Steady-state Markov chain models for certain \(q\)-confluent hypergeometric distributions

DOI10.1016/j.jspi.2005.02.009zbMath1075.60007OpenAlexW2025657810MaRDI QIDQ2568424

Adrienne W. Kemp

Publication date: 10 October 2005

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2005.02.009

zbMATH Keywords

Heine distribution\(q\)-hyper-Poisson I distributionbirth-abort-death processesconfluent \(q\)-Chu-Vandermonde distributionconfluent Bailey-Daum distributioncurrent-age modelsexton distributionM/M/1 queues with balkingMorse distributionO/U distributionover-and-underdispersionsuccess-run processessuccess-run processes with stagnationthird \(q\)-Poisson analogue

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Queueing theory (aspects of probability theory) (60K25) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

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Synchronized reneging in queueing systems with vacations ⋮ On a \(q\)-steady state Markov chain model based on transformed dual \(q\)-Krawtchouk orthogonal polynomials and its limiting behaviour ⋮ Multivariate q-Pólya and inverse q-Pólya distributions ⋮ A \(q\)-analogue of the Stirling formula and a continuous limiting behaviour of the \(q\)-binomial distribution -- numerical calculations ⋮ A \(q\)-Pólya urn model and the \(q\)-Pólya and inverse \(q\)-Pólya distributions ⋮ The \(M/M/1\) queue with synchronized abandonments ⋮ \(q\)-discrete distributions based on \(q\)-Meixner and \(q\)-Charlier orthogonal polynomials-asymptotic behaviour ⋮ q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS ⋮ Synchronized abandonments in a single server unreliable queue ⋮ Continuous Stieltjes-Wigert limiting behaviour of a family of confluent \(q\)-Chu-Vandermonde distributions

Cites Work

• Random walks and other aspects of the Bailey-Daum distribution
• Existence conditions and properties for the generalized Euler family of distributions
• \(q\)-analogues of the hyper-Poisson distribution
• Heine-euler extensions of the poisson distribution
• Oil exploration: sequential decisions in the face of uncertainty
• Steady-state Markov chain models for the Heine and Euler distributions
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