In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 41, No. 03 ( 2004-09), p. 778-790
Abstract:
This paper investigates the rate of convergence to the probability distribution of the embedded M/G/1 and GI/M/ n queues. We introduce several types of ergodicity including l -ergodicity, geometric ergodicity, uniformly polynomial ergodicity and strong ergodicity. The usual method to prove ergodicity of a Markov chain is to check the existence of a Foster–Lyapunov function or a drift condition, while here we analyse the generating function of the first return probability directly and obtain practical criteria. Moreover, the method can be extended to M/G/1- and GI/M/1-type Markov chains.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
DOI:
10.1017/S0021900200020544
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2004
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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