Steady-state analysis of a discrete-time batch arrival queue with working vacations

Authors:
Ji-hong Li;Wei-qi Liu;Nai-shuo Tian
Affiliations:
College of Management, Shanxi University, Taiyuan, 030006, China;College of Management, Shanxi University, Taiyuan, 030006, China;College of Sciences, Yanshan University, Qinhuangdao, 066004, China
Venue:
Performance Evaluation
Year:
2010

Citing 11
Cited 2

Queueing systems with vacations—a survey

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On stochastic decomposition in M/G/1 type queues with generalized server vacations

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Performance analysis of a finite-buffer discrete-time queue with bulk arrival, bulk service and vacations

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M/G/1 queue with multiple working vacations

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Vacation Queueing Models: Theory and Applications (International Series in Operations Research & Management Science)

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Discrete-time GI/Geo/1 queue with multiple working vacations

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Discrete-time GeoX/G(a,b)/1/N queues with single and multiple vacations

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Stochastic decompositions in the M/M/1 queue with working vacations

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Analysis of a GI/M/1 queue with multiple working vacations

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A queue with working breakdowns

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Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling

Computers and Industrial Engineering

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Abstract

This paper analyzes a discrete-time batch arrival queue with working vacations. In a Geo^X/G/1 system, the server works at a lower speed during the vacation period which becomes a lower speed operation period. This model is more appropriate for the communication systems with the transmit units arrived in batches. We formulate the system as an embedded Markov chain at the departure epoch and by the M/G/1-type matrix analytic approach, we derive the probability generating function (PGF) of the stationary queue length. Then, we obtain the distribution for the number of the customers at the busy period initiation epoch, and use the stochastic decomposition technique to present another equivalent PGF of the queue length. We also develop a variety of stationary performance measures for this system. Some special models and numerical results are presented. Finally, a real-world example in an Ethernet Passive Optical Network (EPON) is provided.