摘要 : This paper presents the large-buffer asymptotics for a multiplexer which serves N types of heterogeneous sessions which have long-tailed session lengths. Specifically, the model considered is that sessions of type i is an element ... 展开 This paper presents the large-buffer asymptotics for a multiplexer which serves N types of heterogeneous sessions which have long-tailed session lengths. Specifically, the model considered is that sessions of type i is an element of {1, ..., N} arrive as a Poisson process with rate lambda (i) Each type of session (independently) remains active for a random duration, say tau (i), where P(tau (i) > x) similar to alpha (i)x(-(1+betai)) for positive numbers alpha (i) and beta (i). While active, a session transmits at a rate ri. Under the assumption that the average load rho = Sigma (N)(i=l) r(i)lambda E-i[tau (i)] < C, where C denotes the server capacity, we show that both the tail distribution of the stationary buffer content and the loss asymptotics in finite buffers of size z behave approximately as z(-kJ0), where k(J0) depends not only on the <beta>(i) but also on the transmission rates r(i): it is the ratio of beta (i) to r(i) which determines K-J0 When specialized to the homogeneous case, i.e., when r(i) = r and beta (i) = beta for all i, the result coincides with results reported in the literature which have been shown under more restrictive hypotheses. Finally, it is a simple observation that light-tailed sessions only have the effect of reducing the available capacity for long-tailed sessions, but do not contribute otherwise to the definition of K-J0. [References: 21] 收起