:
1925:
1910:
1841:
1417:
1300:
1198:
1000:
838:
805:
565:
45:
517:
2044:
1930:
1432:
1407:
1352:
1127:
1023:
810:
661:
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2150:
2026:
1808:
1733:
1547:
1412:
1268:
1223:
1111:
906:
93:
44:
under certain conditions. Under heavy traffic conditions a bulk queue is known to behave like a
2287:
2215:
1640:
1630:
1474:
1106:
896:
745:
512:
503:
92:
The optimal maximum size of batch, subject to operating cost constraints, can be modelled as a
2310:
2292:
2272:
2267:
1986:
1818:
1798:
1645:
1588:
1427:
1337:
937:
927:
800:
104:
Optimal service-provision procedures to minimize long run expected cost have been published.
57:
443:
132:
Chiamsiri, Singha; Leonard, Michael S. (1981). "A Diffusion
Approximation for Bulk Queues".
2385:
2340:
2330:
2016:
1991:
1960:
1940:
1778:
1700:
1685:
1552:
848:
767:
8:
2380:
2220:
2145:
1950:
1710:
1620:
1510:
1096:
1076:
1071:
843:
779:
2350:
2315:
2230:
2200:
2031:
1970:
1965:
1788:
1625:
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1228:
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1086:
1053:
947:
718:
639:
604:
569:
466:
391:
347:
312:
275:
241:
151:
21:
587:
Deb, Rajat K.; Serfozo, Richard F. (1973). "Optimal
Control of Batch Service Queues".
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143:
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2001:
1935:
1613:
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1540:
1285:
959:
932:
826:
730:
684:
85:
33:
17:
2170:
1402:
969:
444:"Multiple Channel Queues in Heavy Traffic. II: Sequences, Networks, and Batches"
2360:
2325:
2245:
1851:
1598:
1515:
1484:
1479:
1459:
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1392:
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1312:
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1028:
526:
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1357:
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1213:
1081:
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308:
147:
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1836:
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1657:
1652:
1464:
1397:
1372:
1208:
1038:
865:
73:
635:
343:
293:
Deb, Rajat K. (1978). "Optimal
Dispatching of a Finite Capacity Shuttle".
237:
2365:
1900:
1884:
1879:
1874:
1864:
1667:
1608:
1603:
1567:
1327:
1218:
1061:
1018:
985:
762:
757:
752:
735:
725:
713:
708:
703:
698:
61:
351:
264:
Bailey, Norman T. J. (1954). "On
Queueing Processes with Bulk Service".
2375:
1915:
1743:
1696:
Generalized autoregressive conditional heteroskedasticity (GARCH) model
1136:
643:
608:
573:
470:
439:
424:
395:
316:
279:
245:
155:
112:
The waiting time distribution of bulk
Poisson arrival is presented in.
1869:
860:
600:
64:
where the arrivals are in batches determined by the random variable
653:
496:"Product-forms in batch networks: Approximation and asymptotics"
221:
554:
Downton, F. (1955). "Waiting Time in Bulk
Service Queues".
68:
and the services in bulk determined by the random variable
1676:
Autoregressive conditional heteroskedasticity (ARCH) model
171:
Discrete Time
Analysis of Consolidated Transport Processes
490:
1204:
Independent and identically distributed random variables
1681:
Autoregressive integrated moving average (ARIMA) model
367:"A General Class of Bulk Queues with Poisson Input"
84:Customers arrive at random instants according to a
557:Journal of the Royal Statistical Society, Series B
267:Journal of the Royal Statistical Society, Series B
193:
2421:
1563:Stochastic chains with memory of variable length
194:Chaudhry, M. L.; Templeton, James G. C. (1983).
131:
408:
364:
1152:
669:
437:
329:
107:
40:Networks of such queues are known to have a
127:
125:
1691:Autoregressiveâmoving-average (ARMA) model
1159:
1145:
676:
662:
586:
516:
494:; Hayden, R. A.; Knottenbelt, W. (2013).
