M/M/1算子的复谱

Complex Spectra of the M/M/1

研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明集合{γ∈C|R_(γ)≤-(λ+μ)}包含于该模型主算子的连续谱与剩余谱的并集.由此指出偏微分方程形式的M/M/1排队模型和常微分方程形式的M/M/1排队模型的本质区别.

This paper studies spectrum of the underlying operator,which corresponds to the M/M/1 queueing model described by partial differential equations,on the left half complex plane and proves that{γ∈C|R_(γ)≤-(λ+μ)}belongs to union of its continuous spectra and residual spectra,thus points out the essential difference between the M/M/1 queueing model described by partial differential equations and the M/M/1 queueing model described by ordinary differential equations.