On steady‐state simulation of some weak regenerative networks

Abstract

Abstract. We discuss the possibilities of the so-called weak regeneration in the steady-state analysis of multiserver queues and some Jackson-type and multiclass queueing networks when classical regenerative simulation is ineffective. A few constructions of weak regeneration for open Jackson-type and multiclass queueing networks are given in an explicit form. Conditions are found when efficiency of weak regeneration (expressed in the simulation time needed for confidence estimation with a given precision) stays very high while the efficiency of classical regeneration is rapidly decreasing. Numerical results are also considered which illustrate an advantage of the weak regeneration in simulation of some tandem queueing networks.

Nonexistence of a class of variate generation schemes

“…Of course, these results do not rule out the possibility of identifying nonrandomized regeneration times such as those generated by visits to an atom in a Markov chain. For nontrivial examples of such regeneration times in queueing systems, see [15,13,14,18].…”

“…We would like to thank Evsey Morozov and Irina Aminova for sharing working versions of their paper [14] with us. The work of the first author was supported by National Science Foundation Grant DMI-0085165.…”

Accelerated Consistent Estimation of a High Load Probability in M/G/1 and GI/G/1 Queues*

“…All cases considered in the paper satisfy this condition because the number of dependent cycles is upper bounded by the finite constant D := R 0 R 1 · · · R M , and thus at most D successive cycles are dependent. (For the one-dependent cycles the confidence interval includes an estimate of the covariance between two adjacent cycles and is given in [14]. )…”

“…Before presenting the simulation results, we mention that the workload process in a GI/G/1 system (with renewal input and the i.i.d service times) is still a Markov chain and satisfies Lindley's recursion (14). Of course in general the exact expression for a high load probability for such a system is unknown.…”

On The Effective Bandwidth Estimation In Communication Network

“…To use estimator (12), we need to construct regenerations {β n }. For a general acyclic network it can done as in [10]. Note, however, that it is a rather complicated construction.…”