On Regenerative Estimation of Extremal Index in Queueing Systems

Bounds and Maxima for the Workload in a Multiclass Orbit Queue

“…Before proving Theorem 2, we note that ( 27) is an extension of the result (26) in [34] to the finite-mixture case. Since the original result of [34] is required for the proof, we discuss it in brief hereafter.…”

“…. , M, transform (26), on D = C \ (−∞, 0] (complex plane with negative axis removed), is equivalent to…”

“…of W (2) seems to be not straightforward. Instead, we suggest to apply numerical LST inversion after using explicit expressions (26) for the LST of the steady-state workload W (2) of the form (23) given in Lemma 2.…”

“…We also mention some works in this field of the authors of this research [26][27][28][29][30]. The extreme behaviour of the stationary waiting time in classical GI/G/1 systems has been studied in the works [26,27]. Moreover, it has been proved in [30] that, if service times are stochastically ordered in two systems, then the extremal indexes of stationary waiting times are ordered in the opposite way.…”

“…The topic of extreme values of the performance indexes in the queuing setting is studied in [19][20][21][22][23][24][25], to mention a few. We also mention some works in this field of the authors of this research [26][27][28][29][30]. The extreme behaviour of the stationary waiting time in classical GI/G/1 systems has been studied in the works [26,27].…”