Covariance Properties for the Departure Process of M/E_k/1/N Queues

The asymptotic variance rate of the output process of finite capacity birth-death queues

“…Fewer papers have considered the output process of loss systems (cf. [2,10,23]) and to the best of our knowledge none have analyzed the asymptotic variance rate of the outputs. µ the finite queue is hardly ever full and it behaves almost like an M/M/1 queue.…”

“…[1] and [11]). It is possible numerically to compute V D , and even Var(D(t)) for any t, using well established matrix analytic results (see formulas (10) and (11) and references [22] and [23]). Thus, discovery of BRAVO did not require any new machinery beyond formula (10).…”

“…It can be shown that the expectation and the variance functions of D are O(t) (cf. formulas (9,10) and accompanying discussion and references) and may thus be described by the flow rate, λ * and asymptotic variance rate, V D :…”

The effects of correlated arrivals at a server with credit‐based traffic policing

“…The cell loss probabilities presented in this section make use of the steady state and transient vectors derived from formulas (12) and (15). The probability of cell loss at the leaky bucket mechanism is the probability that a cell arrives when all N slots in the cell queue are "lled.…”

“…The vectors ?Q (m; W t X) in Equation (13) are the embedded vectors for the discrete process with transition probability matrix P. Matrix P is constructed of the same probability transitions as in the P matrix for the steady-state analysis*see Equation (12). Since deterministic tokens are assumed, transient state transitions which occur between token arrivals are in#uenced by the arrival and service processes only.…”