bluuebunny/crossref_metadata_2025 huggingface dataset:
Existence principles for second order nonresonant boundary value problems
Authors: O′Regan Donal
Published: March 2007

We discuss the two point singular “nonresonant” boundary value problem
a.e. on [0, 1] with y satisfying Sturm Liouville, Neumann,
Periodic or Bohr boundary conditions. Here f is an L1‐Carathéodory function
and p ∈ C[0, 1]∩C1(0, 1) with p > 0 on (0, 1).
Existence of solutions for second‐order evolution inclusions
Authors: Papageorgiou Nikolaos S.
Published: March 2007

In this paper we examine second‐order nonlinear evolution inclusions and
prove two existence theorems; one with a convex‐valued orientor field and the
other with a nonconvex‐valued field. An example of a hyperbolic partial differential inclusion is also presented.
Well posedness for evolution inclusions
Authors: Balachandran K. , Anguraj A.
Published: March 2007

We prove the existence of a continuous selection of the multivalued map
φ → Φ(φ) which is the set of all mild solutions of the evolution inclusion

urn:x-wiley:20903332:media:ista615767:ista615767-math-0001

Here F is a multivalued map, Lipschitzian with respect to x, and A is the
infinitesimal generator of a C0‐semigroup.
Further generalization of generalized quasilinearization method
Authors: Lakshmikantham V. , Shahzad N.
Published: March 2007

The question whether it is possible to develop monotone sequences that
converge to the solution quadratically when the function involved in the initial
value problem admits a decomposition into a sum of two functions, is answered
positively. This extends the method of generalized quasilinearization to a large
class.
Asymptotic properties of the solutions of a class of operator‐differential equations
Authors: Akça A. , Bainov D. D. , Dimitrova M. B.
Published: March 2007

Some asymptotic properties of the nonoscillating solutions of opreator‐differential equations of arbitrary order are investigated.
Almost periodic solutions to systems of parabolic equations
Authors: Nee Janpou
Published: March 2007

In this paper we show that the second‐order differential solution is 𝕃2‐almost
periodic, provided it is 𝕃2‐bounded, and the growth of the components of a non‐linear function of a system of parabolic equation is bounded by any pair of con‐secutive eigenvalues of the associated Dirichlet boundary value problems.
Diffusion approximation for first overflow time in GI/G/m system with finite capacity
Authors: Choi Bong Dae , Lee Yong Wan , Shin Yang Woo
Published: March 2007

We present a diffusion approximation of the first overflow time in the
GI/G/m system with finite capacity. We derive the Laplace Stieltjes transform
of the first passage time of diffusion process which approximates the system size
in the GI/G/m system with finite capacity. We use the first passage time of diffusion process as the first overflow time in the GI/G/m system with finite capacity. To check on accuracy of this approximation, the analytical results for the
mean of the first overflow time in the GI/G/m system with finite capacity is numerically compared with the diffusion approximation results. Numerical results
show that the diffusion approximation is a good approximation for heavy traffic
systems.
A system of impulsive degenerate nonlinear parabolicfunctional‐differential inequalities
Authors: Byszewski Ludwik
Published: March 2007

A theorem about a system of strong impulsive degenerate nonlinear parabolic
functional‐differential inequalities in an arbitrary parabolic set is proved. As a
consequence of the theorem, some theorems about impulsive degenerate nonlinear
parabolic differential inequalities and the uniqueness of a classical solution of an
impulsive degenerate nonlinear parabolic differential problem are established.
Existence of asymptotic solutions of second order neutraldifferential equation with multiple delays
Authors: Palaniswami S. C.
Published: March 2007

The existence of positive solutions of second order neutral differential
equation of the form

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is investigated. Some sufficient conditions are given for the existence of positive
solutions with asymptotic decay of (A). Examples are presented to illustrate the
results.
Random variational inequalities in the absence of sample path continuity
Authors: Elsanousi S. A.
Published: March 2007

In this paper we investigate the existence of solutions to stochastic variational inequalities under conditions that are not imposed sample‐path‐wise.
A discrete single server queue with Markovian arrivals and phase type group services
Authors: Alfa Attahiru Sule , Dolhun K. Laurie , Chakravarthy S.
Published: March 2007

