Journal of Applied Probability

Published on behalf of the Applied Probability Trust

MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

< Back to all issues

Volume 33 - Issue 2 - September 1996

Contents

Page 2 of 2

Stability of feed-forward fluid networks with Lévy input
Part of:
- Operations research and management science
- Special processes
Haya Kaspi, Offer Kella
Published online by Cambridge University Press:

14 July 2016, pp. 513-522
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
We consider a stochastic fluid network with independent subordinator inputs to the various stations and deterministic internal flow which is of feed-forward type. We show that under suitable conditions the process of fluid contents in the station has a limiting distribution, where the limit holds in total variation and is independent of the initial condition. We also show that this limiting distribution is of product form only for trivial setups.

Rate modulation in dams and ruin problems
Part of:
Søren Asmussen, Offer Kella
Published online by Cambridge University Press:

14 July 2016, pp. 523-535
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
We consider a dam in which the release rate depends both on the state and some modulating process. Conditions for the existence of a limiting distribution are established in terms of an associated risk process. The case where the release rate is a product of the state and the modulating process is given special attention, and in particular explicit formulas are obtained for a finite state space Markov modulation.

Optimal policies for scheduling repairs and allocating heterogeneous servers
Part of:
- Operations research and management science
- Computer system organization
Rhonda Righter
Published online by Cambridge University Press:

14 July 2016, pp. 536-547
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
We consider the machine repairman, or resource utilization, model in which there is a finite source of jobs with non-identically distributed exponential return times and a single server with job dependent service times. We also consider a related problem of scheduling jobs at heterogeneous servers. We construct a coupling framework that provides a simple unified proof that strengthens many of the results in the literature, and generalizes easily to prove several new results.

More on optimal allocation of components in coherent systems
Part of:
- Survival analysis and censored data
- Operations research and management science
Fan C. Meng
Published online by Cambridge University Press:

14 July 2016, pp. 548-556
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

A modified block replacement policy with two variables and general random minimal repair cost
Part of:
Shey-Huei Sheu
Published online by Cambridge University Press:

14 July 2016, pp. 557-572
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at times kT (k= 1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T, (k − 1)T+ T0) it is either replaced by a new one or minimally repaired, and if in [(k − 1) T + T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the system at age y depends on the random part C(y) and the deterministic part ci (y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

Asymptotic expansions for functionals of dilation of point processes
Part of:
- Stochastic processes
- Computer system organization
A. A. Borovkov
Published online by Cambridge University Press:

14 July 2016, pp. 573-591
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register Recommend to librarian
- Export citation
This paper provides a direct approach to obtaining formulas for derivatives of functionals of point processes in rare perturbation analysis ([2], [6]). Results are obtained for arbitrary (not necessarily stationary) point processes in and d, d 2, under transparent conditions, close to minimal. Formulas for higher-order derivatives allow one to construct asymptotical expansions. The results can be useful in sensitivity analysis, in light traffic theory for queues and for computation by simulation of derivatives at positive intensity, while the computation of the derivatives via statistical estimation of the functional itself and its increments usually gives poor results.

Page 2 of 2