???????(Queuing Model)

1
????????

• ?1?
• ??
• ????
• ?????

2
???????(Queuing Model)

????(queue)
??????(serviced)
??(arrival)
???(server)
????(service time)
????(wait time)
????(response time)
3
???????(Queuing Model)

• ????(queue)???????????????(???)??????????????????
  ??????????????????????????????
• ??????????????????????????????????????????????
• ????0?????????????????????????(???)?????????????
  ??????????????????

4
?????(D.G. Kendall)???

• ??
• ???????? X/X/s ???
• ?1?????????2?????????
• M?????????????????(????)
• D?????(???????????)
• G?????
• Ek??k???????
• ?3??
• s????
• M/M/1???????????????
• M/D/1?????????????
• ?)???????????????????????????????????????????????
  ????????????????????????????????????

5
????

• ????(response time)?????????????????????????????
  ???????????????????????
• ????(service time)?????????????????????????????
  ??????????????
• ????(wait time)????????????????????????????????
  ?????????????????
• ????????????

6
????

• ???(service rate)???????????????????
  ???1/??????
• ???(arrival rate)?????????????
• ????(arrival interval)?????????????????????
  ??????1/???

??
??????
???
??
??????
???
7
????

• ???(utilization)???(???)???????
  ??????/???
• ???1 ????????????????????0 ???????? ?????

8
????(?????????)

• ?????????????(deterministic)???????????????????
• ?????????????????? ??????gt????????????????
  ????(???????)
• ??????????????? ??????????????????????????
  ????(?????????) ?????1 ???1

9
????(?????????)

• ?????????????(probabilistic)???
• ????????????????????????????(?????
  ?????1??)??????????(?????????????????????????????
  ?????????????????????)
• ???????????????????????????????????????
• ???????? M/M/1 ?????????????????????????????????
  ????????1 ???2

10
????(M/M/1)

• ?????????????(probabilistic)???
• ???????M/M/1 ???????????????????????????????????
  ??????????????????? TS/(1-?)T
  ????(??)S ????(??)? ?????????S?
  ???(??) ??????????µ ???(??) µ1/S
• ????W(??) WT-S?S/(1-?)

11
????(M/M/1)

• ???????????
• ??????????????????????????????????????????????????
  ???????????????????????????????????(?????????????
  ?????)
• ??????????????????????????????????????????????????
  ??????????????????
• ?????(????????)
• ?????????? ? ?????????
• ????????? ? ??????????

12
????(M/M/1)

??????(?????????)??????? ?1 ??????????????????
0 ???????? ????? ?1?????????????????
13
????(M/M/1)
14
????(M/M/1)
15
????(M/D/1)

• ????????(deterministic)??????????(probabilistic)?
  ??
• ???????M/D/1 ???????????????????????????????????
  ??????????????? TS(2-?)/(2(1-?))T
  ????(??)S ????(??)? ?????????S?
  ???(??) ??????????µ ???(??) µ1/S
• ????W(??) WT-S?S/(2(1-?))
  M/M/1??????????

16
????(M/M/1?M/D/1???)
17
????(M/M/1?M/D/1???)
18
???

• ??????(Mean Time Between Failure)????????????????
  ???????MTBF
• ????????????(Mean Time To Repair)????????????????
  ???MTTR
• ???????(Availability)????????????????Availabilit
  yMTBF/(MTBFMTTR)

19
???(??????????)

• ???????Availability

Av1
Av2
AvAv1Av2
20
???(??????????)

• ???????Availability

Av1
Av2
??????????????
(1?Av)(1?Av1)(1?Av2)
?????????????
Av1?(1?Av1)(1?Av2)
21
(No Transcript)