We consider a single‐server discrete queueing system in which arrivals occur
according to a Markovian arrival process. Service is provided in groups of size no
more than M customers. The service times are assumed to follow a discrete
phase type distribution, whose representation may depend on the group size.
Under a probabilistic service rule, which depends on the number of customers
waiting in the queue, this system is studied as a Markov process. This type of
queueing system is encountered in the operations of an automatic storage retrieval system. The steady‐state probability vector is shown to be of (modified)
matrix‐geometric type. Efficient algorithmic procedures for the computation of
the rate matrix, steady‐state probability vector, and some important system performance measures are developed. The steady‐state waiting time distribution is
derived explicitly. Some numerical examples are presented.
Error estimate for optimality of distributed parameter control problems via duality
Authors: Chan W. L. , Yung S. P.
Published: March 2007

Sharp error estimates for optimality are established for a class of distributed
parameter control problems that include elliptic, parabolic, hyperbolic systems
with impulsive control and boundary control. The estimates are obtained by
constructing manageable dual problems via the extremum principle.
Remarks on the controllability of nonlinear perturbations ofVolterra integrodifferential systems
Authors: Balachandran K. , Balasubramaniam P.
Published: March 2007

Sufficient conditions for the complete controllability of nonlinear perturbations of Volterra integrodifferential systems with implicit derivative are established. The results generalize the results of Dauer and Balachandran [9] and are obtained through the notions of condensing map and measure of noncompactness of
a set.
Brownian local times
Authors: Takács Lajos
Published: March 2007

In this paper explicit formulas are given for the distribution functions
and the moments of the local times of the Brownian motion, the reflecting Brownian motion, the Brownian meander, the Brownian bridge, the reflecting Brownian
bridge and the Brownian excursion.
Extreme solutions of nonlinear, second order integro‐differential equations in Banach spaces
Authors: Guo Dajun
Published: March 2007

After establishing a comparison result by means of a new method, we obtain
the existence of maximal and minimal solutions for nonlinear, second order integro‐differential equations of mixed type in Banach spaces.
Comments on a single server queue
Authors: Syski Ryszard
Published: March 2007

A review of the work of V.E. Benĕs and P. Brémaud on a single‐server queue
G/G/1 is interpreted in terms of point processes and associated martingales.

A concept of a discounted workload is introduced, and its connection with
random Dirichlet series and associated semigroups is investigated.
The transient M/G/1/0 queue: some bounds and approximations for light traffic with application to reliability
Authors: Atkinson J. Ben
Published: March 2007

We consider the transient analysis of the M/G/1/0 queue, for which Pn(t)
denotes the probability that there are no customers in the system at time t, given
that there are n(n = 0, 1) customers in the system at time 0. The analysis,
which is based upon coupling theory, leads to simple bounds on Pn(t) for the
M/G/1/0 and M/PH/1/0 queues and improved bounds for the special case
M/Er/1/0. Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon
the above bounds in light traffic, i.e., as λ → 0. An important area of application
for the M/G/1/0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that
context. A duality relation between the M/G/1/0 and GI/M/1/0 queues is also
described.
Some new deterministic and random variational inequalities and their applications
Authors: Yuan Xian-Zhi , Roy Jean-Marc
Published: March 2007

A non‐compact deterministic variational inequality which is used to prove an
existence theorem for saddle points in the setting of topological vector spaces and
a random variational inequality. The latter result is then applied to obtain the
random version of the Fan′s best approximation theorem. Several random fixed
point theorems are obtained as applications of the random best approximation
theorem.
On weak solutions of random differential inclusions
Authors: Michta Mariusz
Published: March 2007

In the paper we study the existence of solutions of the random differential inclusion

urn:x-wiley:20903332:media:ista802365:ista802365-math-0001

where G is a given set‐valued mapping value in the space Kn of all nonempty,
compact and convex subsets of the space ℝn, and μ is some probability measure
on the Borel σ‐algebra in ℝn. Under certain restrictions imposed on F and μ, we
obtain weak solutions of problem (I), where the initial condition requires that the
solution of (I) has a given distribution at time t = 0.
Some extensions of Bateman′s product formulas for the Jacobi polynomials
Authors: Chen Ming-Po , Srivastava H. M.
Published: March 2007

The authors derive generalizations of some remarkable product formulas of
Harry Bateman (1882‐1946) for the classical Jacobi polynomials. They also show
how the results considered here would lead to various families of linear, bilinear,
and bilateral generating functions for the Jacobi and related polynomials.
On an infinite‐dimensional differential equation in vectordistribution with discontinuous regular functions in a right hand side
Authors: Basin Michael V.
Published: March 2007

