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.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Queues with Non-Stationary Input Stream: Ross's Conjecture

Tomasz Rolski
Advances in Applied Probability
Vol. 13, No. 3 (Sep., 1981), pp. 603-618
DOI: 10.2307/1426787
Stable URL: http://www.jstor.org/stable/1426787
Page Count: 16
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Queues with Non-Stationary Input Stream: Ross's Conjecture
Preview not available

Abstract

Characteristics of queues with non-stationary input streams are difficult to evaluate, therefore their bounds are of importance. First we define what we understand by the stationary delay and find out the stability conditions of single-server queues with non-stationary inputs. For this purpose we introduce the notion of an ergodically stable sequence of random variables. The theory worked out is applied to single-server queues with stationary doubly stochastic Poisson arrivals. Then the interarrival times do not form a stationary sequence ('time stationary' does not imply 'customer stationary'). We show that the average customer delay in the queue is greater than in a standard M/G/1 queue with the same average input rate and service times. This result is used in examples which show that the assumption of stationarity of the input point process is non-essential.

Page Thumbnails

  • Thumbnail: Page 
603
    603
  • Thumbnail: Page 
604
    604
  • Thumbnail: Page 
605
    605
  • Thumbnail: Page 
606
    606
  • Thumbnail: Page 
607
    607
  • Thumbnail: Page 
608
    608
  • Thumbnail: Page 
609
    609
  • Thumbnail: Page 
610
    610
  • Thumbnail: Page 
611
    611
  • Thumbnail: Page 
612
    612
  • Thumbnail: Page 
613
    613
  • Thumbnail: Page 
614
    614
  • Thumbnail: Page 
615
    615
  • Thumbnail: Page 
616
    616
  • Thumbnail: Page 
617
    617
  • Thumbnail: Page 
618
    618