Properties and performance bounds for closed free choice synchronized monoclass queueing networks
Properties and performance bounds for closed free choice synchronized monoclass queueing networks
复制标题
封闭自由选择同步单类排队网络的属性和性能界限
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
Manuel Silva
中科院分区：
文献类型：
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作者：
J. Campos;G. Chiola;Manuel Silva
结果表明，许多具有同步的单类排队网络(QN)可以自然地用称为自由选择网(FC)的一类Petri网(PN)建模，并得到了广泛的定性、行为和结构结果。其中一些网理论结果被用来刻画闭自由选择同步QN的遍历性、有界性和活性。吞吐量的上下限是基于服务时间的平均值来定义的，而不需要对概率分布进行任何假设(因此包括确定性和随机性两种情况)。结果表明，该模型的吞吐量上界与模型参数之间存在关于人口和服务时间的单调性。基于定义在底层FC网关联矩阵上的线性规划问题，提出了计算这些界的算法(理论上是多项式的，实际上是线性的)。利用排队论中的经典定律，给出了平均排队长度和响应时间的界。>；
It is shown that many monoclass queuing networks (QN) with synchronizations can naturally be modeled with a subclass of Petri nets (PN) called free-choice nets (FC), for which a wide gamut of qualitative behavioral and structural results have been derived. Some of these net theoretic results are used to characterize the ergodicity, boundedness, and liveness of closed free-choice synchronized QNs. Upper and lower throughput bounds are defined based on the mean value of the service times, without any assumption on the probability distributions (thus including both the deterministic and the stochastic cases). It is shown that monotonicity properties exist between the throughput bounds and the parameters of the model in terms of population and service times. Proposed are (theoretically polynomial and practically linear complexity) algorithms for the computation of these bounds, based on linear programming problems defined on the incidence matrix of the underlying FC net. Using classical laws from queuing theory, bounds are provided for mean queue lengths and response time. >