385:
173:. KIT Scientific Publishing. p. 14.
1166:
259:
257:
255:
122:
553:
187:
20:, a discipline within the mathematical
2422:
1997:Doob's martingale convergence theorems
263:
217:
215:
1749:Constant elasticity of variance (CEV)
1739:ChanâKarolyiâLongstaffâSanders (CKLS)
1140:
657:
621:
374:The Annals of Mathematical Statistics
252:
168:
51:
42:product form stationary distribution
683:
292:
212:
13:
2236:Skorokhod's representation theorem
2017:Law of large numbers (weak/strong)
14:
2441:
2206:Martingale representation theorem
2251:Stochastic differential equation
2141:Doob's optional stopping theorem
2136:DoobâMeyer decomposition theorem
1123:
1122:
2121:Convergence of random variables
2007:FisherâTippettâGnedenko theorem
615:
589:Advances in Applied Probability
580:
547:
484:
451:Advances in Applied Probability
431:
99:
79:
1719:Binomial options pricing model
402:
358:
323:
286:
162:
1:
2186:Kolmogorov continuity theorem
2022:Law of the iterated logarithm
953:Flow-equivalent server method
196:A first course in bulk queues
115:
2191:Kolmogorov extension theorem
1870:Generalized queueing network
1378:Interacting particle systems
1034:Adversarial queueing network
923:Continuous-time Markov chain
7:
1323:Continuous-time random walk
996:Heavy traffic approximation
741:PollaczekâKhinchine formula
10:
2446:
2331:Extreme value theory (EVT)
2131:Doob decomposition theorem
1423:OrnsteinâUhlenbeck process
1194:Chinese restaurant process
527:10.1016/j.peva.2013.08.011
2399:
2303:
2211:Optional stopping theorem
2108:
2070:
2012:Large deviation principle
1979:
1893:
1850:
1817:
1764:HeathâJarrowâMorton (HJM)
1709:
1701:Moving-average (MA) model
1686:Autoregressive (AR) model
1666:
1576:
1511:Hidden Markov model (HMM)
1493:
1445:SchrammâLoewner evolution
1249:
1174:
1120:
1052:
1011:
1001:Reflected Brownian motion
978:
915:
874:
819:
806:Markovian arrival process
793:
691:
566:Royal Statistical Society
463:10.1017/s0001867800037435
108:Waiting Time Distribution
46:reflected Brownian motion
2126:DolĂŠans-Dade exponential
1956:Progressively measurable
1754:CoxâIngersollâRoss (CIR)
1024:Layered queueing network
811:Rational arrival process
365:Marcel F. Neuts (1967).
72:. In a similar way, the
2346:Mathematical statistics
2336:Large deviations theory
2166:Infinitesimal generator
2027:Maximal ergodic theorem
1946:Piecewise-deterministic
1548:Random dynamical system
1413:Markov additive process
1112:Teletraffic engineering
907:Shortest remaining time
387:10.1214/aoms/1177698869
309:10.1287/mnsc.24.13.1362
148:10.1287/mnsc.27.10.1188
94:Markov decision process
76:is extended to GI/G/1.
2181:KarhunenâLoève theorem
2116:CameronâMartin formula
2080:BurkholderâDavisâGundy
1475:Variance gamma process
1107:Scheduling (computing)
746:Matrix analytic method
504:Performance Evaluation
332:Transportation Science
2430:Single queueing nodes
2311:Actuarial mathematics
2273:Uniform integrability
2268:Stratonovich integral
2196:LĂŠvyâProkhorov metric
2100:MarcinkiewiczâZygmund
1987:Central limit theorem
1589:Gaussian random field
1418:McKeanâVlasov process
1338:Dyson Brownian motion
1199:GaltonâWatson process
938:Product-form solution
839:GordonâNewell theorem
801:Poisson point process
692:Single queueing nodes
636:10.1287/mnsc.21.7.777
438:Iglehart, Donald L.;
344:10.1287/trsc.21.4.273
238:10.1287/mnsc.44.5.684
22:theory of probability
2386:Time series analysis
2341:Mathematical finance
2226:Reflection principle
1553:Regenerative process
1353:FlemingâViot process
1168:Stochastic processes
965:Decomposition method
2381:Stochastic analysis
2221:Quadratic variation
2216:Prokhorov's theorem
2151:FeynmanâKac formula
1621:Markov random field
1269:Birthâdeath process
1097:Pipeline (software)
1077:Flow control (data)
1072:Erlang distribution
1054:Information systems
844:Mean value analysis
169:Ăzden, Eda (2012).
