Insensitivity bounds for the moments of the sojourn times in M/GI systems under state-dependent processor sharing

Please always quote using this URN: urn:nbn:de:0297-zib-11092

We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times.

Metadaten
Author:	Andreas Brandt, Manfred Brandt
Document Type:	ZIB-Report
Tag:	M/GI/m-PS; bounds; moments; sojourn time; state-dependent processor sharing
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) / 60Exx Distribution theory [See also 62Exx, 62Hxx] / 60E15 Inequalities; stochastic orderings
	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]
	90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B22 Queues and service [See also 60K25, 68M20]
Date of first Publication:	2009/01/07
Series (Serial Number):	ZIB-Report (09-02)
ISSN:	1438-0064
ZIB-Reportnumber:	09-02
Published in:	Appeared in: Adv. in Appl. Probab., 42 (2010) 246-267

Open Access