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Nonexistence of a Class of Variate Generation Schemes
, 2001
"... Motivated by a problem arising in the regenerative analysis of discreteevent system simulation, we ask whether a certain class of random variate generation schemes exists or not. Under very reasonable conditions, we prove that such variate generation schemes do not exist. The implications of this r ..."
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Motivated by a problem arising in the regenerative analysis of discreteevent system simulation, we ask whether a certain class of random variate generation schemes exists or not. Under very reasonable conditions, we prove that such variate generation schemes do not exist. The implications of this result for regenerative steadystate simulation of discreteevent systems are discussed.
REGENERATIVE SIMULATION FOR MULTICLASS OPEN QUEUEING NETWORKS
"... Conceptually, under restrictions, multiclass open queueing networks are positive Harris recurrent Markov processes, making them amenable to regenerative simulation for estimating the steadystate performance measures. However, regenerations in such networks are difficult to identify when the interar ..."
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Conceptually, under restrictions, multiclass open queueing networks are positive Harris recurrent Markov processes, making them amenable to regenerative simulation for estimating the steadystate performance measures. However, regenerations in such networks are difficult to identify when the interarrival times are generally distributed. We assume that the interarrival times have exponential or heavier tails and show that such distributions can be decomposed into mixture of sums of independent random variables such that at least one of the components is exponentially distributed. This allows an implementable regenerative simulation for these networks. We show that the regenerative mean and standard deviation estimators are consistent and satisfy a joint central limit theorem. We also show that amongst all such interarrival decompositions, the one with largest mean exponential component minimizes the asymptotic variance of the standard deviation estimator. We also propose a regenerative simulation method that is applicable even when the interarrival times have superexponential tails. 1
Petrozavodsk State University,
, 2002
"... We discuss new possibilities which the weakly regenerative approach (when a dependence between two adjacent regeneration cycles is allowed) opens in modeling and simulation of queueing network processes. First we extend the class of regenerative inputs constructing weak regeneration for a superposit ..."
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We discuss new possibilities which the weakly regenerative approach (when a dependence between two adjacent regeneration cycles is allowed) opens in modeling and simulation of queueing network processes. First we extend the class of regenerative inputs constructing weak regeneration for a superposition of n independent, stationary renewal processes in which case generally, classical regeneration does not exist. We assume that process i is generated by the i.i.d. interrenewal times {ξ (i) n}n with d.f. Fi and expectation ai ∈ (0, ∞), i = 1,..., n. Let ξi(t), ( ˜ ξi(t)) be rightcontinuous unfinished (attained) renewal time at instant t in the renewal process i. By the stationarity, P(ξi(t) ≤ x) = P ( ˜ ξi(t) ≤ x) = 1 ai � x 0 (1 − Fi(u))du, for all i, t ≥ 0, x ≥ 0. Fix arbitrary a> 0 such that mini(1 − Fi(a))> 0, and introduce an increasing sequence of the instants
Regenerative Simulation for Queueing Networks with Exponential or Heavier Tail Arrival Distributions
, 2014
"... Multiclass open queueing networks find wide applications in communication, computer and fabrication networks. Often one is interested in steadystate performance measures associated with these networks. Conceptually, under mild conditions, a regenerative structure exists in multiclass networks, mak ..."
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Multiclass open queueing networks find wide applications in communication, computer and fabrication networks. Often one is interested in steadystate performance measures associated with these networks. Conceptually, under mild conditions, a regenerative structure exists in multiclass networks, making them amenable to regenerative simulation for estimating the steadystate performance measures. However, typically, identification of a regenerative structure in these networks is difficult. A well known exception is when all the interarrival times are exponentially distributed, where the instants corresponding to customer arrivals to an empty network constitute a regenerative structure. In this paper, we consider networks where the interarrival times are generally distributed but have exponential or heavier tails. We show that these distributions can be decomposed into a mixture of sums of independent random variables such that at least one of the components is exponentially distributed. This allows an easily implementable embedded regenerative structure in the Markov process. We show that under mild conditions on the network primitives, the regenerative mean and standard deviation estimators are consistent and satisfy a joint central limit theorem useful for constructing asymptotically valid confidence intervals. We also show that amongst all such interarrival time decompositions, the one with the largest mean exponential component minimizes the asymptotic variance of the standard deviation estimator. 1