The Research Of Single Vacation M/M/c/K Queue System With Impatient Waiting Of Partial Servers

Tian, Zhang have analyzed several models of vacation of partial servers, proved the property of conditional stochastic decomposition in the multi-service synchronized vacation queue system, and listed the stable performance of the queue length and waiting time. However, the strategy of partial servers' vacation has not been paid much attention. Tian,Zhang & Xu,Zhang have made further development on this aspect.On the basis of the above researches, this thesis focused on the single vacation M/M/c/K queue system with impatient waiting of partial servers. First it gives the model of the single vacation M/M/c/K queue system with impatient waiting of partial servers, and has drawn system's condition shift chart, then it has used plans of the birth-death process and the matrix geometry solution method to solve the matrix equation R~2B + RA + C = 0, and has obtained the system rate, thus it can prove the stability of the system. From the stable state distribution, we can obtain the statistical equilibrium condition of the system, and also the distribution of steady state queue length and the customers' waiting time. Finally, with the determined model parameter of the special value from this thesis, the solution of homogeneous system of linear equationsπB[R] = 0 has achieved the same conclusion in Reference [13], and thus has confirmed the accuracy of the thesis conclusion.