2351:Probability theory
2231:Skorokhod integral
2201:Malliavin calculus
1784:Korn-Kreer-Lenssen
1668:Time series models
1631:PitmanâYor process
1102:Quality of service
1087:Network congestion
948:Quasireversibility
928:Kendall's notation
624:Management Science
425:10.1007/BF02411466
296:Management Science
225:Management Science
135:Management Science
58:Kendall's notation
52:Kendall's notation
2417:
2416:
2371:Signal processing
2090:Doob's upcrossing
2085:Doob's martingale
2049:EngelbertâSchmidt
1992:Donsker's theorem
1926:Feller-continuous
1794:RendlemanâBartter
1584:Dirichlet process
1501:Branching process
1470:Telegraph process
1363:Geometric process
1343:Empirical process
1333:Diffusion process
1189:Branching process
1184:Bernoulli process
1134:
1133:
1092:Network scheduler
991:Mean-field theory
902:Shortest job next
892:Processor sharing
849:Buzen's algorithm
832:Traffic equations
820:Queueing networks
794:Arrival processes
768:Kingman's formula
303:(13): 1362â1372.
142:(10): 1188â1199.
2437:
2391:Machine learning
2278:Usual hypotheses
2161:Girsanov theorem
2146:Dynkin's formula
1911:Continuous paths
1819:Actuarial models
1759:GarmanâKohlhagen
1729:BlackâKarasinski
1724:BlackâDermanâToy
1711:Financial models
1577:Fields and other
1506:Gaussian process
1455:Sigma-martingale
1259:Additive process
1161:
1154:
1147:
1138:
1137:
1126:
1125:
943:Balance equation
875:Service policies
773:Lindley equation
678:
671:
664:
655:
654:
648:
647:
619:
613:
612:
584:
578:
577:
551:
545:
544:
542:
541:
535:
529:. Archived from
520:
500:
488:
482:
481:
479:
477:
448:
435:
429:
428:
412:Queueing Systems
406:
400:
399:
389:
371:
362:
356:
355:
327:
321:
320:
290:
284:
283:
261:
250:
249:
219:
210:
209:
191:
185:
184:
166:
160:
159:
129:
2445:
2444:
2440:
2439:
2438:
2436:
2435:
2434:
2420:
2419:
2418:
2413:
2395:
2356:Queueing theory
2299:
2241:Skorokhod space
2104:
2095:KunitaâWatanabe
2066:
2032:Sanov's theorem
2002:Ergodic theorem
1975:
1971:Time-reversible
1889:
1852:Queueing models
1846:
1842:SparreâAnderson
1832:CramĂŠrâLundberg
1813:
1799:SABR volatility
1705:
1662:
1614:Boolean network
1572:
1558:Renewal process
1489:
1438:Non-homogeneous
1428:Poisson process
1318:Contact process
1281:Brownian motion
1251:Continuous time
1245:
1239:Maximal entropy
1170:
1165:
1135:
1130:
1116:
1048:
1007:
974:
960:Arrival theorem
911:
870:
827:Jackson network
815:
789:
780:Forkâjoin queue
719:Burke's theorem
687:
685:Queueing theory
682:
652:
651:
620:
616:
601:10.2307/1426040
585:
581:
552:
548:
539:
537:
533:
518:10.1.1.352.5769
498:
492:Harrison, P. G.
