Functional equations with multiple recursive terms

Ivo Adan (), Onno Boxma () and Jacques Resing ()
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Ivo Adan: Eindhoven University of Technology
Onno Boxma: Eindhoven University of Technology
Jacques Resing: Eindhoven University of Technology

Queueing Systems: Theory and Applications, 2022, vol. 102, issue 1, No 2, 7-23

Abstract: Abstract In this paper, we study a functional equation for generating functions of the form $$f(z) = g(z) \sum _{i=1}^M p_i f(\alpha _i(z)) + K(z)$$ f ( z ) = g ( z ) ∑ i = 1 M p i f ( α i ( z ) ) + K ( z ) , viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the $$\alpha _i(z)$$ α i ( z ) are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.

Keywords: Recursion; Generating function; Stochastic process; Queueing model; Laplace–Stieltjes transform; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-022-09861-9

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