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Loss behavior in space priority queue with batch Markovian arrival process — continuous-time case

Authors
Journal
Performance Evaluation
0166-5316
Publisher
Elsevier
Publication Date
Volume
64
Issue
1
Identifiers
DOI: 10.1016/j.peva.2006.05.003
Keywords
  • Space Priority Queue
  • Batch Markovian Arrival Process (Bmap)
  • Phase-Type (Ph) Distribution
Disciplines
  • Computer Science

Abstract

Abstract This paper applies a matrix-analytic approach to analyze both the long-term and the short-term loss behaviors of a queue with space priority scheme. Five related performance measures are derived from conditional statistics, including the long-term high-priority and low-priority packet loss probabilities, and the three short-term measures — the average length of a critical period, the average length of a non-critical period, and the conditional high-priority packet loss probability during a critical period. The overall complexity of computing these performance measures is of the order O ( K 2 m 1 3 m 2 3 σ 3 ) , where m 1 , m 2 are the numbers of phases of the underlying Markovian structures for the high-priority and the low-priority packet arrival processes respectively and σ is the number of phases of the phase-type server.

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