Presentation 2001/10/12
Departure Process of the MAP/SM/1 Queue
Shigeo SHIODA,
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Abstract(in English) We study the departure process of a single server queue with Markovian arrival input and Markov renewal service time. First, we derive the joint transform of departure time and the number of departures, from which we obtain alternate proof of Burke's classical result. Next, we establish several expressions for burstiness(variance) and correlation(covariance sequence) of the departure process. These expressions reveal that burstiness and correlation of the arrival process have very little impact on the departure process when a queueing system is heavily loaded. In contrast, both burstiness and correlation of the service-time process greatly affect those of the departure process regardless of the load of the system. Finally, we show that, even when an arrival process is short-range dependent, the departure process could has long-range dependence if the service-time process is long-range dependent.
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Keyword(in English) output process / queueing system / correlation / burstiness / MAP / long-range dependence
Paper # IN2001-98
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Committee IN
Conference Date 2001/10/12(1days)
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Language JPN
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Title (in English) Departure Process of the MAP/SM/1 Queue
Sub Title (in English)
Keyword(1) output process
Keyword(2) queueing system
Keyword(3) correlation
Keyword(4) burstiness
Keyword(5) MAP
Keyword(6) long-range dependence
1st Author's Name Shigeo SHIODA
1st Author's Affiliation Urban Environment Systems, Faculty of Engineering, Chiba University()
Date 2001/10/12
Paper # IN2001-98
Volume (vol) vol.101
Number (no) 374
Page pp.pp.-
#Pages 8
Date of Issue