基于休假串联排队的三值光学计算机请求数分析
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摘要
三值光学计算机(ternary optical computer, TOC)性能受到其研究者和潜在用户的关注。本文引入同步多重休假建立四阶段串联排队建立请求数数学模型对TOC性能进行分析。数值仿真结果表明均分成的小光学处理器数目对系统性能有重要影响。
Performance evaluation of ternary optical computer has attracted increasing attention of its providers and potential customers. This paper built the mathematics model of request number by introducing the simultaneous multi-vacations and the tandem queuing. The numerical results illustrated that the number of small optical processors has an important effect on the performance of TOC.
Performance evaluation of ternary optical computer has attracted increasing attention of its providers and potential customers. This paper built the mathematics model of request number by introducing the simultaneous multi-vacations and the tandem queuing. The numerical results illustrated that the number of small optical processors has an important effect on the performance of TOC.
引文
[1]JIN Y,HE H C,LüY T.Ternary optical computer principle[J].Science in China Series F:Information Sciences,2003,46(2):145-150.
[2]XU Q,WANG X C,XU C.Design and implementation of the modified signed digit multiplication routine on a ternary optical compute[J].Applied Optics,2017,56(16):4661-4669.
[3]欧阳山,彭俊杰,金翊,等.三值光学计算机双空间存储器的结构和理论[J].中国科学:信息科学,2016,46(6):743-762.
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[8]KHODEMANI-YAZDI M,TAVAKKOLI-MOGHAD-DAM R,BASHIRI M,et al.Solving a new bi-objective hierarchical hub location problem with an M/M/c queuing framework[J].Engineering Applications of Artificial Intelligence,2019,78:53-70.
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[14]迟学芬,赵莹莹.串联排队RED/ERED网络分析模型[J].通信学报,2011,32(9):174-181.
[15]FREY A,TAKAHASHI Y.An explicit solution for an M/GI/1/N queue with vacation time and exhaustive service discipline[J].Journal of the Operations Research Society of Japan,2017,41(3):430-441.
[16]AMMAR S I.Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations[J].Applied Mathematics and Computation,2015,260:97-105.
[17]张杰.带休假延迟和启动时间的M/M/1多重休假排队系统分析[J].阜阳师范学院学报(自然科学版),2015,32(3):21-24,34.
[18]张宏波.带有Bernoulli控制策略的M/M/1多重休假排队模型[J].运筹学学报,2013,17(3):93-100.
[19]TIAN N S,LI Q L.The M/M/c queue with PH synchronous vacations[J].System Science and Mathematical Sciences,2000,13(1):7-16.
[20]NEUTS M F.Matrix-geometric solutions on stochastic models-an algorithmic approach[M].Baltimore and London:The Johns Hopkins University Press,1981.
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[23]PENG J J,SHEN R,JIN Y,et al.Design and implementation of modified signed-digit adder[J].IEEETransactions on Computers,2014,63(5):1134-1143.
[2]XU Q,WANG X C,XU C.Design and implementation of the modified signed digit multiplication routine on a ternary optical compute[J].Applied Optics,2017,56(16):4661-4669.
[3]欧阳山,彭俊杰,金翊,等.三值光学计算机双空间存储器的结构和理论[J].中国科学:信息科学,2016,46(6):743-762.
[4]江家宝,陈迅雷,欧阳山.三值光学计算机MSD转换为标准二进制数的硬件实现[J].南京理工大学学报,2016,40(3):278-284.
[5]王宏健,金翊,欧阳山.一位可重构三值光学处理器的设计和实现[J].计算机学报,2014,37(7):1500-1507.
[6]WANG X C,ZHANG S L,ZHANG M,et al.Performance analysis of a ternary optical computer based on M/M/1 queueing system[C]//ICA3PP 2017,2017:331-344.
[7]王先超,张冕,王春生,等.基于M/M/1排队系统的三值光学计算机请求服务模型[J].阜阳师范学院学报(自然科学版),2016,33(1):1-5,10.
[8]KHODEMANI-YAZDI M,TAVAKKOLI-MOGHAD-DAM R,BASHIRI M,et al.Solving a new bi-objective hierarchical hub location problem with an M/M/c queuing framework[J].Engineering Applications of Artificial Intelligence,2019,78:53-70.
[9]GUILLEMIN F,SLIM F.Sojourn time in an M/M/1processor sharing queue with permanent customers[J].Stochastic Models,2018,34(1):115-137.
[10]DENG H,HUANG L S,YANG C K,et al.Optimizing virtual machine placement in distributed clouds with M/M/1 servers[J].Computer Communications,2017,102:107-119.
[11]HAVIV M.The performance of a single-server queue with preemptive random priorities[J].Performance Evaluation,2016,103:60-68.
[12]BALBO G,VIGLIOTTI M G.On the analysis of a M/M/1 queue with bulk services[J].Computer Journal,2015,58(1):57-74.
[13]徐光辉,袁学明.有限容量两级串联排队系统的平稳性态[J].系统科学与数学,1992,12(4):317-325.
[14]迟学芬,赵莹莹.串联排队RED/ERED网络分析模型[J].通信学报,2011,32(9):174-181.
[15]FREY A,TAKAHASHI Y.An explicit solution for an M/GI/1/N queue with vacation time and exhaustive service discipline[J].Journal of the Operations Research Society of Japan,2017,41(3):430-441.
[16]AMMAR S I.Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations[J].Applied Mathematics and Computation,2015,260:97-105.
[17]张杰.带休假延迟和启动时间的M/M/1多重休假排队系统分析[J].阜阳师范学院学报(自然科学版),2015,32(3):21-24,34.
[18]张宏波.带有Bernoulli控制策略的M/M/1多重休假排队模型[J].运筹学学报,2013,17(3):93-100.
[19]TIAN N S,LI Q L.The M/M/c queue with PH synchronous vacations[J].System Science and Mathematical Sciences,2000,13(1):7-16.
[20]NEUTS M F.Matrix-geometric solutions on stochastic models-an algorithmic approach[M].Baltimore and London:The Johns Hopkins University Press,1981.
[21]GROSS D,SHORTIE J F,THOMPSON J M,et al.Fundamentals of queueing theory(Fourth Edition)[M].New Jersey:John Wiley&Sons,Inc,2008.
[22]Burke P J.The output process of a stationary M/M/s queueing system[J].Annals of Mathematical Statistics,1968,39(4):1144-1152.
[23]PENG J J,SHEN R,JIN Y,et al.Design and implementation of modified signed-digit adder[J].IEEETransactions on Computers,2014,63(5):1134-1143.