Asymptotics of Subexponential Max Plus Networks: the Stochastic Event Graph Case
Asymptotics of Subexponential Max Plus Networks: the Stochastic Event Graph Case
复制标题
次指数最大加网络的渐进：随机事件图案例
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
S. Foss
中科院分区：
文献类型：
--
作者：
F. Baccelli;M. Lelarge;S. Foss
我们计算开放随机事件图在不可约和可约情况下平稳响应时间的精确尾部渐近。这些网络允许在随机介质中表示为 (max, plus)-线性系统。我们研究更新输入和独立同分布的情况。具有次指数分布的服务时间。我们表明，平稳响应时间的尾部渐近与服务时间的积分尾部具有相同的阶数。乘法常数仅涉及到达过程的强度和(max, plus)-矩阵序列的(max, plus)-Lyapunov指数。
We calculate the exact tail asymptotics of stationary response times for open stochastic event graphs, in the irreducible and reducible cases. These networks admit a representation as (max, plus)-linear systems in a random medium. We study the case of renewal input and i.i.d. service times with subexponential distributions. We show that the stationary response times have tail asymptotics of the same order as the integrated tail of service times. The mutiplicative constants only involve the intensity of the arrival process and the (max, plus)-Lyapunov exponents of the sequence of (max, plus)-matrices.