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(116 citation statements)

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“…We take some more efficient approaches to get these stationary results. On the one hand, based on the algorithmic method proposed by Li (2010), a simpler UL-type RG-factorization has been employed to find the distribution of the queue length at an arbitrary epoch. On the other hand, in order to develop an optimal management policy for the system, the expected length of the regeneration cycle is investigated by using an extended definition of the busy period that might be initiated with multiple customers.…”

confidence: 99%

“…We take some more efficient approaches to get these stationary results. On the one hand, based on the algorithmic method proposed by Li (2010), a simpler UL-type RG-factorization has been employed to find the distribution of the queue length at an arbitrary epoch. On the other hand, in order to develop an optimal management policy for the system, the expected length of the regeneration cycle is investigated by using an extended definition of the busy period that might be initiated with multiple customers.…”

confidence: 99%

“…However, the direct solving is time and resource consuming and hence can only be used for the low dimensional system. In order to efficiently solve the above system of linear algebraic equations, we use the UL-type RG-factorization, given in Li (2010), to find the solution of Eq. (1).…”

confidence: 99%

“…Comparing with the results given in Li and Lui [16] and Li [12], this paper provides more necessary phase-level probability analysis in setting up the infinitedimensional system of differential vector equations, which leads some new results and methodologies in the study of block-structured supermarket models. Note that the PH distributions constitute a versatile class of distributions that can approximate arbitrarily closely any probability distribution defined on the nonnegative real line, and the MAPs are a broad class of renewal or non-renewal point processes that can approximate arbitrarily closely any stochastic counting process (e.g., see Neuts [27,28] and Li [11] for more details), thus the results of this paper are a key advance of those given in Mitzenmacher [23] and Vvedenskaya et al [32] under the Poisson and exponential setting.…”

confidence: 99%

“…It is achieved by considering a Markov reward process (cf. Li, 2010) defined on an absorbing continuous time Markov chain (Horváth and Telek, 2007).…”

confidence: 99%