Asymptotic Property Of The Time-Dependent Solution Of A Queuing System For Customers And Taxis

This thesis consists of two chapters. The first chapter is splited into two sections. In the first section, we introduce briefly the history of queueing theory and in the second section, we introduce supplementary variable technique and then put forward the problems we are concerned in this paper. The second chapter consists of two sections. In the first section, we present the mathematical model of the queueing system for customers and taxis and the main results obtained by predecessors. In the second section, we study asymptotic property of the time-dependent solution of the queueing model. Firstly, we study the spectral properties of the operator corresponding to the queueing model and obtain that 0 is an eigenvalue of the operator and its adjoint operator with geometric and algebraic multiplicity one, all points on the imaginary axis except for zero belong to the resolvent set of the operator. Thus we derive that the time-dependent solution of the queueing model converges strongly to its static solution as time tends to infinite.