The depletion time forM/G/1 systems and a related limit theorem
- 1 June 1983
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 15 (2) , 420-443
- https://doi.org/10.2307/1426443
Abstract
Waiting-time distributions for M/G/1 systems with priority dependent on class, order of arrival, service length, etc., are difficult to obtain. For single-server multipurpose processors the difficulties are compounded. A certain ergodic post-arrival depletion time is shown to be a true maximum for all delay times of interest. Explicit numerical evaluation of the distribution of this time is available. A heavy-traffic distribution for this time is shown to provide a simple and useful engineering tool with good results and insensitivity to service-time distribution even at modest traffic intensity levels. The relationship to the diffusion approximation for heavy traffic is described.Keywords
This publication has 15 references indexed in Scilit:
- The bilateral Laguerre transformApplied Mathematics and Computation, 1981
- Laguerre transformation as a tool for the numerical solution of integral equations of convolution typeApplied Mathematics and Computation, 1979
- Monotone matrices and monotone Markov processesStochastic Processes and their Applications, 1977
- Sojourn times, exit times and jitter in multivariate Markov processesAdvances in Applied Probability, 1974
- Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and NormalityThe Annals of Probability, 1974
- Stochastically monotone Markov ChainsProbability Theory and Related Fields, 1968
- The First Passage Time Density for Homogeneous Skip-free Walks on the ContinuumThe Annals of Mathematical Statistics, 1963
- Properties of Probability Distributions with Monotone Hazard RateThe Annals of Mathematical Statistics, 1963
- Queues Subject to Service InterruptionThe Annals of Mathematical Statistics, 1962
- On Time Dependent Queuing ProcessesThe Annals of Mathematical Statistics, 1960