Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Exponential Ergodicity of the M/G/1 Queue

Marcel F. Neuts and Jozef L. Teugels
SIAM Journal on Applied Mathematics
Vol. 17, No. 5 (Sep., 1969), pp. 921-929
Stable URL: http://www.jstor.org/stable/2099280
Page Count: 9
  • Subscribe ($19.50)
  • Cite this Item
Exponential Ergodicity of the M/G/1 Queue
Preview not available

Abstract

If an M/G/1 queue either is transient or is positive and has a service time distribution which is exponentially bounded, then the most important quantities of the queue have distributions which tend exponentially fast to their limits. If we assume somewhat more, i.e., if condition (PE) below is satisfied, then accurate estimates on these distributions are obtained in the positive recurrent case. Some of the studied quantities are: the busy period, the number of customers served during a busy period, the waiting times and the queue length in continuous time. The method of proof is based on the exponential ergodicity theorems for semi-Markov processes and on standard theorems from the theory of Laplace-Stieltjes transforms.

Page Thumbnails

  • Thumbnail: Page 
921
    921
  • Thumbnail: Page 
922
    922
  • Thumbnail: Page 
923
    923
  • Thumbnail: Page 
924
    924
  • Thumbnail: Page 
925
    925
  • Thumbnail: Page 
926
    926
  • Thumbnail: Page 
927
    927
  • Thumbnail: Page 
928
    928
  • Thumbnail: Page 
929
    929