Exponential upper bounds via martingales for multiplexers with Markovian arrivals
Exponential upper bounds via martingales for multiplexers with Markovian arrivals
复制标题
通过马尔可夫到达的多路复用器的鞅的指数上限
DOI：
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发表时间：
1994
影响因子：
1
通讯作者：
N. Duffield
中科院分区：
文献类型：
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作者：
E. Buffet;N. Duffield
对于服务需求为状态空间{0，1}上的独立马尔可夫过程之和的时隙时间FCFS排队，我们得到了队长的闭式显式上界，且服务率为整数.界限的形式为[任意队列长度，其中c&t；1和y>；1是根据模型的参数显式给出的。该模型可以看作是ATM复用器中队列的突发级分量的近似值。我们得到了平均队列长度的繁忙业务量界限，并表明对于典型参数，这远远超过相同负载下独立到达的平均队列长度。对于单位服务率的情况，我们将我们的平均排队长度的结果与解析表达式进行了比较，并将我们关于全分布的结果与计算机模拟进行了比较。
We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {0, 1}, with integral service rate. The bound is of the form [queue length for any where c < 1 and y > 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations.