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Some reflected autoregressive processes with dependencies

Ioannis Dimitriou and Dieter Fiems (UGent)
(2024) QUEUEING SYSTEMS. 106(1-2). p.67-127
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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.
Keywords
Workload, Queueing systems, Laplace-Stieltjes transform, Generating function, Recursion, Wiener-Hopf boundary value problem

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MLA
Dimitriou, Ioannis, and Dieter Fiems. “Some Reflected Autoregressive Processes with Dependencies.” QUEUEING SYSTEMS, vol. 106, no. 1–2, 2024, pp. 67–127, doi:10.1007/s11134-023-09899-3.
APA
Dimitriou, I., & Fiems, D. (2024). Some reflected autoregressive processes with dependencies. QUEUEING SYSTEMS, 106(1–2), 67–127. https://doi.org/10.1007/s11134-023-09899-3
Chicago author-date
Dimitriou, Ioannis, and Dieter Fiems. 2024. “Some Reflected Autoregressive Processes with Dependencies.” QUEUEING SYSTEMS 106 (1–2): 67–127. https://doi.org/10.1007/s11134-023-09899-3.
Chicago author-date (all authors)
Dimitriou, Ioannis, and Dieter Fiems. 2024. “Some Reflected Autoregressive Processes with Dependencies.” QUEUEING SYSTEMS 106 (1–2): 67–127. doi:10.1007/s11134-023-09899-3.
Vancouver
1.
Dimitriou I, Fiems D. Some reflected autoregressive processes with dependencies. QUEUEING SYSTEMS. 2024;106(1–2):67–127.
IEEE
[1]
I. Dimitriou and D. Fiems, “Some reflected autoregressive processes with dependencies,” QUEUEING SYSTEMS, vol. 106, no. 1–2, pp. 67–127, 2024.
@article{01HXRPZS5J30N44ETNEEQJ8CGS,
  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.}},
  author       = {{Dimitriou, Ioannis and Fiems, Dieter}},
  issn         = {{0257-0130}},
  journal      = {{QUEUEING SYSTEMS}},
  keywords     = {{Workload,Queueing systems,Laplace-Stieltjes transform,Generating function,Recursion,Wiener-Hopf boundary value problem}},
  language     = {{eng}},
  number       = {{1-2}},
  pages        = {{67--127}},
  title        = {{Some reflected autoregressive processes with dependencies}},
  url          = {{http://doi.org/10.1007/s11134-023-09899-3}},
  volume       = {{106}},
  year         = {{2024}},
}
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