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 Limiting Distributions in Queueing Systems with Deadlines

M. Drmota and U. Schmid
SIAM Journal on Applied Mathematics
Vol. 53, No. 1 (Feb., 1993), pp. 301-318
Stable URL: http://www.jstor.org/stable/2102287
Page Count: 18
  • Subscribe ($19.50)
  • Cite this Item
Exponential Limiting Distributions in Queueing Systems with Deadlines
Preview not available

Abstract

This paper contains some general theorems on the limiting distribution of a certain random variable ST arising in the context of recurrent events. ST is especially meaningful to the investigation of discrete-time queueing systems subjected to service time deadlines. It may be viewed as a sum of mutually independent conditional random variables BT having the same distribution. It is assumed that BT depends on a parameter T and tends to an unconditional random variable B for T → ∞. Under some weak conditions concerning the conditional probability generating function BT(z), it follows that ST is approximately exponentially distributed with parameter λT = 1/μT, μT = B'T(1)/(1 - BT(1)), which tends to infinity for T → ∞. Provided here are uniform asymptotic expansions for the appropriate probabilities and for all moments, also.

Page Thumbnails

  • Thumbnail: Page 
301
    301
  • Thumbnail: Page 
302
    302
  • Thumbnail: Page 
303
    303
  • Thumbnail: Page 
304
    304
  • Thumbnail: Page 
305
    305
  • Thumbnail: Page 
306
    306
  • Thumbnail: Page 
307
    307
  • Thumbnail: Page 
308
    308
  • Thumbnail: Page 
309
    309
  • Thumbnail: Page 
310
    310
  • Thumbnail: Page 
311
    311
  • Thumbnail: Page 
312
    312
  • Thumbnail: Page 
313
    313
  • Thumbnail: Page 
314
    314
  • Thumbnail: Page 
315
    315
  • Thumbnail: Page 
316
    316
  • Thumbnail: Page 
317
    317
  • Thumbnail: Page 
318
    318