489:
485:
475:
473:
446:
436:
432:
407:
403:
369:
363:
359:
328:
324:
291:
287:
262:
253:
220:
213:
206:
192:
188:
181:
167:
163:
130:
123:
118:
110:
102:
86:Poisson process
82:
54:
32:) is a general
18:queueing theory
12:
11:
5:
2443:
2433:
2432:
2415:
2414:
2412:
2411:
2406:
2404:List of topics
2400:
2397:
2396:
2394:
2393:
2388:
2383:
2378:
2373:
2368:
2363:
2361:Renewal theory
2358:
2353:
2348:
2343:
2338:
2333:
2328:
2326:Ergodic theory
2323:
2318:
2316:Control theory
2313:
2307:
2305:
2301:
2300:
2298:
2297:
2296:
2295:
2290:
2280:
2275:
2270:
2265:
2260:
2259:
2258:
2248:
2246:Snell envelope
2243:
2238:
2233:
2228:
2223:
2218:
2213:
2208:
2203:
2198:
2193:
2188:
2183:
2178:
2173:
2168:
2163:
2158:
2153:
2148:
2143:
2138:
2133:
2128:
2123:
2118:
2112:
2110:
2106:
2105:
2103:
2102:
2097:
2092:
2087:
2082:
2076:
2074:
2068:
2067:
2065:
2064:
2045:BorelâCantelli
2034:
2029:
2024:
2019:
2014:
2009:
2004:
1999:
1994:
1989:
1983:
1981:
1980:Limit theorems
1977:
1976:
1974:
1973:
1968:
1963:
1958:
1953:
1948:
1943:
1938:
1933:
1928:
1923:
1918:
1913:
1908:
1903:
1897:
1895:
1891:
1890:
1888:
1887:
1882:
1877:
1872:
1867:
1862:
1856:
1854:
1848:
1847:
1845:
1844:
1839:
1834:
1829:
1823:
1821:
1815:
1814:
1812:
1811:
1806:
1801:
1796:
1791:
1786:
1781:
1776:
1771:
1766:
1761:
1756:
1751:
1746:
1741:
1736:
1731:
1726:
1721:
1715:
1713:
1707:
1706:
1704:
1703:
1698:
1693:
1688:
1683:
1678:
1672:
1670:
1664:
1663:
1661:
1660:
1655:
1650:
1649:
1648:
1643:
1633:
1628:
1623:
1618:
1617:
1616:
1611:
1601:
1599:Hopfield model
1596:
1591:
1586:
1580:
1578:
1574:
1573:
1571:
1570:
1565:
1560:
1555:
1550:
1545:
1544:
1543:
1538:
1533:
1528:
1518:
1516:Markov process
1513:
1508:
1503:
1497:
1495:
1491:
1490:
1488:
1487:
1485:Wiener sausage
1482:
1480:Wiener process
1477:
1472:
1467:
1462:
1460:Stable process
1457:
1452:
1450:Semimartingale
1447:
1442:
1441:
1440:
1435:
1425:
1420:
1415:
1410:
1405:
1400:
1395:
1393:Jump diffusion
1390:
1385:
1380:
1375:
1370:
1368:Hawkes process
1365:
1360:
1355:
1350:
1348:Feller process
1345:
1340:
1335:
1330:
1325:
1320:
1315:
1313:Cauchy process
1310:
1309:
1308:
1303:
1298:
1293:
1288:
1278:
1277:
1276:
1266:
1264:Bessel process
1261:
1255:
1253:
1247:
1246:
1244:
1243:
1242:
1241:
1236:
1231:
1226:
1216:
1211:
1206:
1201:
1196:
1191:
1186:
1180:
1178:
1172:
1171:
1164:
1163:
1156:
1149:
1141:
1132:
1131:
1121:
1118:
1117:
1115:
1114:
1109:
1104:
1099:
1094:
1089:
1084:
1079:
1074:
1069:
1064:
1058:
1056:
1050:
1049:
1047:
1046:
1041:
1036:
1031:
1029:Polling system
1026:
1021:
1015:
1013:
1009:
1008:
1006:
1005:
1004:
1003:
993:
988:
982:
980:
979:Limit theorems
976:
975:
973:
972:
967:
962:
957:
956:
955:
950:
945:
935:
930:
925:
919:
917:
913:
912:
910:
909:
904:
899:
894:
889:
884:
878:
876:
872:
871:
869:
868:
863:
858:
853:
852:
851:
846:
836:
835:
834:
823:
821:
817:
816:
814:
813:
808:
803:
797:
795:
791:
790:
788:
787:
782:
777:
776:
775:
770:
760:
755:
750:
749:
748:
743:
733:
728:
723:
722:
721:
711:
706:
701:
695:
693:
689:
688:
681:
680:
673:
666:
658:
650:
649:
630:(7): 777â782.
