A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain | Zendy

Uri Yechiali | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain

Author(s) -

Uri Yechiali

Publication year - 1973

Publication title -

operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.797

H-Index - 140

eISSN - 1526-5463

pISSN - 0030-364X

DOI - 10.1287/opre.21.2.604

Subject(s) - queueing theory , generalization , birth–death process , markov chain , queue , type (biology) , computer science , limiting , simple (philosophy) , mathematics , chain (unit) , state (computer science) , mathematical optimization , markov process , algorithm , statistics , physics , mathematical analysis , population , philosophy , computer network , ecology , sociology , engineering , biology , epistemology , machine learning , mechanical engineering , demography , astronomy , programming language

This paper considers an n-phase generalization of the typical M/M/1 queuing model, where the queuing-type birth-and-death process is defined on a continuous-time n-state Marker chain. It shows that many models analyzed in the literature can be considered special cases of this framework. The paper focuses on the steady-state regime, and observes that, in general, closed-form results for the limiting probabilities are difficult to obtain, if at all possible. Hence, numerical methods should be employed. For an interesting special case, explicit results are obtained that are analogous to the classical solutions for the simple M/M/1 queue.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research