An infinite‐dimensional differential equation in vector distribution in a Hilbert space is studied in case of an unbounded operator and discontinuous regular
functions in a right‐hand side. A unique solution (vibrosolution) is defined for
such an equation, and the necessary and sufficient existence conditions for a vibrosolution are proved. An equivalent equation with a measure, which enables us to
directly compute jumps of a vibrosolution at discontinuity points of a distribution function, is also obtained. The application of the obtained results to control
theory is discussed in the conclusion.
M/G/1/K system with push‐out scheme under vacation policy
Authors: Kasahara Shoji , Takagi Hideaki , Takahashi Yutaka , Hasegawa Toshiharu
Published: March 2007

We consider an M/G/1/K system with push‐out scheme and multiple vacations. This model is particularly important in situations where it is essential to
provide short waiting times to messages which are selected for service. We
analyze the behavior of two types of messages: one that succeeds in transmission
and the other that fails. We derive the Laplace‐Stieltjes transform of the waiting
time distribution for the message which is eventually served. Finally, we show
some numerical results including the comparisons between the push‐out and the
ordinary blocking models.
Queueing system with passive servers
Authors: Dudin Alexander N. , Klimenok Valentina I.
Published: March 2007

In this paper the authors introduce systems in which customers are served by one active server and a group of passive servers. The calculation of response time for such systems is rendered by analyzing a special kind of queueing system in a synchronized random environment. For an embedded Markov chain, sufficient conditions for the existence of a stationary distribution are proved. A formula for the corresponding vector generating function is obtained. It is a matrix analog of the Pollaczek‐Khinchin formula and is simultaneously a matrix functional equation. A method for solving this equation is proposed.
Quantitative results for perturbed stochastic differentialequations
Authors: Stoyanov Jordan , Botev Dobrin
Published: March 2007

The paper is devoted to Itô type stochastic differential equations (SDE′s)
with “small“ perturbations. Our goal is to present strong results showing how
“close” are the 2m‐order moments of the solutions of the perturbed SDE′s and
the unperturbed SDE.
A stochastic model for the financial market with discontinuous prices
Authors: Minkova Leda D.
Published: March 2007

This paper models some situations occurring in the financial market. The
asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth
process covers some obligation. A solution to a linear stochastic integral equation
is obtained in a class of cadlag stochastic processes.
Two‐parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane
Authors: Mishura Yu. , Tomilov Yu.
Published: March 2007

We study two‐parameter coordinate‐wise C0‐semigroups and their generators,
as well as two‐parameter evolutions and differential equations up to the second
order for them. These results are applied to obtain the Hille‐Yosida theorem for
homogeneous Markov fields of the Feller type and to establish forward, backward, and mixed Kolmogorov equations for nonhomogeneous diffusion fields on
the plane.
Approximation of solutions to evolution integrodifferentialequations
Authors: Bahuguna D. , Srivastava S. K.
Published: March 2007

In this paper we study a class of evolution integrodifferential equations. We
first prove the existence and uniqueness of solutions and then establish the
convergence of Galerkin approximations to the solution.
Mixed problem with boundary integral conditions for a certain parabolic equation
Authors: Bouziani Abdelfatah
Published: March 2007

The present article is devoted to a proof of the existence and uniqueness of a
solution of a mixed problem with boundary integral conditions for a certain parabolic equation. The proof is based on an energy inequality and on the fact that
the range of the operator generated by the problem is dense.
Dobrushin′s approach to queueing network theory
Authors: Karpelevich F. I. , Pechersky E. A. , Suhov Yu. M.
Published: March 2007

R.L. Dobrushin (1929‐1995) made substantial contributions to Queueing Network Theory (QNT). A review of results from QNT which arose from his ideas
or were connected to him in other ways is given. We also comment on various
related open problems.
Sojourn times
Authors: Takács Lajos
Published: March 2007

Let {ζ(u), u ≥ 0} be a stochastic process with state space A ∪ B where A and
B are disjoint sets. Denote by β(t) the total time spent in state B in the interval
(0, t). This paper deals with the problem of finding the distribution of β(t) and
the asymptotic distribution of β(t) as t → ∞ for various types of stochastic processes. The main result is a combinatorial theorem which makes it possible to find
in an elementary way, the distribution of β(t) for homogeneous stochastic processes with independent increments.