614:
595:(2): 340â361.
579:
546:
483:
457:(2): 355â369.
430:
401:
380:(3): 759â770.
357:
338:(4): 273â278.
322:
285:
251:
232:(5): 684â697.
211:
205:978-0471862604
204:
186:
180:978-3866448018
179:
161:
120:
119:
117:
114:
109:
106:
101:
98:
81:
78:
53:
50:
34:queueing model
9:
6:
4:
3:
2:
2442:
2431:
2428:
2427:
2425:
2410:
2407:
2405:
2402:
2401:
2398:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
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2263:Stopping time
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2078:
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2073:
2069:
2062:
2058:
2054:
2053:HewittâSavage
2050:
2046:
2042:
2038:
2037:Zeroâone laws
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1636:Point process
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1594:Gibbs measure
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1383:ItĂ´ diffusion
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1359:
1358:Gamma process
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1260:
1257:
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1248:
1240:
1237:
1235:
1232:
1230:
1229:Self-avoiding
1227:
1225:
1222:
1221:
1220:
1217:
1215:
1214:Moran process
1212:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1182:
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1179:
1177:
1176:Discrete time
1173:
1169:
1162:
1157:
1155:
1150:
1148:
1143:
1142:
1139:
1129:
1119:
1113:
1110:
1108:
1105:
1103:
1100:
1098:
1095:
1093:
1090:
1088:
1085:
1083:
1082:Message queue
1080:
1078:
1075:
1073:
1070:
1068:
1067:Erlang (unit)
1065:
1063:
1060:
1059:
1057:
1055:
1051:
1045:
1044:Retrial queue
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1016:
1014:
1010:
1002:
999:
998:
997:
994:
992:
989:
987:
984:
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977:
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963:
961:
958:
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951:
949:
946:
944:
941:
940:
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936:
934:
931:
929:
926:
924:
921:
920:
918:
914:
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905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
879:
877:
873:
867:
864:
862:
859:
857:
856:Kelly network
854:
850:
847:
845:
842:
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840:
837:
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830:
829:
828:
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824:
822:
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734:
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629:
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618:
610:
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602:
598:
594:
590:
583:
575:
571:
567:
563:
559:
558:
550:
536:on 2016-03-03
532:
528:
524:
519:
514:
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487:
472:
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460:
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105:
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77:
75:
71:
67:
63:
59:
49:
47:
43:
38:
35:
31:
27:
23:
19:
2321:Econometrics
2283:Wiener space
2171:ItĂ´ integral
2072:Inequalities
1961:Self-similar
1931:GaussâMarkov
1921:Exchangeable
1901:CĂ dlĂ g paths
1859:
1837:Risk process
1789:LIBOR market
1658:Random graph
1653:Random field
1465:Superprocess
1403:LĂŠvy process
1398:Jump process
1373:Hunt process
1209:Markov chain
1039:Loss network
970:BeneĹĄ method
933:Little's law
916:Key concepts
866:BCMP network
784:
627:
623:
617:
592:
588:
582:
561:
555:
549:
538:. Retrieved
531:the original
508:
502:
486:
474:. Retrieved
454:
450:
433:
416:
410:
404:
377:
373:
360:
335:
331:
325:
300:
294:
288:
274:(1): 80â87.
