Comparison of the Discriminatory Processor Sharing Policies

Discriminatory Processor Sharing (DPS) policy introduced by Kleinrock [5] is of a great interest in many application areas, including telecommunications, web applications and TCP flow modelling. Under the DPS policy the jobs priority is controlled by a vector of weights. Verifying the vector of weights, it is possible to control the service rates of the jobs and optimize system characteristics. The proper vector weights selection is an important and difficult task because of the system complexity. The previously achieved results on DPS model are of Kleinrock [5], Fayolle et al. [3]. Most of the results obtained for the DPS model were collected together in the survey paper of of Altman et al. [1]. The problem of weights selection in the DPS policy when the job size distributions are exponential was studied by Avrachenkov et al. in [2] and by Kim and Kim in [4]. In [4] it was shown that the DPS policy reduces the expected sojourn time in comparison with PS policy when the weights increase in the opposite order with the means of job classes. Also in [4] the authors formulate a conjecture about the monotonicity of the expected sojourn time of the DPS policy. The idea of conjecture is that comparing two DPS policies, one which has a weight vector closer to the optimal strict priority policy vector has smaller expected sojourn time. Using the method described in [4] we prove this conjecture with some restrictions on system parameters. The proofs can be found in the technical report [6].