Ergodicity bounds for the Markovian queue with time-varying transition intensities, batch arrivals and one queue skipping policy

被引：0

作者：

Zeifman, A., I ^{[1
]}

Razumchik, R., V ^{[2
]}

Satin, Y. A. ^{[3
]}

Kovalev, I. A. ^{[3
]}

机构：

[1] Vologda State Univ, Moscow Ctr Fundamental & Appl Math, Vologda Res Ctr RAS, Inst Informat Problems FRC CSC RAS, Vologda, Vologda Oblast, Russia

[2] Inst Informat Problems FRC CSC RAS, Moscow Ctr Fundamental & Appl Math, Moscow, Russia

[3] Vologda State Univ, Vologda, Vologda Oblast, Russia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 395卷

基金：

俄罗斯科学基金会;

关键词：

Time-varying queueing system; Queue skipping policy; Rate of convergence bounds; ORDERED ENTRY; PRODUCT-FORMS; CONVERGENCE; NETWORKS; SYSTEMS;

D O I：

10.1016/j.amc.2020.125846

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and one special queue skipping policy. Customers arrive in batches but are served one by one in any order. The size of the arriving batch becomes known upon its arrival and at any time instant the total number of customers in the system is also known. According to the adopted queue skipping policy if a batch, which size is greater than the current total number of customers in the system, arrives, all customers currently residing in the system are removed from it and the new batch is placed in the queue. Otherwise the new batch is lost and does not have effect on the system. The distribution of the total number of customers in the system is under consideration under assumption that the arrival intensity.(t) and/or the service intensity mu(t) are non-random functions of time. We provide the method for the computation of the upper bounds for the rate of convergence of system size to the limiting regime, whenever it exists, for any bounded lambda(t) and mu(t) (not necessarily periodic) and any distribution of the batch size. For periodic intensities lambda(t) and/or mu(t) and light-tailed distribution of the batch size it is shown how the obtained bounds can be used to numerically compute the limiting distribution of the queue size with the given error. Illustrating numerical examples are provided. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：11