This article is dedicated to the memory of Roland L. Dobrushin.
On the regularity of many‐particle dynamical systems perturbed by white noise
Authors: Skorokhod Anatoli V.
Published: March 2007

We consider a system of finite number of particles that are moving in Rd under mutual interaction. It is assumed that the particles are subjected to some
additional random forces which cause diffusion motion of the particles. The latter is described by a system of stochastic differential equations of the first order
for noninertia particles and the second order for inertial particles. The coefficient of the system are unbounded because the interaction force tends to infinity
if the distance between two particles tends to zero. The system is called regular
if no particle can hit the other. We investigate conditions of regularity.

This article is dedicated to the memory of Roland L. Dobrushin.
Population‐size‐dependent branching processes
Authors: Jagers Peter
Published: March 2007

In a recent paper [7] a coupling method was used to show that if population
size, or more generally population history, influence upon individual reproduction
in growing, branching‐style populations disappears after some random time, then
the classical Malthusian properties of exponential growth and stabilization of composition persist. While this seems self‐evident, as stated, it is interesting that it
leads to neat criteria via a direct Borel‐Cantelli argument: If m(n) is the expected number of children of an individual in an n‐size population and m(n) ≥ m > 1,
then essentially

urn:x-wiley:20903332:media:ista678052:ista678052-math-0001

suffices to guarantee Malthusian behavior with the same parameter as a limiting
independent‐individual process with expected offspring number m. (For simplicity the criterion is stated for the single‐type case here.)

However, this is not as strong as the results known for the special cases of
Galton‐Watson processes [10], Markov branching [13], and a binary splitting
tumor model [2], which all require only something like

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.

This note studies such latter criteria more generally. It is dedicated to the
memory of Roland L. Dobrushin.
Descriptors for point processes based on runs: the Markovian arrival process
Authors: Neuts Marcel F.
Published: March 2007

This paper is part of a broader investigation of properties of a point process
that can be identified by imagining that the process is involved in a competition
for the generation of runs of events. The general purpose of that methodology is
to quantify the prevalence of gaps and bursts in realizations of the process. The
Markovian arrival process (MAP) is highly versatile in qualitative behavior and
its analysis is numerically tractable by matrix‐analytic methods. It can therefore
serve well as a benchmark process in that investigation. In this paper, we consider the MAP and a regular grid competing for runs of lengths at least r1 and
r2, respectively. A run of length r in one of the processes is defined as a string of
r successive events occurring without an intervening event in the other process.

This article is dedicated to the memory of Roland L. Dobrushin.
The structure distribution in a mixed Poisson process
Authors: Teugels Jozef L. , Vynckier Petra
Published: March 2007

We use a variety of real inversion formulas to derive the structure distribution in a mixed Poisson process. These approaches should prove to be useful in
applications, e.g., in insurance where such processes are very popular.

This article is dedicated to the memory of Roland L. Dobrushin.
On applications of excess level processes to (N,D)‐policy bulk queueing systems
Authors: Dshalalow Jewgeni H.
Published: March 2007

The paper deals with queueing systems in which N‐ and D‐policies are
combined into one. This means that an idle or vacationing server will resume his
service if the queueing or workload process crosses some specified fixed level N or
D, respectively. For the proposed (N, D)‐policy we study the queueing processes in
models with and without server vacations, with compound Poisson input, and
with generally distributed service and vacation periods. The analysis of the
models is essentially based on fluctuation techniques for two‐dimensional marked
counting processes newly developed by the author. The results enable us to arrive
at stationary distributions for the embedded and continuous time parameter
queueing processes in closed analytic forms, enhancing the well‐known Kendall
formulas and their modifications.

This article is dedicated to the memory of Roland L. Dobrushin.
On the variance of the number of real zeros of a random trigonometric polynomial
Authors: Farahmand K.
Published: March 2007

The asymptotic estimate of the expected number of real zeros of the polynomial T(θ) = g1cosθ + g2cos2θ + …+gncosnθ where gj(j = 1, 2, …, n)
is a sequence of independent normally distributed random variables is
known. The present paper provides an upper estimate for the variance of
such a number. To achieve this result we first present a general formula
for the covariance of the number of real zeros of any normal process, ξ(t),
occurring in any two disjoint intervals. A formula for the variance of the
number of real zeros of ξ(t) follows from this result.
Mean number of real zeros of a random trigonometric polynomial IV
Authors: Wilkins J. Ernest
Published: March 2007

