On a random interval graph and the maximum throughput rate in the system GI/G/1/0

W.M. Nawijn

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/GI1/0, under the assumption of perfect information regarding the sequences {X,, i = 1, 2, - - - } and {Yi, i = 1, 2, ..--- } of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs.
Original languageUndefined
Pages (from-to)945-956
Number of pages12
JournalAdvances in applied probability
Volume23
Issue number4
Publication statusPublished - 1991

Keywords

  • IR-98369
  • METIS-140489

Cite this

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abstract = "The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/GI1/0, under the assumption of perfect information regarding the sequences {X,, i = 1, 2, - - - } and {Yi, i = 1, 2, ..--- } of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs.",
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On a random interval graph and the maximum throughput rate in the system GI/G/1/0. / Nawijn, W.M.

In: Advances in applied probability, Vol. 23, No. 4, 1991, p. 945-956.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On a random interval graph and the maximum throughput rate in the system GI/G/1/0

AU - Nawijn, W.M.

PY - 1991

Y1 - 1991

N2 - The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/GI1/0, under the assumption of perfect information regarding the sequences {X,, i = 1, 2, - - - } and {Yi, i = 1, 2, ..--- } of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs.

AB - The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/GI1/0, under the assumption of perfect information regarding the sequences {X,, i = 1, 2, - - - } and {Yi, i = 1, 2, ..--- } of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs.

KW - IR-98369

KW - METIS-140489

M3 - Article

VL - 23

SP - 945

EP - 956

JO - Advances in applied probability

JF - Advances in applied probability

SN - 0001-8678

IS - 4

ER -