Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation peri...

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Vydané v:The Journal of the Operational Research Society Ročník 71; číslo 3; s. 447 - 455
Hlavní autori: Kempa, Wojciech M., Marjasz, Rafał
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Taylor & Francis 03.03.2020
Predmet:
Buffer overflow
embedded Markov chain
multiple vacation policy
Poisson process
queueing system
ISSN:0160-5682, 1476-9360
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Abstract A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation period, consisting of a number of independent generally-distributed server vacations, is being started each time when the system becomes empty. During this period, the processing of jobs is suspended. Successive server vacations are being initialised until at least one job is present in the buffer at the completion epoch of one of them. A compact formula for the Laplace transform of the distribution of the time to the first buffer overflow, conditioned by initial number of packets present in the buffer, is found. The analytical approach is based on the paradigm of embedded Markov chain, integral equations and Korolyuk's potential idea. Numerical illustrating examples are attached as well.
AbstractList A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation period, consisting of a number of independent generally-distributed server vacations, is being started each time when the system becomes empty. During this period, the processing of jobs is suspended. Successive server vacations are being initialised until at least one job is present in the buffer at the completion epoch of one of them. A compact formula for the Laplace transform of the distribution of the time to the first buffer overflow, conditioned by initial number of packets present in the buffer, is found. The analytical approach is based on the paradigm of embedded Markov chain, integral equations and Korolyuk's potential idea. Numerical illustrating examples are attached as well.
Author Marjasz, Rafał
Kempa, Wojciech M.
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Snippet A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound...
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SubjectTerms Buffer overflow
embedded Markov chain
multiple vacation policy
Poisson process
queueing system
Title Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy
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