A sample path relation for the sojourn times in G/G/1-PS systems and its applications

Please always quote using this URN: urn:nbn:de:0297-zib-7401
  • For the general G/G/1 processor sharing (PS) system a sample path result for the sojourn times in a busy period is proved, which yields a relation between the sojourn times under PS and FCFS discipline. In particular, the result provides a formula for the mean sojourn time in G/D/1-PS in terms of the mean sojourn time in the corresponding G/D/1-FCFS, generalizing known results for GI/M/1 and M/GI/1. Extensions of the formula provide the basis for a two-moment approximation of the mean sojourn time in G/GI/1-PS in terms of a related G/D/1-FCFS.

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Metadaten
Author:Andreas Brandt, Manfred Brandt
Document Type:ZIB-Report
Tag:G/D/1; G/G/1; G/GI/1; G/M/1; busy period; first come first served; processor sharing; sample path; sojourn time; two-moment ap; waiting time
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K25 Queueing theory [See also 68M20, 90B22]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M20 Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
Date of first Publication:2003/06/26
Series (Serial Number):ZIB-Report (03-18)
Published in:Appeared in: Qeueing Systems 52 (2006) 281 - 286