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1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
In this note we first define the notions of (weak, strong) implicative hyper K-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we obtain some relations between these notions and (weak) implicative hyper K-ideals. Finally, we study the implicative hyper K-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper K-algebras and (weak, strong) implicative hyper K-algebras under a simple condition. 相似文献
9.
Hong Ya GAO Shu Qing ZHOU 《数学学报(英文版)》2007,23(12):2241-2246
We obtain a new inequality for weakly (K1,K2)-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of (K1, K2)-Quasiregular Mappings. 相似文献
10.
For given a graph H, a graphic sequence π = (d
1, d
2,..., d
n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K
5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to
be potentially K
5-graphic, where K
r is a complete graph on r vertices and K
r-e is a graph obtained from K
r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence
π to be potentially K
6-graphic.
Project supported by National Natural Science Foundation of China (No. 10401010). 相似文献
11.
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
12.
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
13.
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
14.
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
15.
Artur Piękosz 《Central European Journal of Mathematics》2003,1(4):441-456
We prove rectilinearization and uniformization theorems for K-subanalytic (∝
an
K
-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic
case. 相似文献
16.
R. Norvaiša 《Lithuanian Mathematical Journal》2008,48(4):418-426
Let B
H,K
= {B
H,K
(t)}
t⩾0 be a bifractional Brownian motion with parameters H ∈ (0, 1) and K ∈ (0, 1]. For a function Φ: [0, ∞) → [0, ∞) and for a partition κ = {t
i
}n
i=0 of an interval [0, T] with T > 0, let {ie418-01}. We prove that, for a suitable Φ depending on H and K, {ie418-02} almost surely.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-16/08 相似文献
17.
Andrej Dujella 《The Ramanujan Journal》2008,15(1):37-46
A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine
sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine
m-tuples for m=2, 3 and 4.
In this paper, we derive asymptotic estimates for the number of Diophantine pairs, triples and quadruples with elements less
than given positive integer N.
The author was supported by the Ministry of Science and Technology, Republic of Croatia, grants 0037110 and 037-0372781-2821. 相似文献
18.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(4):1099-1105
A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.
This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.
The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
19.
Amalendu Ghosh Ramesh Sharma Jong Taek Cho 《Annals of Global Analysis and Geometry》2008,34(3):287-299
We show that a non-Sasakian contact metric manifold with η-parallel torsion tensor and sectional curvatures of plane sections containing the Reeb vector field different from 1 at some
point, is a (k, μ)-contact manifold. In particular for the standard contact metric structure of the tangent sphere bundle the torsion tensor
is η-parallel if and only if M is of constant curvature, in which case its associated pseudo-Hermitian structure is CR- integrable. Next we show that if
the metric of a non-Sasakian (k, μ)-contact manifold (M, g) is a gradient Ricci soliton, then (M, g) is locally flat in dimension 3, and locally isometric to E
n+1 × S
n
(4) in higher dimensions.
相似文献
20.
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