Taylor series expansions for Poisson-driven (max,+)-linear systems

DOI10.1214/aoap/1034968069zbMath0863.60092OpenAlexW2014584836MaRDI QIDQ1921436

François Baccelli, Volker Schmidt

Publication date: 10 June 1997

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1034968069

zbMATH Keywords

stochastic Petri netsqueueing networksmarked point processesmultinomial expansionPoisson inputvectorial recurrence equationfactorial moment measuresstationary state variables

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Ergodic and light traffic properties of a complex repairable system ⋮ A note on expansion for functionals of spatial marked point processes ⋮ Closed-form formulae for moment, tail probability, and blocking probability of waiting time in a buffer-sharing deterministic system ⋮ A coupling approach to estimating the Lyapunov exponent of stochastic max-plus linear systems ⋮ Explicit expressions for moments of waiting times in Poisson driven deterministic two-node tandem queues with blocking ⋮ Taylor series expansions for stationary Markov chains ⋮ Differentiability of functionals of Poisson processes via coupling. With applications to queueing theory ⋮ An Approximation Method for Blocking Probabilities in M/D/1/K₁→ ⋅/D/1/K₂Queues

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