On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue

Liu, Xiaoyuan; Fralix, Brian

doi:10.1007/s11009-018-9658-8

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…Baek et al (2014); Griffiths et al (2006); Yu et al (2011); Yue et al (2009); Zhang et al (2016)). Besides, Liu and Fralix (2019) employed the lattice path counting techniques to examine the time-dependent and equilibrium behavior of continuous-time Markov chains (CTMC) and Markovian queueing systems. More recently, Pandey and Gangeshwer (2020) utilized the probability-generating function approach to derive the steady-state 10.3389/fenrg.2023.1329899 queue-size distribution by employing the ambulance service as a server.…”

Section: Service In Phasesmentioning

confidence: 99%

Optimal management strategies of renewable energy systems with hyperexponential service provisioning: an economic investigation

Varshney,

Shekhar,

Dhanunjaya Reddy

et al. 2023

Front. Energy Res.

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The current research proposes optimal management strategies for queueing modeling-based renewable energy systems with hyper-exponentially distributed maintenance/repair under the assumption of an admission control policy. Using the concept and steps of the matrix-analytical method, the steady-state probability distribution associated with energy systems is explicitly presented. A relatively straightforward computation that can help with modeling wind energy generation, investigating wind farm performance, optimizing energy based on system storage, reliability inspection, service maintenance planning, and numerous other purposes can be employed to mathematically derive several system performance indicators. The investigation findings are validated via quantitative outcomes, illustrative possesses, and a step-by-step recursive methodology for efficient management of the renewable energy system. Additionally, considering multiple governing parameter values, the nature-inspired optimization technique, Cuckoo Search (CS), is employed to demonstrate the optimum anticipated cost of renewable energy system. A comparison with other metaheuristics and semi-classical approaches is also presented to establish the best convergence results. In order to help system designers, policymakers, engineers, and researchers, several numerical examples are also provided to construct more practical strategies based on the production of energy, storage, and system management. The economic, parametric, and performance investigation findings are highlighted, and the opportunities and recommendations for further research are provided. In a nutshell, the outcomes of the present analysis can be adopted to formulate the most effective economic strategies and regulate decision-making processes in the energy sectors.

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