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On the integral of the workload process of the single server queue
- Source :
- Journal of Applied Probability, 40(1), 200-225. University of Sheffield
- Publication Year :
- 2003
- Publisher :
- University of Sheffield, 2003.
-
Abstract
- This paper is devoted to a study of the integral of the workload process of the single server queue, in particular during one busy period. Firstly, we find asymptotics of the area 𝒜 swept under the workload process W(t) during the busy period when the service time distribution has a regularly varying tail. We also investigate the case of a light-tailed service time distribution. Secondly, we consider the problem of obtaining an explicit expression for the distribution of 𝒜. In the general GI/G/1 case, we use a sequential approximation to find the Laplace—Stieltjes transform of 𝒜. In the M/M/1 case, this transform is obtained explicitly in terms of Whittaker functions. Thirdly, we consider moments of 𝒜 in the GI/G/1 queue. Finally, we show asymptotic normality of .
- Subjects :
- D/M/1 queue
Discrete mathematics
Statistics and Probability
M/G/k queue
General Mathematics
M/D/1 queue
010102 general mathematics
M/M/1 queue
G/G/1 queue
01 natural sciences
010104 statistics & probability
Burke's theorem
M/G/1 queue
M/M/c queue
0101 mathematics
Statistics, Probability and Uncertainty
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 00219002
- Volume :
- 40
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....0d3c10e836bbe6f93dffea61d70f027e