On the Bounds for a Two-Dimensional Birth-Death Process with Catastrophes

被引：1

作者：

Sinitcina, Anna ^{[1
]}

Satin, Yacov ^{[1
]}

Zeifman, Alexander ^{[2
]}

Shilova, Galina ^{[1
]}

Sipin, Alexander ^{[1
]}

Kiseleva, Ksenia ^{[1
]}

Panfilova, Tatyana ^{[1
]}

Kryukova, Anastasia ^{[1
]}

Gudkova, Irina ^{[3
]}

Fokicheva, Elena ^{[1
]}

机构：

[1] Vologda State Univ, Fac Appl Math Comp Technol & Phys, Vologda 160000, Russia

[2] Vologda State Univ, Fac Appl Math Comp Technol & Phys, Inst Informat Problems,Fed Res Ctr Comp Sci & Con, Russian Acad Sci,Vologda Res Ctr,Russian Acad Sci, Vologda 160000, Russia

[3] RUDN Univ, Russian Acad Sci, Inst Informat Problems,Fed Res Ctr Comp Sci & Con, Appl Probabil & Informat Dept Peoples Friendship, Moscow 117198, Russia

来源：

MATHEMATICS | 2018年 / 6卷 / 05期

关键词：

continuous-time Markov chains; catastrophes; bounds; birth-death process; rate of convergence; JUMP-DIFFUSION APPROXIMATION; BMAP/SM/1 QUEUING SYSTEM; MARKOVIAN ARRIVAL INPUT; ADDITIONAL TRANSITIONS; INHOMOGENEOUS BIRTH; PERTURBATION BOUNDS; M/M/1; QUEUE; MASS EXODUS; IDLE TIME; DISASTERS;

D O I：

10.3390/math6050080

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The model of a two-dimensional birth-death process with possible catastrophes is studied. The upper bounds on the rate of convergence in some weighted norms and the corresponding perturbation bounds are obtained. In addition, we consider the detailed description of two examples with 1-periodic intensities and various types of death (service) rates. The bounds on the rate of convergence and the behavior of the corresponding mathematical expectations are obtained for each example.

引用

页数：17

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