Stability analysis of regenerative queueing systems

A State-Dependent Control for Green Computing

“…In other words, inf k P(V n k D) ε, for some finite constant D, some ε > 0 and a deterministic subsequence of the arrival instants {t n k }, t n k → ∞, k → ∞. Then, using condition (1), we can prove as in [13] that a non-waiting customer arrives in a finite interval [t n k , t n k + C] with a positive probability, and both the constant C and the probability do not depend on t n k and n k . In other words,…”

“…The process {W n } is called positive recurrent if Eθ < ∞. This condition is crucial for stability analysis [13]. More exactly, define the remaining regeneration time at instant t n as…”

Stability of multiwavelength optical buffers with delay‐oriented scheduling

“…Note that the negative drift assumption in our work has a natural form arising in stability analysis of general Markov chains and statedependent queues [29,30]. Finally, note that although the basic process considered in the paper is Markovian (and the Markovity is useful in intermediate steps of analysis), the present method also works successfully outside of a Markovian framework [25][26][27]. Further, note that the present approach is different from but compatible with the conventional approach to stability analysis of classical multiserver system using regeneration of Harris Markov chains (for more detail, see Chapter VII in [31].…”

“…In the following, we adhere a regenerative approach to stability . Therefore, we construct regeneration instants for the process H as follows.…”

“…In such a system, the waiting room is a continuum, A D R C , and the waiting time is simply identical to the horizon, which consistently leads to smaller waiting times. In the following, we adhere a regenerative approach to stability [26,27]. Therefore, we construct regeneration instants for the process H as follows.…”