271:
265:
229:
223:
195:
189:
170:
164:
139:
133:
111:
103:
100:Bulk arrival
91:
83:
80:Bulk service
74:GI/G/1 queue
69:
65:
55:
39:
29:
25:
15:
2366:Ruin theory
2304:Disciplines
2176:ItĂ´'s lemma
1951:Predictable
1626:Percolation
1609:Potts model
1604:Ising model
1568:White noise
1526:Differences
1388:ItĂ´ process
1328:Cox process
1224:Loop-erased
1219:Random walk
1062:Data buffer
1019:Fluid queue
986:Fluid limit
897:Round-robin
763:G/G/1 queue
758:G/M/1 queue
753:M/G/k queue
736:M/G/1 queue
731:M/M/â queue
726:M/M/c queue
714:M/M/1 queue
709:M/D/c queue
704:M/D/1 queue
699:D/M/1 queue
568:: 256â261.
511:(10): 822.
440:Ward, Whitt
62:M/M/1 queue
30:batch queue
28:(sometimes
2376:Statistics
2156:Filtration
2057:Kolmogorov
2041:Blumenthal
1966:Stationary
1906:Continuous
1894:Properties
1779:HullâWhite
1521:Martingale
1408:Local time
1296:Fractional
1274:pure birth
1012:Extensions
785:Bulk queue
540:2015-09-04
116:References
26:bulk queue
2288:Classical
1301:Geometric
1291:Excursion
861:G-network
513:CiteSeerX
419:: 71â87.
198:. Wiley.
2424:Category
2409:Category
2293:Abstract
1827:BĂźhlmann
1433:Compound
1128:Category
442:(1970).
352:25768286
1916:Ergodic
1804:VaĹĄĂÄek
1646:Poisson
1306:Meander
644:2629773
609:1426040
574:2983959
471:1426324
396:2238992
317:2630642
280:2984011
246:2634473
156:2631086
2256:Tanaka
1941:Mixing
1936:Markov
1809:Wilkie
1774:HoâLee
1769:Heston
1541:Super-
1286:Bridge
1234:Biased
642:
607:
572:
515:
476:30 Nov
469:
394:
350:
315:
278:
244:
202:
177:
154:
2109:Tools
1885:M/M/c
1880:M/M/1
1875:M/G/1
1865:Fluid
1531:Local
640:JSTOR
605:JSTOR
570:JSTOR
564:(2).
534:(PDF)
499:(PDF)
467:JSTOR
447:(PDF)
392:JSTOR
370:(PDF)
348:JSTOR
313:JSTOR
276:JSTOR
242:JSTOR
152:JSTOR
24:, a
2061:LĂŠvy
1860:Bulk
1744:Chen
1536:Sub-
1494:Both
887:LIFO
882:FIFO
478:2012
200:ISBN
175:ISBN
1641:Cox
632:doi
597:doi
523:doi
459:doi
421:doi
382:doi
340:doi
305:doi
234:doi
144:doi
56:In
16:In
2426::
2059:,
2055:,
2051:,
2047:,
2043:,
638:.
628:21
626:.
603:.
591:.
562:17
560:.
521:.
509:70
507:.
501:.
465:.
453:.
449:.
415:.
390:.
378:38
376:.
372:.
346:.
336:21
334:.
311:.
301:24
299:.
272:61
270:.
254:^
240:.
230:44
228:.
214:^
150:.
140:27
138:.
124:^
96:.
48:.
2063:)
2039:(
1160:e
1153:t
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677:e
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646:.
634::
611:.
599::
593:5
576:.
543:.
525::
480:.
461::
455:2
427:.
423::
417:6
398:.
384::
354:.
342::
319:.
307::
282:.
248:.
236::
208:.
183:.
158:.
146::
70:Y
66:X
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.