为什么会这样？ Q-MWS能达到吞吐最佳（队列稳定）的本质原因： 四每个时隙都努力“压制”最长队列.从而长远来看保持队列稳定 换句话说，追求的目标是“队列平衡”. 为什么上例中Q-MWS并未达到这个目标？ 因为它完全没有“综合考虑”多个信道的安排。 四每个信道都在努力“压制”最长队列，信道之间并未配合. 四结果是：最长队列得到的服务超过了“必要的”服务；其他队列 得到的服务又太少. ◆反而不利于队列之间的平衡. 2020年秋季 11/62 无线互联网
为什么会这样? 2020年秋季 11 / 62 无线互联网 Q-MWS能达到吞吐最佳(队列稳定)的本质原因: 每个时隙都努力“压制”最长队列. 从而长远来看保持队列稳定. 换句话说, 追求的目标是“队列平衡”. 为什么上例中Q-MWS并未达到这个目标? 因为它完全没有“综合考虑”多个信道的安排. 每个信道都在努力“压制”最长队列, 信道之间并未配合. 结果是: 最长队列得到的服务超过了“必要的”服务; 其他队列 得到的服务又太少. 反而不利于队列之间的平衡
直觉性地改进：Q-SSG 解决方案很自然： 四逐个Server进行选择；依次进行. 四每个Serveri选择后都更新队列长度 Q-SSG:Queue-based-Server-Side-Greedy 0S1 100 Round 1 ●S, 10-1 S. 10-2 Round 2 103 ∀Q-MWS ×-D-MWS 104 e-Q-SSG S 0 20 40 60 80 100 Round 3 n(number of users or channels) 2; S. ①果然好了很多 2020年秋季 12/62 无线互联网
直觉性地改进:Q-SSG 2020年秋季 12 / 62 无线互联网 解决方案很自然: 逐个Server进行选择; 依次进行. 每个Server选择后都更新队列长度. Q-SSG: Queue-based-Server-Side-Greedy */53"$&-- 4$)&%6-*/( Q1 Q2 S2 S3 S1 Q3 Round 1 Q1 Q2 S2 S3 S1 Q3 Round 2 Q1 Q2 S2 S3 S1 Q3 Round 3 Q1 Q2 S2 S3 S1 Q3 'JHVSF "O JMMVTUSBUJPO PG UIF PQFSBUJPOT PG 244( n(number of users or channels) Delay Violation Probability 0 20 40 60 80 100 100 10-1 10-2 10-3 10-4 Q-MWS D-MWS Q-SSG 'JHVSF " UZQJDBM QMPU PG UIF EFMBZWJPMBUJPO QSPCBCJMJUZ GPS B HJWFO UISFTIPME WT UIF TZTUFN TJ[F n JF UIF OVNCFS PG VTFSTDIBOOFMT GPS 2.84 %.84 BOE 244( BT UIF TZTUFN TJ[F n JODSFBTFT BOE JT PSEFST PG NBHOJUVEF TNBMMFS UIBO UIBU PG UIF .BY8FJHIU QPMJDJFT FTQFDJBMMZ XIFO n CFDPNFT MBSHFS #VJMEJOH VQPO UIF BCPWF JOUVJUJWF JEFB B TFSJFT PG TUVEJFT IBWF CFFO EFWPUFE UP EFTJHOJOH FċDJFOU TDIFEVMJOH QPMJDJFT XJUI HVBSBOUFFE TNBMM QFSVTFS RVFVFT GPS NVMUJDIBOOFM TZTUFNT /FYU XF QSPWJEF BO PWFSWJFX PG JNQPSUBOU BEWBODFNFOUT GSPN UIJT MJOF PG TUVEJFT UIBU GPDVT PO UIF RVFVFMFOHUICBTFE BQQSPBDIFT FH <o> *O <> B DMBTT PG *UFSBUFE -POHFTU 2VFVFT 'JSTU J-2' QPMJDJFT BSF EFWFMPQFE 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244( JO FBDI UJNFTMPU BO J-2' QPMJDZ BMMPDBUFT TFSWFST JO BO JUFSBUJWF NBOOFS BDSPTT NVMUJQMF SPVOET *O FBDI SPVOE BO J-2' QPMJDZ BUUFNQUT UP NBUDI BT NBOZ MPOHFTU RVFVFT BT QPTTJCMF XJUI UIF BWBJMBCMF TFSWFST