Explicit Convergence Rates of the Embedded M/G/1 Queue

This paper investigates the explicit convergence rates to the stationary distribution π of the embedded M/G/1 queue; specifically, for suitable rate functions r(n) which may be polynomial with r(n) = n ^l , l > 0 or geometric with r(n) = α ⁿ , α > 1 and "moments" f = 1, we find the conditions under which for all i ∈ E. For the polynomial case, the explicit bounds on M(i) are given in terms of both "drift functions" and behavior of the first hitting time on the state 0; and for the geometric case, the largest geometric convergence rate α* is obtained. Supported by National Natural Science Foundation of China (No. 10171009)