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.

Limit Theorems for Generalized Single Server Queues: The Exceptional System

Austin J. Lemoine
SIAM Journal on Applied Mathematics
Vol. 28, No. 3 (May, 1975), pp. 596-606
Stable URL: http://www.jstor.org/stable/2100382
Page Count: 11
  • Subscribe ($19.50)
  • Cite this Item
Limit Theorems for Generalized Single Server Queues: The Exceptional System
Preview not available

Abstract

This paper studies a single server queueing system in which the first service time and the first interarrival time of each busy period deviate from the pattern of a given GI|G|1 scheme. Under conditions insuring stability, we discuss properties of the stationary waiting time, the stationary workload, and the stationary number in system. In addition, we provide limit theorems for such extreme processes as W* n = max {Wj:0 ≤ j ≤ n} and $W^\ast(t) = \sup \{W(u):0 \leqq u \leqq t\}$, where Wj is the waiting time of customer j and W(u) is the workload of the server at time u.

Page Thumbnails

  • Thumbnail: Page 
596
    596
  • Thumbnail: Page 
597
    597
  • Thumbnail: Page 
598
    598
  • Thumbnail: Page 
599
    599
  • Thumbnail: Page 
600
    600
  • Thumbnail: Page 
601
    601
  • Thumbnail: Page 
602
    602
  • Thumbnail: Page 
603
    603
  • Thumbnail: Page 
604
    604
  • Thumbnail: Page 
605
    605
  • Thumbnail: Page 
606
    606