Queues with workload-dependent arrival and service rates
Queues with workload-dependent arrival and service rates
复制标题
DOI：
10.1023/b:ques.0000027998.95375.ee
复制
发表时间：
2004-03-01
期刊：
影响因子：
1.2
通讯作者：
Kella, O
中科院分区：
文献类型：
--
作者：
Bekker, R;Borst, SC;Kella, O
我们考虑两种类型的队列与工作负载相关的到达率和服务速度。我们的研究是出于对服务器的到达率和/或速度取决于当前工作量（如生产系统和互联网）的假设。首先，在M/G/1的情况下，我们比较了稳态分布的工作量（无论是在任意时期和在到达时刻）在两个模型中，在到达率和服务速度的比率是相等的。应用水平交叉参数，我们表明，稳态分布成比例。其次，我们考虑了一个G/G/1型排队系统，该系统的到达间隔时间和服务速度都与负载相关。利用随机平均值方法，推广了普通G/G/1排队系统中各时刻工作负荷的几个著名关系。
We consider two types of queues with workload-dependent arrival rate and service speed. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet. First, in the M/G/1 case, we compare the steady-state distribution of the workload ( both at arbitrary epochs and at arrival instants) in two models, in which the ratio of arrival rate and service speed is equal. Applying level crossing arguments, we show that the steady-state distributions are proportional. Second, we consider a G/G/1-type queue with workload-dependent interarrival times and service speed. Using a stochastic mean-value approach, several well-known relations for the workload at various epochs in the ordinary G/G/1 queue are generalized.