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1.
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
2.
Tommaso Flaminio 《Archive for Mathematical Logic》2007,46(3-4):301-319
In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a
purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be
characterized by means of the logical consistency of a suitable theory T
χ defined on the modal-fuzzy logic FP
k
(RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. 3571, 2005) in order
to treat conditional probability by means of a list of simple probabilities following the well known (smart) ideas exposed
by Halpern (Proceedings of the eighth conference on theoretical aspects of rationality and knowledge, pp 17–30, 2001) and
by Coletti and Scozzafava (Trends Logic 15, 2002). Roughly speaking, such logic is obtained by adding to the language of RŁΔ a list of k modalities for “probably” and axioms reflecting the properties of simple probability measures. Moreover we prove that the satisfiability problem for
modal formulas of FP
k
(RŁΔ) is NP-complete. Finally, as main result of this paper, we prove FP
k
(RŁΔ) in order to prove that the problem of establishing the coherence of rational assessments of conditional probability is NP-complete.
相似文献
3.
Let (Ω,ℬ,P) be a probability space,
a sub-σ-field, and μ a regular conditional distribution for P given
. For various, classically interesting, choices of
(including tail and symmetric), we prove the following 0–1 law: There is a set
such that P(A
0)=1 and μ(ω)(A)∈{0,1} for all
and ω∈A
0. If ℬ is countably generated (and certain regular conditional distributions exist), the result applies whatever P is.
相似文献
4.
Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure
operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVá,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
5.
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
6.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
7.
Age-dependent branching processes in random environments 总被引:4,自引:0,他引:4
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. 相似文献
8.
For a big number of varieties
of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups
in the class
does not coincide with the variety
of all o-approximable lattice-ordered groups.
Supported by FP “Universities of Russia” grant No. UR.04.01.001.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 20–27, January–February, 2006. 相似文献
9.
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
10.
A construction of codes of length n = q + 1 and minimum Hamming distance 3 over is given. Substitution of the derived codes into a concatenation construction yields nonlinear binary single-error correcting codes with better than known parameters. In particular, new binary single-error correcting codes having more codewords than the best previously known in the range n ≤ 512 are obtained for the lengths 64–66, 128–133, 256–262, and 512. 相似文献
11.
A frequently occurring problem is to find a probability vector,p∈D, which minimizes theI-divergence between it and a given probability vector π. This is referred to as theI-projection of π ontoD. Darroch and Ratcliff (1972,Ann. Math. Statist.,43, 1470–1480) gave an algorithm whenD is defined by some linear equalities and in this paper, for simplicity of exposition, we propose an iterative procedure whenD is defined by some linear inequalities. We also discuss the relationship betweenI-projection and the maximum likelihood estimation for multinomial distribution. All of the results can be applied to isotonic
cone. 相似文献
12.
P. Wojtaszczyk 《Foundations of Computational Mathematics》2010,10(1):1-13
In compressed sensing, we seek to gain information about a vector x∈ℝ
N
from d
≪
N nonadaptive linear measurements. Candes, Donoho, Tao et al. (see, e.g., Candes, Proc. Intl. Congress Math., Madrid, 2006; Candes et al., Commun. Pure Appl. Math. 59:1207–1223, 2006; Donoho, IEEE Trans. Inf. Theory 52:1289–1306, 2006) proposed to seek a good approximation to x via ℓ
1 minimization. In this paper, we show that in the case of Gaussian measurements, ℓ
1 minimization recovers the signal well from inaccurate measurements, thus improving the result from Candes et al. (Commun.
Pure Appl. Math. 59:1207–1223, 2006). We also show that this numerically friendly algorithm (see Candes et al., Commun. Pure Appl. Math. 59:1207–1223, 2006) with overwhelming probability recovers the signal with accuracy, comparable to the accuracy of the best k-term approximation in the Euclidean norm when k∼d/ln N. 相似文献
13.
Mark Voorneveld 《International Journal of Game Theory》2006,34(1):105-121
The t-solutions introduced in R. W. Rosenthal (1989, Int J Game Theory 18:273–292) are quantal response equilibria based on the linear probability model. Choice probabilities in t-solutions are related to the determination of leveling taxes in taxation problems. The set of t-solutions coincides with the set of Nash equilibria of a game with quadratic control costs. Evaluating the set of t-solutions for increasing values of t yields that players become increasingly capable of iteratively eliminating never-best replies and eventually only play rationalizable actions with positive probability. These features are not shared by logit quantal response equilibria. Moreover, there exists a path of t-solutions linking uniform randomization to Nash equilibrium 相似文献
14.
