We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Some reflected autoregressive processes with dependencies.
- Authors
Dimitriou, Ioannis; Fiems, Dieter
- Abstract
Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered.
- Subjects
GENERATING functions; RANDOM variables; QUEUEING networks; AUTOREGRESSIVE models; LAPLACE distribution; RECURSION theory; BOUNDARY value problems; ORBITS (Astronomy)
- Publication
Queueing Systems, 2024, Vol 106, Issue 1/2, p67
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-023-09899-3