Time to Buffer Overflow in a Queueing Model with Working Vacation Policy

Kempa, Wojciech M.; Kobielnik, Martyna

doi:10.1007/978-3-319-92459-5_18

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2020

2023

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Cited by 2 publications

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“…The model of a production line with unreliable machine is investigated in [15]. In [12] the distribution of the time to buffer overflow is analyzed in the case of a model with server working vacations. In [20] the representation for the mean time to reach the fixed level in the M/G/1-type queue with infinite buffer is obtained.…”

Section: Introductionmentioning

confidence: 99%

On Time-to-Buffer Overflow Distribution in a Single-Machine Discrete-Time System With Finite Capacity

Kempa

2020

Mathematical Modelling and Analysis

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A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.

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Section: Introductionmentioning

confidence: 99%