Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Journals
  3. Advances in Applied Probability
  4. Volume 9
Journal Home
Refine listing

Refine listing

Access:
Publication date:

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×
< Back to all issues

Volume 9 - March 1977

Contents

Page 5 of 7

II B. Queueing—Theory and Applications

II. Contributed Papers

Research Article

  • Fluctuations of random walk in Rd and storage systems

  • Priscilla Greenwood, Moshe Shaked
  • Published online by Cambridge University Press:
    01 July 2016, pp. 566-587

  • Two Wiener-Hopf type factorization identities for multivariate distributions are introduced. Properties of associated stopping times are derived. The structure that produces one factorization also provides the unique solution of the Wiener-Hopf convolution equation on a convex cone in Rd. Some applications for multivariate storage and queueing systems are indicated. For a few cases explicit formulas are obtained for the transforms of the associated stopping times. A result of Kemperman is extended.

  • Integrals on a moving manifold and geometrical probability

  • Adrian Baddeley
  • Published online by Cambridge University Press:
    01 July 2016, pp. 588-603

  • For a manifold which is moving and changing with time, consider some numerical property which at each instant is equal to an integral over the manifold. We derive a general expression for the time rate of change of this integral. Corollaries include a precise general form of Crofton's boundary theorem, de Hoff's interface displacement equations (with some new extensions) and a theorem in fluid mechanics.

II B. Queueing—Theory and Applications

II. Contributed Papers

II C. Applications of Stochastic Processes

II. Contributed Papers

Research Article

  • The M/G/1 queue with several types of customers and change-over times

  • Marcel F. Neuts
  • Published online by Cambridge University Press:
    01 July 2016, pp. 604-644

  • We study an M/G/1 queue with m types of customer, operating under the first-come, first-served discipline. It is assumed that the server expends a random length of time in change-over from one type of customer to another. Various priority rules have been proposed to reduce the amount of time spent in change-over. These queue disciplines generally require a separate monitoring, whose cost is frequently non-negligible. As a basis for evaluating the merits of alternate queue disciplines, it is important to have information on the M/G/1 queue with m customer types when service is first-come, first-served. By appealing to general methods for the M/SM/1 queue, a large number of detailed and explicit results are obtained. In addition, algorithmic solutions are given for the steady-state distributions which are analytically intractable.

  • Stationary distributions for dams with additive input and content-dependent release rate

  • P. J. Brockwell
  • Published online by Cambridge University Press:
    01 July 2016, pp. 645-663

  • Conditions are derived under which a probability measure on the Borel subsets of [0, ∞) is a stationary distribution for the content {Xt} of an infinite dam whose cumulative input {At} is a pure-jump Lévy process and whose release rate is a non-decreasing continuous function r(·) of the content. The conditions are used to find stationary distributions in a number of special cases, in particular when and when r(x) = xα and {At} is stable with index β ∊ (0, 1). In general if EAt, < ∞ and r(0 +) > 0 it is shown that the condition sup r(x)>EA1 is necessary and sufficient for a stationary distribution to exist, a stationary distribution being found explicitly when the conditions are satisfied. If sup r(x)>EA1 it is shown that there is at most one stationary distribution and that if there is one then it is the limiting distribution of {Xt} as t → ∞. For {At} stable with index β and r(x) = xα, α + β = 1, we show also that complementing results of Brockwell and Chung for the zero-set of {Xt} in the cases α + β < 1 and α + β > 1. We conclude with a brief treatment of the finite dam, regarded as a limiting case of infinite dams with suitably chosen release functions.

II C. Applications of Stochastic Processes

II. Contributed Papers

Front Matter

II C. Applications of Stochastic Processes

II. Contributed Papers

Back Matter

II C. Applications of Stochastic Processes

II. Contributed Papers

II D. Ergodic Theory

II. Contributed Papers

Page 5 of 7