共查询到20条相似文献,搜索用时 15 毫秒
1.
Colin M. Ramsay 《Queueing Systems》2007,57(4):147-155
This paper solves the problem of finding exact formulas for the waiting time cdf and queue length distribution of first-in-first-out
M/G/1 queues in equilibrium with Pareto service. The formulas derived are new and are obtained by directly inverting the relevant
Pollaczek-Khinchin formula and involve single integrals of non-oscillating real valued functions along the positive real line.
Tables of waiting time and queue length probabilities are provided for certain parameter values under heavy traffic conditions.
相似文献
2.
We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service
requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where
the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results
of Morrison (SIAM J. Appl. Math. 45:152–167, [1985]) and Flatto (Ann. Appl. Probab. 7:382–409, [1997]).
This work was partly supported by NSF grant DMS 05-03745. 相似文献
3.
Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′)
n
assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given.
This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation
of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development
(Grant No. G-809-234.6/2003) 相似文献
4.
G. Falin 《Queueing Systems》2008,58(1):65-76
We consider the M/M/∞ queueing system with arrival and service rate depending on the state of an auxiliary semi-Markov process (which can be
viewed as an external environment) and find the mean number of customers in the system in steady state. In a particular case
when the external environment can be only in two states we find the distribution of the number of customers in the system.
相似文献
5.
In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single
server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute
the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution
is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions.
Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical
experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.
相似文献
6.
Using recursive method,this paper studies the queue size properties at any epoch n + in Geom/G/1(E,SV) queueing model with feedback under LASDA (late arrival system with delayed access) setup.Some new results about the recursive expressions of queue size distribution at different epoch (n+,n,n-) are obtained.Furthermore the important relations between stationary queue size distribution at different epochs are discovered.The results are different from the relations given in M/G/1 queueing system.The model discussed in this paper can be widely applied in many kinds of communications and computer network. 相似文献
7.
We consider an M
[X]/G/1 retrial queue subject to breakdowns where the retrial time is exponential and independent of the number of customers applying
for service. If a coming batch of customers finds the server idle, one of the arriving customers begins his service immediately
and the rest joins a retrial group (called orbit) to repeat his request later; otherwise, if the server is busy or down, all
customers of the coming batch enter the orbit. It is assumed that the server has a constant failure rate and arbitrary repair
time distribution. We study the ergodicity of the embedded Markov chain, its stationary distribution and the joint distribution
of the server state and the orbit size in steady-state. The orbit and system size distributions are obtained as well as some
performance measures of the system. The stochastic decomposition property and the asymptotic behavior under high rate of retrials
are discussed. We also analyse some reliability problems, the k-busy period and the ordinary busy period of our retrial queue. Besides, we give a recursive scheme to compute the distribution
of the number of served customers during the k-busy period and the ordinary busy period. The effects of several parameters on the system are analysed numerically.
I. Atencia’s and Moreno’s research is supported by the MEC through the project MTM2005-01248. 相似文献
8.
9.
We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M
X
/G/1/n systems. 相似文献
10.
William D. BANKS Florian LUCA 《数学学报(英文版)》2007,23(10):1915-1918
In this note, we show that the number of composite integers n ≤ x such that φ(n)|n - 1 is at most O(x^1/2(loglog x)^1/2), thus improving earlier results by Pomerance and by Shan. 相似文献
11.
A. M. Bratiichuk 《Ukrainian Mathematical Journal》2007,59(9):1300-1312
For finite-capacity queuing systems of the type M
θ/G/1, convenient formulas for the ergodic distribution of the queue length are found, an estimate for the rate of convergence
of the distribution of the queue length in the transient mode to the ergodic distribution is obtained, and computational algorithms
for finding the rate of convergence are presented.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1169–1178, September, 2007. 相似文献
12.
Gautam Choudhury 《TOP》2003,11(1):141-150
This paper examines the steady state behaviour of anM/G/1 queue with a second optional service in which the server may provide two phases of heterogeneous service to incoming units.
We derive the queue size distribution at stationary point of time and waiting time distribution. Moreover we derive the queue
size distribution at the departure point of time as a classical generalization of the well knownPollaczek Khinchin formula. This is a generalization of the result obtained by Madan (2000).
This work is supported by Department of Atomic Energy, Govt. of India, NBHM Project No. 88/2/2001/R&D II/2001. 相似文献
13.
We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system
workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer
content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order
linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve
them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical
examples.
相似文献
14.
Avrachenkov et al. (Queueing Syst. 50:459–480, [2005]) conjectured that in an M/G/1 processor-sharing queue with batch arrivals, the conditional mean sojourn time is concave. In this paper, we show that
this conjecture is generally not true.
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00470). 相似文献
15.
Lascar described E
KP
as a composition of E
L
and the topological closure of E
L
(Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated
by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G
L
. We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories.
The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment
grant N201 032 32/2231. 相似文献
16.
17.
S K Samanta U C Gupta R K Sharma 《The Journal of the Operational Research Society》2007,58(3):368-377
This paper investigates a discrete-time single-server finite-buffer queueing system with multiple vacations in which arrivals occur according to a discrete-time renewal process. Service and vacation times are mutually independent and geometrically distributed. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer's observation epochs under the late arrival system with delayed access and early arrival system. The analysis of actual waiting-time for both the systems has also been carried out. The model has potential application in high-speed computer network, digital communication systems and other related areas. 相似文献
18.
A. M. Bratiichuk 《Ukrainian Mathematical Journal》2007,59(7):976-983
We consider a queuing system of the type M
θ/G/1/b in which the input stream is regulated by a certain threshold level. The asymptotic properties of the first busy period and
the number of calls served during this period are studied.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 884–889, July, 2007. 相似文献
19.
V. A. Belavin 《Theoretical and Mathematical Physics》2007,152(3):1275-1285
We present explicit recursion relations for the four-point superconformal block functions that are essentially particular
contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties
of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra.
We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated
operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation
function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely
conformal symmetry.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 476–487, September, 2007. 相似文献
20.
We prove that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the
p-rank of Ext
ℤ(G, ℤ) is as large as possible for every prime p and for any torsion-free Abelian group G. Moreover, given an uncountable
strong limit cardinal μ of countable cofinality and a partition of Π (the set of primes) into two disjoint subsets Π0 and Π1, we show that in some model which is very close to ZFC, there is an almost free Abelian group G of size 2μ = μ+ such that the p-rank of Ext
ℤ(G, ℤ) equals 2μ = μ+ for every p ∈ Π0 and 0 otherwise, that is, for p ∈ Π1.
Number 874 in Shelah’s list of publications. Supported by the German-Israeli Foundation for Scientific Research & Development
project No. I-706-54.6/2001.
Supported by a grant from the German Research Foundation DFG.
__________
Translated from Algebra i Logika, Vol. 46, No. 3, pp. 369–397, May–June, 2007. 相似文献