TY - JOUR
T1 - ASYMPTOTIC ANALYSIS OF A STATE-DEPENDENT M/G/1 QUEUEING SYSTEM.
AU - Knessl, C.
AU - Matkowsky, B. J.
AU - Schuss, Z.
AU - Tier, C.
N1 - Funding Information:
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.
PY - 1986
Y1 - 1986
N2 - 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; 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 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.
AB - 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; 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 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.
UR - http://www.scopus.com/inward/record.url?scp=0022737710&partnerID=8YFLogxK
U2 - 10.1137/0146033
DO - 10.1137/0146033
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AN - SCOPUS:0022737710
SN - 0036-1399
VL - 46
SP - 483
EP - 505
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 3
ER -