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 need an accessible version of this item please contact JSTOR User Support

On the Quasireversibility of a Multiclass Brownian Service Station

J. M. Harrison and R. J. Williams
The Annals of Probability
Vol. 18, No. 3 (Jul., 1990), pp. 1249-1268
Stable URL: http://www.jstor.org/stable/2244425
Page Count: 20
  • Read Online (Free)
  • Download ($19.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
On the Quasireversibility of a Multiclass Brownian Service Station
Preview not available

Abstract

The object of study in this paper is a Brownian model of a multiclass service station. Such Brownian models arise as heavy traffic limits of conventional queueing models in which several different types or classes of customers are processed through a common service facility. Assuming that the Brownian service station is initialized with its stationary distribution, four different model characteristics are shown to be equivalent, and the station is said to be quasireversible if these equivalent conditions pertain. Three of the four conditions characterize the vector departure process from the Brownian service station, and our definition of quasireversibility parallels that proposed by F. P. Kelly for conventional queueing models. The last of our four conditions is expressed directly in terms of primitive model parameters, so one may easily determine from basic data whether or not a Brownian station model is quasireversible. Rather than characterizing the complete vector of departure processes from a Brownian service station, we prove a more general theorem expressed in terms of arbitrary linear combinations of the departure processes; this yields a generalized notion of quasireversibility that will play an important role in future work. To be more specific, in a future paper on multiclass Brownian network models, it will be shown that there is an intimate relationship between product form stationary distributions and the generalized notion of quasireversibility developed here.

Page Thumbnails

  • Thumbnail: Page 
1249
    1249
  • Thumbnail: Page 
1250
    1250
  • Thumbnail: Page 
1251
    1251
  • Thumbnail: Page 
1252
    1252
  • Thumbnail: Page 
1253
    1253
  • Thumbnail: Page 
1254
    1254
  • Thumbnail: Page 
1255
    1255
  • Thumbnail: Page 
1256
    1256
  • Thumbnail: Page 
1257
    1257
  • Thumbnail: Page 
1258
    1258
  • Thumbnail: Page 
1259
    1259
  • Thumbnail: Page 
1260
    1260
  • Thumbnail: Page 
1261
    1261
  • Thumbnail: Page 
1262
    1262
  • Thumbnail: Page 
1263
    1263
  • Thumbnail: Page 
1264
    1264
  • Thumbnail: Page 
1265
    1265
  • Thumbnail: Page 
1266
    1266
  • Thumbnail: Page 
1267
    1267
  • Thumbnail: Page 
1268
    1268