research-article

A heterogeneous two-server network system with balking and a Bernoulli vacation schedule

Authors:

Wuyi YueAuthors Info & Claims

QTNA '09: Proceedings of the 4th International Conference on Queueing Theory and Network Applications

Article No.: 20, Pages 1 - 8

https://doi.org/10.1145/1626553.1626573

Published: 29 July 2009 Publication History

Abstract

In this paper, we study a two-server Markovian network system with balking and a Bernoulli schedule under a single vacation policy where servers have different service rates. After every service, only one server may take a vacation or continue to stay in the system. The vacation time follows an exponential distribution. An arriving customer finding both servers free will choose the faster server. If the customer finds both servers are not free, then this customer may join the system or balk. For this system, we obtain the steady state condition, the stationary distribution of the number of customers in the system and the mean system size by using a matrix geometric method. Some special cases are deduced, which match with earlier exiting results. Extensive numerical illustrations are provided. Motivation for this system model also comes from some computer communication networks with different types of traffic such as real-time traffic and non-real-time traffic, where messages can be processed by two channels (servers) with different transmission rates. The behavior of abandoning messages can be equated with the balking of customers in this system model.

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Cited By

S SKrishnamoorthy AKozyrev D(2023)A Two-Server Queue with Interdependence between Arrival and Service ProcessesMathematics10.3390/math1122469211:22(4692)Online publication date: 18-Nov-2023
https://doi.org/10.3390/math11224692
Kumar RSharma SBura G(2018)Transient and Steady-State Behavior of a Two-Heterogeneous Servers’ Queuing System with Balking and Retention of Reneging CustomersPerformance Prediction and Analytics of Fuzzy, Reliability and Queuing Models10.1007/978-981-13-0857-4_19(251-264)Online publication date: 27-Aug-2018
https://doi.org/10.1007/978-981-13-0857-4_19
Kumar RSharma S(2017)Transient Solution of a Two-Heterogeneous Servers’ Queuing System with Retention of Reneging CustomersBulletin of the Malaysian Mathematical Sciences Society10.1007/s40840-017-0482-z42:1(223-240)Online publication date: 28-Feb-2017
https://doi.org/10.1007/s40840-017-0482-z
Show More Cited By

A heterogeneous two-server network system with balking and a Bernoulli vacation schedule
1. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms

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cover image ACM Conferences

QTNA '09: Proceedings of the 4th International Conference on Queueing Theory and Network Applications

July 2009

143 pages

ISBN:9781605585628

DOI:10.1145/1626553

General Chair:
Winston Seah
Singapore

Copyright © 2009 ACM.

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Published: 29 July 2009

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QTNA '09: International Conference on Queueing Theory and Network Applications

July 29 - 31, 2009

Fusionopolis, Singapore

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Cited By

S SKrishnamoorthy AKozyrev D(2023)A Two-Server Queue with Interdependence between Arrival and Service ProcessesMathematics10.3390/math1122469211:22(4692)Online publication date: 18-Nov-2023
https://doi.org/10.3390/math11224692
Kumar RSharma SBura G(2018)Transient and Steady-State Behavior of a Two-Heterogeneous Servers’ Queuing System with Balking and Retention of Reneging CustomersPerformance Prediction and Analytics of Fuzzy, Reliability and Queuing Models10.1007/978-981-13-0857-4_19(251-264)Online publication date: 27-Aug-2018
https://doi.org/10.1007/978-981-13-0857-4_19
Kumar RSharma S(2017)Transient Solution of a Two-Heterogeneous Servers’ Queuing System with Retention of Reneging CustomersBulletin of the Malaysian Mathematical Sciences Society10.1007/s40840-017-0482-z42:1(223-240)Online publication date: 28-Feb-2017
https://doi.org/10.1007/s40840-017-0482-z
Efrosinin DSztrik JFarkhadov MStepanova N(2017)Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control PolicyInformation Technologies and Mathematical Modelling. Queueing Theory and Applications10.1007/978-3-319-68069-9_2(13-27)Online publication date: 27-Sep-2017
https://doi.org/10.1007/978-3-319-68069-9_2

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