一类人与出租车构成的排队模型主算子的谱特征

Spectral Property of the Operator Corresponding to the Queueing Model Describing the System Consisting of Customers and Taxis

运用C0-半群理论研究一类人与出租车构成的排队模型主算子的谱特征.首先证明0是对应于该排队模型的主算子的几何重数为1的特征值,其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集,然后证明0是该主算子共轭算子的特征值.

We study the spectral property of the operator corresponding to the queueing model describing the system consisting of customers and taxis. First we prove that 0 is an eigenvalue of the operator with geometric multiplicity one, next we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator, last we prove that 0 is an eigenvalue of the adjoint operator of the operator.