The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of t...The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.展开更多
In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the as...In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.展开更多
A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. T...A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.展开更多
For M/G/1 and GI/G/1 queues this paper systematically studies the following problem: (i) The ages, the remaining lifes and the total lifes of the service time and the busy period. (ii) The asymptotic expansions of the...For M/G/1 and GI/G/1 queues this paper systematically studies the following problem: (i) The ages, the remaining lifes and the total lifes of the service time and the busy period. (ii) The asymptotic expansions of the expected number of departures that occurs during (0, t]. Some new results are obtained by employing the probability decomosition technique and the renewal theory.展开更多
基金partially supported by the Fundamental Research Funds for the Central Universities (BUPT2011RC0703)
文摘The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.
基金supported by the National Natural Science Foundation of China under Grant No.11471053
文摘In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.
基金Supported by the National Natural Science Foundation of China (No. 10826047 and No.10901023)by the Fundamental Research Funds for the Central Universities under Contract BUPT2009RC0707
文摘A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.
文摘For M/G/1 and GI/G/1 queues this paper systematically studies the following problem: (i) The ages, the remaining lifes and the total lifes of the service time and the busy period. (ii) The asymptotic expansions of the expected number of departures that occurs during (0, t]. Some new results are obtained by employing the probability decomosition technique and the renewal theory.
