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1.
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
2.
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
3.
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
4.
This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology
Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). 相似文献
5.
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
6.
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
7.
We investigate GI
X
/M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the
system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals
and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities.
These results are then used to derive the continuous-time long-run distribution of the number of customers in the system.
Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors
of the computed performance measures.
相似文献
8.
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
9.
Thomas Vougiouklis 《数学学报(英文版)》2008,24(7):1067-1078
The hyperoperations, called theta-operations (δ), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures. 相似文献
10.
Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of
S
S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor
S-posets have property (P
w
).
Research supported by nwnu-kjcxgc-03-18. 相似文献
11.
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
12.
Jinjin Li 《Czechoslovak Mathematical Journal》2005,55(4):941-945
In this note we study the relation between k
R
-spaces and k-spaces and prove that a k
R
-space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k
R
-space with a point-countable k-network consisting of compact subsets need not be a k-space.
This work was supported by the NSF of China (10271056). 相似文献
13.
Florentina Chirte§ 《Central European Journal of Mathematics》2005,3(1):105-124
The aim of this paper is to define the localization LM
n
-algebra of an LM
n
—algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM
n
-algebra of fractions (defined in [3]) and the LM
n
-algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM
n
-algebras of localization. 相似文献
14.
ChangJian Zhao 《中国科学A辑(英文版)》2008,51(12):2172-2188
In this paper the author first introduce a new concept of L
p
-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L
p
intersection body to L
p
-mixed intersection body. Inequalities for L
p
-dual mixed volumes of L
p
-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation
of the Education Department of Zhejiang Province of China (Grant No. 20050392) 相似文献
15.
Abdellah El Kinani 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):229-238
We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.
相似文献
16.
Iddo Eliazar 《Queueing Systems》2007,55(1):71-82
We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated.
We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied
to various examples, including ones with infinite queues and non-summable workloads.
AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10 相似文献
17.
G. I. Falin 《Queueing Systems》2008,58(3):155-160
Sherman and Kharoufeh (Oper. Res. Lett. 34:697–705, [2006]) considered an M/M/1 type queueing system with unreliable server and retrials. In this model it is assumed that if the server fails during service
of a customer, the customer leaves the server, joins a retrial group and in random intervals repeats attempts to get service.
We suggest an alternative method for analysis of the Markov process, which describes the functioning of the system, and find
the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial
group in steady state.
相似文献
18.
Chris Field John Robinson Elvezio Ronchetti 《Annals of the Institute of Statistical Mathematics》2008,60(1):225-227
We obtain marginal tail area approximations for the one-dimensional test statistic based on the appropriate component of the
M-estimate for both standardized and Studentized versions which are needed for tests and confidence intervals. The result is
proved under conditions which allow the application to finite sample situations such as the bootstrap and involves a careful
discretization with saddlepoints being used for each neighbourhood. These results are used to obtain second-order relative
error results on the accuracy of the Studentized and the tilted bootstrap. The tail area approximations are applied to a Poisson
regression model and shown to have very good accuracy.
An erratum to this article can be found at 相似文献
19.
In this paper we develop a theory of companion d-algebras in sufficient detail to demonstrate considerable parallelism with the theory of BCK-algebras as well as obtaining a collection of results of a novel type. Included among the latter are results on certain natural
posets associated with companion d-algebras as well as constructions on Bin(X), the collection of binary operations on the set X, which permit construction of new companion d-algebras from companion d-algebras X also in natural ways.
Supported by Korea Research Foundation Grant (KRF-2002-041-C00003). 相似文献
20.
R. M. Mnatsakanov N. Misra Sh. Li E. J. Harner 《Mathematical Methods of Statistics》2008,17(3):261-277
For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based
on the Euclidean distances between the n sample points and their k
n
-nearest neighbors, where {k
n
: n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.
相似文献