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1.
本文首先证明当服务强度小于1时,GI/G/1排队系统的队长是一个特殊的马尔可夫骨架过程——正常返的Doob骨架过程,然后运用马尔可夫骨架过程的强大数定律和中心极限定理等重要结果,给出了队长的累积过程的期望和方差,并给出了该累积过程满足强大数定律和中心极限定理的充分条件。 相似文献
2.
Necessary and sufficient conditions for the validity of the strong law of large numbers for pairwise negatively dependent random variables with infinite means are formulated. 相似文献
3.
A study is made of an M/G/1-type queuing model in which customers receive one type of service until such time as, at the end of a service, the queue size is found to exceed a given value N, N ≥ 1. Then a second type of service is put into effect and remains in use until the queue size is reduced to a fixed value K, 0 ≤ K ≤ N. Equations are derived for the stationary probabilities both at departure times and at general times. An algorithm is developed that allows the rapid computation of the mean queue length and some important probabilities. 相似文献
4.
A limit of a sequence of fuzzy numbers is defined and its some properties are shown. Based on these concept and properties, an independent sequence of fuzzy random variables is considered and a strong law of large numbers for fuzzy random variables is shown. 相似文献
5.
We find conditions for E(W
) to be finite whereW is the stationary waiting time random variable in a stableG/G/1 queue with dependent service and inter-arrival times.Supported in part by KBN under grant 640/2/9, and at the Center for Stochastic Processes, Department of Statistics at the University of North Carolina Chapel Hill by the Air Force Office of Scientific Research Grant No. 91-0030 and the Army Research Office Grant No. DAAL09-92-G-0008. 相似文献
6.
For a double array of blockwise M-dependent random variables {X mn ,m ?? 1, n ?? 1}, strong laws of large numbers are established for double sums ?? i=1 m ?? j=1 n X ij , m ?? 1, n ?? 1. The main results are obtained for (i) random variables {X mn ,m ?? 1, n ?? 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and (ii) random variables {X mn ,m ?? 1, n ?? 1} being stochastically dominated. The result in Case (i) generalizes the main result of Móricz et al. [J. Theoret. Probab., 21, 660?C671 (2008)] from dyadic to arbitrary blocks, whereas the result in Case (ii) extends a result of Gut [Ann. Probab., 6, 469?C482 (1978)] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples. 相似文献
7.
In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point “environment viewed from the particle”, under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk. 相似文献
8.
John Baxter Roger Jones Michael Lin James Olsen 《Journal of Theoretical Probability》2004,17(1):165-181
For any sequence {a
k
} with sup
for some q>1, we prove that
converges to 0 a.s. for every {X
n
} i.i.d. with E(|X
1|)< and E(X
1)=0; the result is no longer true for q=1, not even for the class of i.i.d. with X
1 bounded. We also show that if {a
k
} is a typical output of a strictly stationary sequence with finite absolute first moment, then for every i.i.d. sequence {X
n
{ with finite absolute pth moment for some p> 1,
converges a.s. 相似文献
9.
Joseph C. Watkins 《Stochastic Processes and their Applications》1985,19(2):189-224
On a separable Banach space, let A(ξ1),A(ξ2),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξi) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions. 相似文献
10.
A. E. Mikusheva 《Mathematical Notes》2000,67(3):301-308
In this paper we study the limiting behavior of sums of dependent random variables under a strong mixing condition. We obtain
conditions for which an analog of the Baum-Katz theorem holds and cite an example showing their optimality.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 360–368, March, 2000. 相似文献
11.
《Stochastic Processes and their Applications》2014,124(5):1942-1973
We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem for thinned power variations. 相似文献
12.
In this paper a fluid approximation, also known as a functional strong law of large numbers (FSLLN) for a GI/G/1 queue under a processor-sharing service discipline is established and its properties are analysed. The fluid limit depends
on the arrival rate, the service time distribution of the initial customers, and the service time distribution of the arriving
customers. This is in contrast to the known result for the GI/G/1 queue under a FIFO service discipline, where the fluid limit is piecewise linear and depends on the service time distribution
only through its mean. The piecewise linear form of the limit can be recovered by an equilibrium type choice of the initial
service distribution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is hereby strengthened. 相似文献
14.
Yong-jiang Guo 《应用数学学报(英文版)》2011,27(1):43-58
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... 相似文献
15.
Three kinds of queues with Markovian arrival process and/or Markovian service process, are considered in this paper. In great generality, their basic steady-state distributions have asymptotically exponential tails. We investigate the sensitivity of these asymptotic decay rates to the small entrywise perturbations in the parameter matrices of the Markovian arrival process. 相似文献
16.
In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N-(V, E)-queue. Exact asymptotic rates of the loss probability are obtained for the cases in which the traffic intensity is smaller than, equal to and greater than one, respectively. When the vacation time is zero, the model considered degenerates to the standard M/G/1/N queue. For this standard queueing model, our analysis provides new or extended asymptotic results for the loss probability. In terms of the duality relationship between the M/G/1/N and GI/M/1/N queues, we also provide asymptotic properties for the standard GI/M/1/N model. 相似文献
17.
We consider a discrete time random environment. We state that when the random walk on real number space in a environment is i.i.d., under the law, the law of large numbers, iterated law and CLT of the process are correct space-time random marginal annealed Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain. 相似文献
18.
Chang-Long Yao 《Stochastic Processes and their Applications》2018,128(2):445-460
Consider (independent) first-passage percolation on the sites of the triangular lattice embedded in . Denote the passage time of the site in by , and assume that . Denote by the passage time from 0 to the halfplane , and by the passage time from 0 to the nearest site to , where . We prove that as , a.s., and Var; in probability but not a.s., and Var. This answers a question of Kesten and Zhang (1997) and improves our previous work (2014). From this result, we derive an explicit form of the central limit theorem for and . A key ingredient for the proof is the moment generating function of the conformal radii for conformal loop ensemble , given by Schramm et al. (2009). 相似文献
19.
Consider a system where units having random magnitude enter according to a Poisson process. While in the system, a unit's magnitude may change with time. In this paper we obtain a functional limit theorem for the sum process of all unit magnitudes present in the system at time t. 相似文献
20.
We consider a GI/G/1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail,
i.e., a tail behaviour like t
−ν with 1 < ν ⩽ 2 , so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the
distribution of the stationary actual waiting time W. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic
load a → 1, then W, multiplied by an appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than
that of the service time distribution, and the traffic load a → 1, then W, multiplied by another appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the negative exponential distribution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献