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

Please always quote using this URN: urn:nbn:de:0297-zib-11414
• We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by $M/GI/SDPS$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related $M/D/SDPS$ and $M/M/SDPS$ systems, respectively. The numerical results presented for $M/GI/m-PS$ systems illustrate that the proposed approximations work well.

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Author: Andreas Brandt, Manfred Brandt ZIB-Report M/GI/m-PS; approximations; moments; sojourn time; state-dependent processor sharing 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] 2009/08/31 ZIB-Report (09-25) 1438-0064 09-25