If aj(j = 1, 2, …, n) are independent, normally distributed random variables with mean 0 and variance 1, if p is one half of any odd positive integer except one, and if vnp is the mean number of zeros on (0, 2π) of the
trigonometric polynomial a1cosx + 2pa2cos2x + …+npancosnx, then
vnp = μp{(2n + 1) + D1p + (2n+1)−1D2p + (2n+1)−2D3p} + O{(2n+1)−3}, in which μp = {(2p + 1)/(2p + 3)} ½, and D1p, D2p and D3p are
explicitly stated constants.
Reduction of differentiable equations with impulse effect
Authors: Sermone Lelde
Published: March 2007

We consider a problem of a partial linearization of noninvertible differential equations with impulse effect and establish sufficient conditions for the
dynamical equivalence.
Positive and oscillatory radial solutions of semilinear elliptic equations
Authors: Chen Shaohua , Derrick William R. , Cima Joseph A.
Published: March 2007

We prove that the nonlinear partial differential equation

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,
with u(0) > 0, where f and g are continuous, f(u) > 0 and g(|x|, u) > 0
for u > 0, and

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,
has no positive or eventually positive radial solutions. For g(|x|, u) ≡ 0,
when n/(n − 2) ≤ q < (n + 2)/(n − 2) the same conclusion holds provided
2F(u) ≥ (1 − 2/n)uf(u), where . We also discuss the
behavior of the radial solutions for f(u) = u3 + u5 and f(u) = u4 + u5 in
ℝ3 when g(|x|, u) ≡ 0.
Initial and boundary value problems for partial functional differential equations
Authors: Ntouyas S. K. , Tsamatos P. Ch.
Published: March 2007

In this paper we study the existence of solutions to initial and boundary
value problems of partial functional differential equations via a fixed‐point
analysis approach. Using the topological transversality theorem we derive
conditions under which an initial or a boundary value problem has a solution.
Lyapunov exponents for higher dimensional random maps
Authors: Góra P. , Boyarsky A. , Lou Y. S.
Published: March 2007

A random map is a discrete time dynamical system in which one of a number of transformations is selected randomly and implemented. Random
maps have been used recently to model interference effects in quantum physics. The main results of this paper deal with the Lyapunov exponents for
higher dimensional random maps, where the individual maps are Jabloński
maps on the n‐dimensional cube.
Continuity properties of solutions of multivalued equations with white noise perturbation
Authors: Michta Mariusz
Published: March 2007

In the paper, we consider a set‐valued stochastic equation with stochastic
perturbation in a Banach space. We prove first the existence theorem and
then study continuity properties of solutions.
Monotone iterations for differential equations with a parameter
Authors: Jankowski Tadeusz , Lakshmikantham V.
Published: March 2007

Consider the problem

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.
Employing the method of upper and lower solutions and the monotone
iterative technique, existence of extremal solutions for the above equation
are proved.
Transformations of certain generalized Kampé de Fériet functions II
Authors: Exton Harold
Published: March 2007

The development of identities of multivariable hypergeometric functions is
further extended based upon the methods of the previous study (H. Exton,
J. Phys. A29 (1996), 357‐363) these functions occur in various applications
in the fields of physics and quantum chemistry.
Boundedness of one‐dimensional branching Markov processes
Authors: Karpelevich F. I. , Suhov Yu. M.
Published: March 2007

A general model of a branching Markov process on ℝ is considered.
Sufficient and necessary conditions are given for the random variable

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to be finite. Here Ξk(t) is the position of the kth particle, and N(t) is the
size of the population at time t. For some classes of processes (smooth
branching diffusions with Feller‐type boundary points), this results in a
criterion stated in terms of the linear . Here σ(x) and a(x) are the diffusion coefficient and
the drift of the one‐particle diffusion, respectively, and λ(x) and k(x) the
intensity of branching and the expected number of offspring at point x, respectively. Similarly, for branching jump Markov processes the conditions are expressed in terms of the relations between the integral
μ(x)∫π(x, dy)(f(y) − f(x)) and the product λ(x)(1 − k(x))f(x), where
λ(x) and k(x) are as before, μ(x) is the intensity of jumping at point x,
and π(x, dy) is the distribution of the jump from x to y.
The empirical TES methodology: modeling empirical time series
Authors: Melamed Benjamin
Published: March 2007

TES (Transform‐Expand‐Sample) is a versatile class of stochastic sequences defined via an autoregressive scheme with modulo‐1 reduction and
additional transformations. The scope of TES encompasses a wide variety
of sample path behaviors, which in turn give rise to autocorrelation functions with diverse functional forms ‐ monotone, oscillatory, alternating,
and others. TES sequences are readily generated on a computer, and their
autocorrelation functions can be numerically computed from accurate
analytical formulas at a modest computational cost.