S. Zamarys 《Lithuanian Mathematical Journal》2006,46(4):494-508
We obtain upper and lower bounds for fractional moments of Dirichlet L-functions.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 606–621, October–December, 2006. 相似文献
15.
Let k and m are positive integers with k ≥ m. The probability generating function of the waiting time for the first occurrence of consecutive k successes in a sequence of m-th order Markov dependent trials is given as a function of the conditional probability generating functions of the waiting
time for the first occurrence of consecutive m successes. This provides an efficient algorithm for obtaining the probability generating function when k is large. In particular, in the case of independent trials a simple relationship between the geometric distribution of order
k and the geometric distribution of order k−1 is obtained.
This research was partially supported by the ISM Cooperative Research Program(2004-ISM-CRP-2006) and by a Grant-in-Aid for
Scientific Research (C) of the JSPI (Grant Number 16500183) 相似文献
16.
Alexej P. Pynko 《Logica Universalis》2010,4(1):41-66
In this paper, we study multiplicative extensions of propositional many-place sequent calculi for finitely-valued logics arising
from those introduced in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) through their translation
by means of singularity determinants for logics and restriction of the original many-place sequent language. Our generalized approach, first of all, covers, on
a uniform formal basis, both the one developed in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004)
for singular finitely-valued logics (when singularity determinants consist of a variable alone) and conventional Gentzen-style
(i.e., two-place sequent) calculi suggested in Pynko (Bull Sect Logic 33(1):23–32, 2004) for finitely-valued logics with equality
determinant. In addition, it provides a universal method of constructing Tait-style (i.e., one-place sequent) calculi for
finitely-valued logics with singularity determinant (in particular, for Łukasiewicz finitely-valued logics) that fits the
well-known Tait calculus (Lecture Notes in Mathematics, Springer, Berlin, 1968) for the classical logic. We properly extend
main results of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) and explore calculi under consideration within
the framework of Sect. 7 of Pynko (Arch Math Logic 45:267–305, 2006), generalizing the results obtained in Sect. 7.5 of Pynko
(Arch Math Logic 45:267–305 2006) for two-place sequent calculi associated with finitely-valued logics with equality determinant
according to Pynko (Bull Sect Logic 33(1):23–32, 2004). We also exemplify our universal elaboration by applying it to some
denumerable families of well-known finitely-valued logics. 相似文献
17.
Roberta Tognari 《Potential Analysis》2007,26(2):163-188
We consider the operator in L
2(B, ν) and in L
1(B, ν) with Neumann boundary condition, where U is an unbounded function belonging to for some q ∈(1, ∞), B is the possibly unbounded convex open set in where U is finite and ν(dx) = C exp (−2U (x))dx is a probability measure, infinitesimally invariant for N
0. We prove that the closure of N
0 is a m-dissipative operator both in L
2(B, ν) and in L
1(B, ν). Moreover we study the properties of ergodicity and strong mixing of the measure ν in the L
2 case.
相似文献
18.
Let X
1, X
2, ... be a sequence obtained by Polya's urn scheme. We consider a waiting time problem for the first occurrence of a pattern in the sequence X
1, X
2, ... , which is generalized by a notion score. The main part of our results is derived by the method of generalized probability generating functions. In Polya's urn scheme, the system of equations is composed of the infinite conditional probability generating functions, which can not be solved. Then, we present a new methodology to obtain the truncated probability generating function in a series up to an arbitrary order from the system of infinite equations. Numerical examples are also given in order to illustrate the feasibility of our results. Our results in this paper are not only new but also a first attempt to treat the system of infinite equations. 相似文献
19.
20.
Vasile Preda Ioan Stancu-Minasian Miruna Beldiman Andreea M?d?lina Stancu 《Journal of Global Optimization》2009,44(1):131-148
In the last time important results in multiobjective programming involving type-I functions were obtained (Yuan et al. in:
Konnov et al. (eds) Lecture notes in economics and mathematical systems, 2007; Mishra et al. An Univ Bucureşti Ser Mat, LII(2):
207–224, 2003). Following one of these ways, we study optimality conditions and generalized Mond-Weir duality for multiobjective
programming involving n-set functions which satisfy appropriate generalized univexity V-type-I conditions. We introduce classes of functions called
(ρ, ρ′)-V-univex type-I, (ρ, ρ′)-quasi V-univex type-I, (ρ, ρ′)-pseudo V-univex type-I, (ρ, ρ′)-quasi pseudo V-univex type-I, and (ρ, ρ′)-pseudo quasi V-univex type-I. Finally, a general frame for constructing functions of these classes is considered.
This research was supported by Grant PN II code ID No. 112/01.10.2007, CEEX code 1/2006 No. 1531/2006, and CNCSIS A No. 105
GR/2006. 相似文献