Birth-Death Queues

  • Hong Chen
  • David D. Yao
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 46)


This chapter introduces three preliminary topics that will serve as the basis for much of the first part of this book (the first four chapters), which focuses on continuous-time Markov chain models. The three topics are (a) the birth—death process and related queueing models in Section 1.1, (b) the notion of time reversibility of a Markov chain in Section 1.2, and (c) likelihood ratio ordering and stochastic ordering in Section 1.3.


Markov Chain Service Rate Sojourn Time Rate Matrix Stochastic Order 
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    Ross, S.M. 1996. Stochastic Processes ( 2nd ed. ). Wiley, New York.zbMATHGoogle Scholar
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    Shanthikumar, J.G. and Yao, D.D. 1986. The Preservation of Likelihood Ratio Ordering under Convolution. Stochastic Processes and Their Applications, 23, 259–267.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Shanthikumar, J.G. and Yao, D.D. 1986. The Effect of Increasing Service Rates in Closed Queueing Networks. Journal of Applied Probability, 23, 474–483.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Stoyan, D. 1983. Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Hong Chen
    • 1
  • David D. Yao
    • 2
  1. 1.Faculty of Commerce and Business AdministrationUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Operations Research and Industrial EngineeringColumbia UniversityNew YorkUSA

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