On Regenerative Envelopes for Cluster Model Simulation

Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution

“…The approach to sensitivity analysis that is presented in this paper can be applied to more sophisticated, and more practically oriented systems, such as the simultaneous service multiserver system [40], which would result, though, in an increased dimension of the system state. However, we note that the steady-state exact sampling by regenerative simulation has several serious drawbacks.…”

“…First, the average working time of the algorithm may be infinite [36], e.g., in a system with large number of servers (which indeed depends on the regenerative cycle length). This problem can be solved either by the coupling-from-the-past technique [35] (which, although, is rather technically tricky), or by non traditional regenerative techniques, such as the artificial regeneration [41] or regenerative envelopes [40]. Finally, the study may be extended to larger classes of service time distributions.…”

On Comparison of Multiserver Systems with Multicomponent Mixture Distributions

“…The proof follows directly from relation (4) of Theorem 1 because inequalities ( 13) imply the required failure rate ordering of the components. 13) are satisfied and it is seen that the distributions are ordered in failure rate as in accordance with inequalities (14). Now we consider three two-component mixtures which are particular cases of (12).…”

“…To construct confidence intervals for the performance measures in the new systems, we use the method of regenerative simulation [4]. On the other hand, the monotonicity of the queueing processes we are discussing in the paper is a key element of the method of regenerative envelops developed in recent papers [11,14]. In this approach, the monotonicity properties are used to derive the lower and upper bounds of the performance measures of a basic, perhaps non-regenerative, system, using minorant and majorant systems with classic regeneration.…”

“…Another important point is that while the basic system may not be regenerative, the simpler systems have this property. An approach that exploits this property is called the method of regenerative envelopes, and it allows one to extend the area of the applicability of the regenerative simulation in the estimation of the QoS of complex systems [11,14].…”