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205
Abstracts of Research Reports
A two-moment approximation for the mean
waiting time in the G I / G / s queue Toshikazu Kimura * Department of Information Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan November 1984; No. B-154 Research Reports on Information Sciences, Series B * I am grateful to Michiel H. van Hoorn for providing me detailed data of the exact mean waiting times. This research was supported in part by the Sakkokai Foundation.
We provide a simple two-moment approximation formula for the mean waiting time in a G I / G / s queue. This formula has the form of a certain combination of the exact mean waiting times for the D / M / s , M / D / s and M / M / s queues, and hence it can be easily calculated b y using some queueing tables. The quality of the approximation is tested by comparing it to known solutions in particular cases.
Asymptotic analysis of a state dependent
M / G / 1 queueing system C. Knessl, B.J. M a t k o w s k y , Z. Schuss a n d C. T i e r Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201, USA August 1984; Technical Report No. 8319
We present new asymptotic methods for the analysis of queueing systems. These methods are applied to a state-dependent M / G / 1 queue. We formulate problems for and compute approximations to (i) the stationary density of the unfinished work; (ii) the mean length of time until the end of
a busy period; (iii) the mean length of a busy period; (iv) the mean time until t h e unfinished work reaches or exceeds a specified capacity; and (v) the distribution of the maximum. The methods are applied to the full Kolmogorov equations, scaled so that the arrival rate is rapid and the mean service is small. Thus, we do not truncate equations as in diffusion approximations. For state-independent M / G / 1 queues, our results are shown to agree with the known exact solutions. We include comparisons, both analytic and numerical, between our results and those obtained from diffusion approximations.
North-Holland Performance Evaluation 5 (1985) 205-208 0166-5316/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)
Abstracts of Research Reports
A two-moment approximation for the mean
waiting time in the G I / G / s queue Toshikazu Kimura * Department of Information Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan November 1984; No. B-154 Research Reports on Information Sciences, Series B * I am grateful to Michiel H. van Hoorn for providing me detailed data of the exact mean waiting times. This research was supported in part by the Sakkokai Foundation.
We provide a simple two-moment approximation formula for the mean waiting time in a G I / G / s queue. This formula has the form of a certain combination of the exact mean waiting times for the D / M / s , M / D / s and M / M / s queues, and hence it can be easily calculated b y using some queueing tables. The quality of the approximation is tested by comparing it to known solutions in particular cases.
Asymptotic analysis of a state dependent
M / G / 1 queueing system C. Knessl, B.J. M a t k o w s k y , Z. Schuss a n d C. T i e r Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201, USA August 1984; Technical Report No. 8319
We present new asymptotic methods for the analysis of queueing systems. These methods are applied to a state-dependent M / G / 1 queue. We formulate problems for and compute approximations to (i) the stationary density of the unfinished work; (ii) the mean length of time until the end of
a busy period; (iii) the mean length of a busy period; (iv) the mean time until t h e unfinished work reaches or exceeds a specified capacity; and (v) the distribution of the maximum. The methods are applied to the full Kolmogorov equations, scaled so that the arrival rate is rapid and the mean service is small. Thus, we do not truncate equations as in diffusion approximations. For state-independent M / G / 1 queues, our results are shown to agree with the known exact solutions. We include comparisons, both analytic and numerical, between our results and those obtained from diffusion approximations.
North-Holland Performance Evaluation 5 (1985) 205-208 0166-5316/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)