This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802-813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.
Bibliographical noteFunding Information:
B. Kim’s research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.
- Abelian-Tauberian theorem
- Fundamental period
- MAP/G/1 queue
- Regular variation
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics