A processor-shared queue that models switching times: Heavy usage asymptotics

Journal Article · Wed Jun 01 04:00:00 EDT 1994 · SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/S0036139992235068· OSTI ID:7032257

Knessl, C; Tier, C ^[1]

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1. Univ. of Illinois, Chicago, IL (United States). Dept. of Mathematics, Statistics, and Computer Science

A closed processor-sharing queueing model that corresponds to M terminals in series with a central processing unit (CPU) is considered under heavy usage conditions. The effects of switching times between the CPU and the individual jobs are included by assuming that the effective service rate that the CPU provides is a decreasing function of the instantaneous number of jobs being processed. Using perturbation methods, asymptotic expansions are constructed for the first two moments of a customer's response (sojourn) time, conditioned on that customer's total required service from the CPU. The asymptotic limit assumes that the number of terminals M is large (M [much gt] 1), that the rate at which the CPU provides service is fast (O(M)), and that the duration of a typical switching time is small compared to the time the CPU actually spends servicing the individual jobs. Extensive numerical comparisons show the quality of the asymptotic approximations.

• DOE Contract Number: FG02-93ER25168
• OSTI ID: 7032257
• Journal Information: SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States) Vol. 54:3; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ASYMPTOTIC SOLUTIONS
COMPUTER NETWORKS
DATA PROCESSING
MATHEMATICAL MODELS
PERFORMANCE
PROCESSING
TASK SCHEDULING