Asymptotic analysis of a state-dependent M/G/1 queueing system
The authors present new asymptotic methods for the analysis of queueing systems. These methods are applied to a state-dependent M/G/1 queue. They 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; and (iv) the mean time until the unfinished work reaches or exceeds a specified capacity. The methods are applied to the full Kolmogorov equations, scaled so that the arrival rate is rapid and the mean device is small. Thus, we do not truncate equations as in diffusion approximations. For state-dependent M/G/1 queues, results are shown to agree with the known exact solutions. The authors include comparisons, both analytic and numerical, between these results and those obtained from diffusion approximations.
- Research Organization:
- Dept. of Engineering Sciences and Applied Mathematics, The Technological Inst., Northwestern Univ., Evanston, IL 60201
- OSTI ID:
- 5480963
- Journal Information:
- SIAM J. Appl. Math.; (United States), Vol. 46:3
- Country of Publication:
- United States
- Language:
- English
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