对M/M/1非抢占优先权排队平稳指标的分析
|
摘要
讨论M/M/1非抢占优先权排队模型.该模型可以用一个具有可数位相的拟生灭(QBD)过程来描述.对该过程采用生成函数法得到平稳状态时低优先权顾客数分布的概率母函数,以及其逗留时间分布的LaplaceStieltjes变换.所得结论同时也说明了这两个分布都不是PH分布.
This paper considers an M/M/1queue that handles arrivals form 2classes of customers on a non-preemptive priority basis.The queue model can be described in a quasi-birth-and-death(QBD)process with infinitely many phases.For the QBD process,based on the generating function method,we give the PGF for thestationary queue length distribution and LST for sojourn time distribution of lower-priority customers.The results show that the distribution for queue length and sojourn time are not PH distribution.
This paper considers an M/M/1queue that handles arrivals form 2classes of customers on a non-preemptive priority basis.The queue model can be described in a quasi-birth-and-death(QBD)process with infinitely many phases.For the QBD process,based on the generating function method,we give the PGF for thestationary queue length distribution and LST for sojourn time distribution of lower-priority customers.The results show that the distribution for queue length and sojourn time are not PH distribution.
引文
[1]Cobham A.Priority Assignment in Waiting Line Problems[J].Operations Research,1954,2(1),70-76.
[2]Miller D R.Computation of steady-stateprobabilities for M/M/1priority queues[J].OperationsResearch,1981,29(5):945-958.
[3]Gail H R,Hantler S L,Taylor B A.Analysis of a non-preemptive priority multiserver queue[J].Advances in Applied Probability,1988,20(4):852-879.
[4]Kao E P C,Narayanan K S.Computing steady-state probabilities of a non-preemptive priority multiserve queue[J].ORSA Journal on Computing,1990,2(2):211-218.
[5]Isotupa K P S,Stanford D A.An infinite-phase quasi-birth-and-death model for the non-preemptive priority M/PH/1queue[J].Stochastic Models,2002,18(3):387-424.
[6]Alfa A S,Queueing theory for telecommunications,discrete time modeling of a single node system[M].New York:Springer,2010.
[7]Alfa A S,Liu B,He Q M.Discrete-time analysis of MAP/PH/1multiclass general preemptive priority queue[J].Naval Research Logistics,2003,50(6):662-682.
[8]Zhao J A,Li B,Cao X R,et al.A matrix-analytic solution for the DBMAP/PH/1priority queue[J].Queueing Systems,2006,53(1):127-145.
[9]Kim K H.(N,n)preemptive priority queues[J].Performance Evaluation,2011,68(7):575-585.
[10]Kim K H.T-preemptive priority queue and its application to the analysis of an opportunistic spectrum access in cognitive radio networks[J].Computers and Operations Research,2012,39(7):1394-1401.
[11]Keilson J,Servi L D.A distributional form of Little's law[J].Operations Research Letters,1988,7(5):223-227.
[12]Cinneide C A.Characterization of phase-type distributions[J].Stochastic Models,1990,6(1):1-57.
[2]Miller D R.Computation of steady-stateprobabilities for M/M/1priority queues[J].OperationsResearch,1981,29(5):945-958.
[3]Gail H R,Hantler S L,Taylor B A.Analysis of a non-preemptive priority multiserver queue[J].Advances in Applied Probability,1988,20(4):852-879.
[4]Kao E P C,Narayanan K S.Computing steady-state probabilities of a non-preemptive priority multiserve queue[J].ORSA Journal on Computing,1990,2(2):211-218.
[5]Isotupa K P S,Stanford D A.An infinite-phase quasi-birth-and-death model for the non-preemptive priority M/PH/1queue[J].Stochastic Models,2002,18(3):387-424.
[6]Alfa A S,Queueing theory for telecommunications,discrete time modeling of a single node system[M].New York:Springer,2010.
[7]Alfa A S,Liu B,He Q M.Discrete-time analysis of MAP/PH/1multiclass general preemptive priority queue[J].Naval Research Logistics,2003,50(6):662-682.
[8]Zhao J A,Li B,Cao X R,et al.A matrix-analytic solution for the DBMAP/PH/1priority queue[J].Queueing Systems,2006,53(1):127-145.
[9]Kim K H.(N,n)preemptive priority queues[J].Performance Evaluation,2011,68(7):575-585.
[10]Kim K H.T-preemptive priority queue and its application to the analysis of an opportunistic spectrum access in cognitive radio networks[J].Computers and Operations Research,2012,39(7):1394-1401.
[11]Keilson J,Servi L D.A distributional form of Little's law[J].Operations Research Letters,1988,7(5):223-227.
[12]Cinneide C A.Characterization of phase-type distributions[J].Stochastic Models,1990,6(1):1-57.