On a fractional queueing model with catastrophes

关于带有灾难的时变出生-死亡过程

On Time-Changed Birth-Death Processes with Catastrophes

本文研究了带有灾难的时变出生-死亡过程，推导了状态概率的分数微分方程，并探讨了灾难发生时间及驻留时间的分布特性。

On the gamma-reflected processes with fBm input

Define a $γ$-reflected process $W_γ(t)=Y_H(t)-γ\inf_{s\in[0,t]}Y_H(s)$, $t\ge0$ with input process $\{Y_H(t), t\ge 0\}$ which is a fractional Brownian motion with Hurst index $H\in (0,1)$ and a negative linear trend. In risk theory $R_γ(t)=u-W_γ(t), t\ge0$ is referred to as the risk process with tax of a loss-carry-forward type, whereas in queueing theory $W_1$ is referred to as the queue length process. In this paper, we investigate the ruin probability and the ruin time of the risk process $R_γ, γ\in [0,1]$ over a surplus dependent time interval $[0, T_u]$.

Conditional limit theorems for regulated fractional Brownian motion

We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process spends above level $b$ over the busy cycle straddling the origin, as $b\to\infty$. Our results can be interpreted as showing that long delays occur in large clumps of size of order $b^{2-1/H}$. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.

活跃时间分数多类队列

A restless time-fractional multiclass queue

本文研究了具有有限类别的单服务器优先队列，其中到达服从分数泊松过程，服务完成由独立分数泊松过程触发。通过时间变换表示，推导出多级薄层分解，并研究了队列的标度极限和空队现象。

Sample path properties of reflected Gaussian processes

We consider a stationary queueing process $Q_X$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function $f$, $\mathbb P (Q_{X}(t) > f(t)\, \text{ i.o.})$ equals 0 or 1 is provided. Furthermore, an Erdös-Révész type law of the iterated logarithm is proven for the last passage time $ξ(t) = \sup\{s:0\le s\le t, Q_{X}(s)\ge f(s)\}$. Both of these findings extend previously known results that were only available for the case when $X$ is a fractional Brownian motion.

分数布朗运动队列的逗留时间：瞬态渐近

Sojourns of fractional Brownian motion queues: transient asymptotics

研究分数布朗运动驱动的排队过程在高阈值之上的逗留时间渐近性，推导布朗运动情形的精确渐近和一般情形的锐渐近近似，并分析两种比率机制。

Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distribution

In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally distributed. In this paper, we establish heavy traffic limit theorems to provide suitable approximations for the system under first-in first-out (FIFO) and work conserving service discipline, which state that, when the lengths of both ON- and OFF-periods are lightly tailed, the sequences of the scaled queue length and workload processes c…