Back to Search
Start Over
A multiplicative version of the Lindley recursion.
- Source :
-
Queueing Systems . Aug2021, Vol. 98 Issue 3/4, p225-245. 21p. - Publication Year :
- 2021
-
Abstract
- This paper presents an analysis of the stochastic recursion W i + 1 = [ V i W i + Y i ] + that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model's stability condition. Writing Y i = B i - A i , for independent sequences of nonnegative i.i.d. random variables { A i } i ∈ N 0 and { B i } i ∈ N 0 , and assuming { V i } i ∈ N 0 is an i.i.d. sequence as well (independent of { A i } i ∈ N 0 and { B i } i ∈ N 0 ), we then consider three special cases (i) V i equals a positive value a with certain probability p ∈ (0 , 1) and is negative otherwise, and both A i and B i have a rational LST, (ii) V i attains negative values only and B i has a rational LST, (iii) V i is uniformly distributed on [0, 1], and A i is exponentially distributed. In all three cases, we derive transient and stationary results, where the transient results are in terms of the transform at a geometrically distributed epoch. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02570130
- Volume :
- 98
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Queueing Systems
- Publication Type :
- Academic Journal
- Accession number :
- 152058179
- Full Text :
- https://doi.org/10.1007/s11134-021-09698-8