BOE UIF RVFVF MFOHUIT XJMM OFFE UP CF VQEBUFE UP BDDPVOU GPS UIF TFSWJDF SFDFJWFE CZ UIF MPOHFTU RVFVFT UIBU BSF NBUDIFE JO UIBU SPVOE /PUF UIBU UIF SBUFGVODUJPO PQUJNBMJUZ IPMET POMZ GPS B TVCTFU PG J-2' QPMJDJFT UIBU TBUJTGZ UIF ESBJO BOE EPNJOBODF QSPQFSUJFT %FmOJUJPOT BOE PG <> "MTP JU SFRVJSFT UIF BSSJWBM QSPDFTT PG FWFSZ VTFS UP CF #FSOPVMMJ 0/0'' BOE JJE PWFS UJNF XIJDI JT NPSF SFTUSJDUJWF UIBO UIF BTTVNQUJPOT UIBU XJMM CF QSFTFOUFE JO 4FDUJPO */53"$&-- 4$)&%6-*/( Q1 Q2 S2 S3 S1 Q3 Round 1 Q1 Q2 S2 S3 S1 Q3 Round 2 Q1 Q2 S2 S3 S1 Q3 Round 3 Q1 Q2 S2 S3 S1 Q3 'JHVSF "O JMMVTUSBUJPO PG UIF PQFSBUJPOT PG 244( n(number of users or channels) Delay Violation Probability 0 20 40 60 80 100 100 10-1 10-2 10-3 10-4 Q-MWS D-MWS Q-SSG 'JHVSF " UZQJDBM QMPU PG UIF EFMBZWJPMBUJPO QSPCBCJMJUZ GPS B HJWFO UISFTIPME WT UIF TZTUFN TJ[F n JF UIF OVNCFS PG VTFSTDIBOOFMT GPS 2.84 %.84 BOE 244( BT UIF TZTUFN TJ[F n JODSFBTFT BOE JT PSEFST PG NBHOJUVEF TNBMMFS UIBO UIBU PG UIF .BY8FJHIU QPMJDJFT FTQFDJBMMZ XIFO n CFDPNFT MBSHFS #VJMEJOH VQPO UIF BCPWF JOUVJUJWF JEFB B TFSJFT PG TUVEJFT IBWF CFFO EFWPUFE UP EFTJHOJOH FċDJFOU TDIFEVMJOH QPMJDJFT XJUI HVBSBOUFFE TNBMM QFSVTFS RVFVFT GPS NVMUJDIBOOFM TZTUFNT /FYU XF QSPWJEF BO PWFSWJFX PG JNQPSUBOU BEWBODFNFOUT GSPN UIJT MJOF PG TUVEJFT UIBU GPDVT PO UIF RVFVFMFOHUICBTFE BQQSPBDIFT FH <o> *O <> B DMBTT PG *UFSBUFE -POHFTU 2VFVFT 'JSTU J-2' QPMJDJFT BSF EFWFMPQFE BOE B TVCTFU PG J-2' QPMJDJFT UIBU TBUJTGZ DFSUBJO QSPQFSUJFT IBWF CFFO TIPXO UP BDIJFWF UIF PQUJNBM RVFVF MFOHUICBTFE SBUFGVODUJPO GPS JJE #FSOPVMMJ 0/0'' BSSJWBM QSPDFTTFT 4JNJMBS UP 244( JO FBDI UJNFTMPU BO J-2' QPMJDZ BMMPDBUFT TFSWFST JO BO JUFSBUJWF NBOOFS BDSPTT NVMUJQMF SPVOET *O FBDI SPVOE BO J-2' QPMJDZ BUUFNQUT UP NBUDI BT NBOZ MPOHFTU RVFVFT BT QPTTJCMF 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PQUJNBMJUZ IPMET POMZ GPS B TVCTFU PG J-2' QPMJDJFT UIBU TBUJTGZ UIF ESBJO BOE EPNJOBODF QSPQFSUJFT %FmOJUJPOT BOE PG <> "MTP JU SFRVJSFT UIF BSSJWBM QSPDFTT PG FWFSZ VTFS UP CF #FSOPVMMJ 0/0'' BOE JJE PWFS UJNF XIJDI JT NPSF SFTUSJDUJWF UIBO UIF BTTVNQUJPOT UIBU XJMM CF QSFTFOUFE JO 4FDUJPO 果然好了很多
