A matrix-analytic solution for the DBMAP/PH/1 priority queue |
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Authors: | Ji-An Zhao Bo Li Xi-Ren Cao Ishfaq Ahmad |
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Institution: | (1) Department of Computer Science, Hong Kong;(2) Department of Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;(3) Computer Science and Engineering Department, The University of Texas at Arlington, Arlington, TX 76019-0015, USA |
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Abstract: | Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models
to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBMAP) has been widely used to model the source behavior of data traffic, while phase-type (PH) distribution has been extensively applied to model the service time. This paper focuses on the computation of the DBMAP/PH/1 queueing system with priorities, in which the arrival process is considered to be a DBMAP with two priority levels and the service time obeys a discrete PH distribution. Such a queueing model has potential in performance evaluation of computer networks such as video transmission
over wireless networks and priority scheduling in ATM or TDMA networks. Based on matrix-analytic methods, we develop computation
algorithms for obtaining the stationary distribution of the system numbers and further deriving the key performance indices
of the DBMAP/PH/1 priority queue.
AMS subject classifications: 60K25 · 90B22 · 68M20
The work was supported in part by grants from RGC under the contracts HKUST6104/04E, HKUST6275/04E and HKUST6165/05E, a grant
from NSFC/RGC under the contract N_HKUST605/02, a grant from NSF China under the contract 60429202. |
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Keywords: | Markovian arrival process Phase-type distribution M/G/1-type Markov chain Matrix-analytic methods |
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