The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Jian Zhou - One of the best experts on this subject based on the ideXlab platform.
-
Renewal Reward Process With Uncertain Interarrival Times and Random Rewards
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Kai Yao, Jian ZhouAbstract:Renewal reward process is used to measure the cumulative occasional rewards up to some given time. So far, two basic types of renewal reward processes with only random parameters or with only uncertain parameters have been proposed. This paper aims at proposing a new type of renewal reward process, which has uncertain Interarrival times and random rewards in the framework of the chance theory. The chance distribution of such an uncertain random renewal reward process is obtained, and the reward rate is derived. A renewal reward theorem is verified to show that the reward rate converges in distribution to an uncertain variable, which is highly related to the Interarrival times and the expected values of random rewards.
Kai Yao - One of the best experts on this subject based on the ideXlab platform.
-
Renewal Reward Process With Uncertain Interarrival Times and Random Rewards
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Kai Yao, Jian ZhouAbstract:Renewal reward process is used to measure the cumulative occasional rewards up to some given time. So far, two basic types of renewal reward processes with only random parameters or with only uncertain parameters have been proposed. This paper aims at proposing a new type of renewal reward process, which has uncertain Interarrival times and random rewards in the framework of the chance theory. The chance distribution of such an uncertain random renewal reward process is obtained, and the reward rate is derived. A renewal reward theorem is verified to show that the reward rate converges in distribution to an uncertain variable, which is highly related to the Interarrival times and the expected values of random rewards.
Junzo Watada - One of the best experts on this subject based on the ideXlab platform.
-
Fuzzy random renewal reward process and its applications
Information Sciences, 2009Co-Authors: Shuming Wang, Junzo WatadaAbstract:This paper studies a renewal reward process with fuzzy random Interarrival times and rewards under the @?-independence associated with any continuous Archimedean t-norm @?. The Interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are @?-independent fuzzy variables. Under these conditions, some limit theorems in mean chance measure are derived for fuzzy random renewal rewards. In the sequel, a fuzzy random renewal reward theorem is proved for the long-run expected reward per unit time of the renewal reward process. The renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory. Finally, some application examples are provided to illustrate the utility of the result.
Shuming Wang - One of the best experts on this subject based on the ideXlab platform.
-
Fuzzy random renewal reward process and its applications
Information Sciences, 2009Co-Authors: Shuming Wang, Junzo WatadaAbstract:This paper studies a renewal reward process with fuzzy random Interarrival times and rewards under the @?-independence associated with any continuous Archimedean t-norm @?. The Interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are @?-independent fuzzy variables. Under these conditions, some limit theorems in mean chance measure are derived for fuzzy random renewal rewards. In the sequel, a fuzzy random renewal reward theorem is proved for the long-run expected reward per unit time of the renewal reward process. The renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory. Finally, some application examples are provided to illustrate the utility of the result.
Jian-qiang Hu - One of the best experts on this subject based on the ideXlab platform.
-
The Departure Process of the GI/G/1 Queue and Its MacLaurin Series
Operations Research, 1996Co-Authors: Jian-qiang HuAbstract:In this paper, we study the departure process of the GI/G/1 queue. We develop a simple recursive procedure to calculate the MacLaurin series of its moments and covariances with respect to a parameter in the service time. Based on this recursive procedure the explicit formulas of the coefficients of these MacLaurin series can be obtained in terms of derivatives of the probability density function of the Interarrival time evaluated at zero and the moments of the Interarrival time and the service time. One important application of these MacLaurin series is that they can be used to obtain the entire response curves of the moments and variances of the departure process, for example, via interpolation by polynomials or rational functions.
-
THE MACLAURIN SERIES FOR THE GI/G/1 QUEUE
Journal of Applied Probability, 1992Co-Authors: Weibo Gong, Jian-qiang HuAbstract:We derive the MacLaurin series for the moments of the system time and the delay with respect to the parameters in the service time or Interarrival time distributions in the GI/G /1 queue. The coefficients in these series are expressed in terms of the derivatives of the Interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The light traffic derivatives can be obtained from these series. For the M/G /1 queue, we are able to recover the formulas for the moments of the system time and the delay, including the Pollaczek–Khinchin mean-value formula.