其他基于队长的方案 iLQF:Iterated Longest Queues First 四同样基于以上直觉，文献中提出了更为精巧的解决方案：LQ「 S.Bodas,S.Shakkottai,L.Ying,and R.Srikant.Scheduling in multi- channel wireless networks:Rate function optimality in the small-buffer regime.In ACM Proc.of the 11th International Joint Conference on Measurement and Modeling of Computer Systems (SIGMETRICS), pages121-132,2009. ◆与Q-SSG的不同之处：每一轮里匹配了更多的队列： 回该文献证明，iLQF是rate-function:最佳的. To()log P(Q()>) n-→on 其中Q(0)表示稳态下的最长队列的队长. 最大化Io(b)意味着随着n→o,队长超过门限b的概率 下降速率被最大化.[典型的大偏差理论的表述方式] g在rate-function的意义上，Q-SSG并非最佳的. 2020年秋季 13/62 无线互联网
其他基于队长的方案 2020年秋季 13 / 62 无线互联网 iLQF: Iterated Longest Queues First 同样基于以上直觉, 文献中提出了更为精巧的解决方案: iLQF S. Bodas, S. Shakkottai, L. Ying, and R. Srikant. Scheduling in multichannel wireless networks: Rate function optimality in the small-buffer regime. In ACM Proc. of the 11th International Joint Conference on Measurement and Modeling of Computer Systems (SIGMETRICS), pages 121–132, 2009. 与Q-SSG的不同之处: 每一轮里匹配了更多的队列. 该文献证明, iLQF是rate-function最佳的. �� � ≜ lim �→* − � � ��� ℙ � � > � 其中� � 表示稳态下的最长队列的队长. 最大化�� � 意味着随着� → ∞, 队长超过门限�的概率 下降速率被最大化. [典型的大偏差理论的表述方式] 在rate-function的意义上, Q-SSG并非最佳的
队长小不一定延迟小 试想： 四一个短队列连续多个时隙都没有（或很少）新的到达. 在基于队长的调度策略下很可能没有机会被调度： ◆从而导致较大的延迟 今本质原因： 四仅在“分组到达数目一直保持不变”的条件下，队长与延迟才严格对应 在更为一般的“突发”到达的现实场景中，队长控制得再好，也可能 出现较大延迟. 今所以： @此后我们不再考虑Queue-based方法，只研究Delay-based方法. ©文献中有同样的趋势：早期文献以队长为主，后面的都以延迟为主. 2020年秋季 14/62 无线互联网
队长小不一定延迟小 2020年秋季 14 / 62 无线互联网 试想: 一个短队列连续多个时隙都没有(或很少)新的到达. 在基于队长的调度策略下很可能没有机会被调度. 从而导致较大的延迟. 本质原因: 仅在“分组到达数目一直保持不变”的条件下, 队长与延迟才严格对应. 在更为一般的“突发”到达的现实场景中, 队长控制得再好, 也可能 出现较大延迟. 所以: 此后我们不再考虑Queue-based方法, 只研究Delay-based方法. 文献中有同样的趋势: 早期文献以队长为主, 后面的都以延迟为主
那就D-SSG D-SSG:Delay-based-Server-Side-Greedy 回逐个Server进行选择；依次进行. ⊙选择依据是HOL延迟；并且每次选择后都更新各队列的权重. 36 36 21 Q 100 Round 1 Q2 S2 10-1 2s S 36 Q 102 Round 2 103 -Q-MWS D-MWS e-Q-SSG 日-D-SSG 104 36 0 20 40 60 80 100 2 S n(number of users or channels) Round 3 2 S Q S; ①直觉又对了！ 2020年秋季 15/62 无线互联网
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