西安电子科技大学：《通信网络基础》课程教学资源（讲义）第三章 网络的时延分析（时延模型）3.2 Basic Queue Theory

Xidian Univ. M/M/1排队系统 P{内阶到达且个离开}=eδe网 =u6+o(6) i>1 P{I内有价到达且1个离开 }=e(1-e-m) =u6+o(6)i=1 .P-1=u0+o(δ)i≥1 Broadband Wireless Communications Laboratory,Xidian University

Xidian Univ. Broadband Wireless Communications Laboratory, Xidian University M/M/1排队系统 { } ( ) 0 1 1 P Ik e e i λδ µδ µδ µδ ο δ − − = =+ > 内个到达且个离开 { } ( ) ( ) 0 1 1 P Ik e e i λδ µδ µδ ο δ − − = − =+ = 内有个到达且1个离开 , 1 () 1 P oi i i µδ δ ∴ =+ ≥ −

Xidian Univ. M/M/1排队系统 P{I内个到达且个离开}=（δ）ee6 =16+o(8) i>0 P{I内个到达且个离开}=(8)e =16+o(6) i=0 ∴.P1=δ+o(δ) i≥0 P,=o(δ)i与i≠i,i+1,i-1 Broadband Wireless Communications Laboratory.Xidian University

Xidian Univ. Broadband Wireless Communications Laboratory, Xidian University M/M/1排队系统 { } ( ) ( ) 1 0 0 P Ik e i λδ λδ λδ ο δ − = =+ = 内个到达且个离开 { } ( ) ( ) 1 0 0 P Ik e e i λδ µδ λδ λδ ο δ − − = =+ > 内个到达且个离开 , 1 ( ) 0 P i i i λδ ο δ ∴ =+ ≥ + , ( ) , 1, 1 P o i i ii i i j = ≠+− δ 与

Xidian Univ. M/M/1排队系统 。状态转移概率小结 P,0=1-元6+o(6) P,=1-δ-u6+o(δ) i≥1 P.+1=6+o(δ) i≥0 P-1=δ+o(δ) i≥1 Py=o(δ)i与i≠i,i+1,i-1 P.+1+P.-1+Pm=1+o(δ) Broadband Wireless Communications Laboratory,Xidian University

Xidian Univ. Broadband Wireless Communications Laboratory, Xidian University M/M/1排队系统  状态转移概率小结 , ( ) , 1, 1 P o i i ii i i j = ≠+− δ 与 P i i i, 1+ =+ ≥ λδ ο δ( ) 0 , 1 () 1 P oi i i µδ δ − =+ ≥ 0,0 P o =− + 1 () λδ δ , 1 () 1 P oi i i =− − + ≥ λδ µδ δ + + = +ο(δ ) Pi,i+1 Pi,i−1 Pii 1

Xidian Univ. 系统的状态转移图 1-λ8 1-λ6-μ6 1-λδ-u61-λ8-61-λ6-46 8…8 n+1 ·设系统状态的稳态概率为 pn=lim P N&=n)=lim P(N()=n) roadband Wireless communications caboratory.xidian university

Xidian Univ. Broadband Wireless Communications Laboratory, Xidian University 系统的状态转移图  设系统状态的稳态概率为 p P{N n} P{N(t) n} k k k n = = = = →∞ →∞ lim lim

Xidian Univ. M/M/1排队系统 1-λ6 1-λ6-u6 1-λδ-u61-λ6-u61-λ6-u6 888:…848 Pk-1+Pk+1-(元+川)Pk=0 -p0+p1=0 入P-1-P=九P&-HPk+ 2p-up1=0 Broadband Wireless Communications Laboratory,Xidian University

Xidian Univ. Broadband Wireless Communications Laboratory, Xidian University M/M/1排队系统    − + = − + + − + = 0 ( ) 0 0 1 1 1 p p p p p k k k λ µ λ µ λ µ 1 1 0 1 0 k kkk p ppp p p λ µλµ λ µ − + −=− − =