Journal of Applied Probability: Volume 21 - Issue 1

On the transition density of a multidimensional parameter Wiener process with one barrier
E. M. Cabaña
Published online by Cambridge University Press:

14 July 2016, pp. 197-200
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
An upper estimate of the probability density of d-parameter Wiener process with one barrier, already known for d = 2, is extended for general d.

On a problem of the busy-period determination in queues with infinitely many servers
A. Dvurečenskij, L. A. Kuljukina, G. A. Ososkov
Published online by Cambridge University Press:

14 July 2016, pp. 201-206
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
In this paper the probability distribution of the discrete busy period of the 〈M, 1, GI/∞, 1〉 queue and some of its stability properties are given.

The busy period of order n in the GI/D/∞ queue
A. Dvurečenskij
Published online by Cambridge University Press:

14 July 2016, pp. 207-212
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
The busy period of the GI/D/∞ queue is determined as the time when at least one customer is served. Let v be the number of customers served during this period. The busy period of order n is defined as a busy period for which v ≧ n. In this paper we derive the exact distributions, integral equations, characteristic functions and all moments of those periods. Finally, some properties of the idle periods of order n are established.

Journal of Applied Probability