This paper presents the empirical TES modeling methodology which
uses TES process theory to model empirical records. The novel feature of
the TES methodology is that it expressly aims to simultaneously capture
the empirical marginal distribution (histogram) and autocorrelation function. We draw attention to the non‐parametric nature of TES modeling in
that it always guarantees an exact match to the empirical marginal distribution. However, fitting the corresponding autocorrelation function calls
for a heuristic search for a TES model over a large parametric space. Consequently, practical TES modeling of empirical records must currently rely
on software assistance. A visual interactive software environment, called
TEStool, has been designed and implemented to support TES modeling.
The paper describes the empirical TES modeling methodology as implemented in TEStool and provides numerically‐computable formulas for
TES autocorrelations. Two examples illustrate the efficacy of the TES
modeling approach. These examples serve to highlight the ability of TES
models to capture first‐order and second‐order properties of empirical
sample paths and to mimic their qualitative appearance.
On the level crossing of multi‐dimensional delayed renewal processes
Authors: Dshalalow Jewgeni H.
Published: March 2007

The paper studies the behavior of an (l + 3)th‐dimensional, delayed renewal process with dependent components, the first three (called active) of
which are to cross one of their respective thresholds. More specifically, the
crossing takes place when at least one of the active components reaches or
exceeds its assigned level. The values of the other two active components,
as well as the rest of the components (passive), are to be registered. The
analysis yields the joint functional of the “crossing level” and other
characteristics (some of which can be interpreted as the first passage time)
in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.
The theory of networks of single server queues and the tandem queue model
Authors: Le Gall Pierre
Published: March 2007

We consider the stochastic behavior of networks of single server queues
when successive service times of a given customer are highly correlated.
The study is conducted in two particular cases: 1) networks in heavy
traffic, and 2) networks in which all successive service times have the same
value (for a given customer), in order to avoid the possibility of breaking
up the busy periods. We then show how the local queueing delay (for an
arbitrary customer) can be derived through an equivalent tandem queue on
the condition that one other local queueing delay is added: the jitter delay
due to the independence of partial traffic streams.

We consider a practical application of the results by investigating the
influence of long packets on the queueing delay of short packets in modern
packet switched telecommunication networks. We compare these results
with the results given by traffic simulation methods to conclude that there
is good agreement between results of calculation and of traffic simulation.
A hidden Markov model for an inventory system with perishable items
Authors: Aggoun L. , Benkherouf L. , Tadj L.
Published: March 2007

This paper deals with a parametric multi‐period integer‐valued inventory
model for perishable items. Each item in the stock perishes in a given period of time with some probability. Demands are assumed to be random
and the probability that an item perishes is not known with certainty. Expressions for various parameter estimates of the model are established and
the problem of finding an optimal replenishment schedule is formulated as
an optimal stochastic control problem.
Queueing systems with renovation
Authors: Kreinin A. Ya.
Published: March 2007

We study in this paper‐single channel queueing systems with renovation.
Such models are often encountered in computer science applications. Explicit solutions are discussed for the queues with Poisson input flow and
for queues with general input and exponential service times.
Singularly perturbed telegraph equations with applications in the random walk theory
Authors: Banasiak Jacek , Mika Janusz R.
Published: March 2007

In the paper we analyze singularly perturbed telegraph systems applying
the newly developed compressed asymptotic method and show that the
diffusion equation is an asymptotic limit of singularly perturbed telegraph
system of equations. The results are applied to the random walk theory
for which the relationship between correlated and uncorrelated random
walks is explained in asymptotic terms.
A non‐nonstandard proof of Reimers′ existence result for heat SPDEs
Authors: Allouba Hassan
Published: March 2007

In 1989, Reimers gave a nonstandard proof of the existence of a solution to
heat SPDEs, driven by space‐time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non‐nonstandard proof of this fact,
and with the aid of Girsanov′s theorem for continuous orthogonal martingale measures (proved in a separate paper by the author), the result is extended to the case of a measurable drift.
Linear distribution processes
Authors: Bel L. , Oppenheim G. , Robbiano L. , Viano M. C.
Published: March 2007

In this paper, we propose a generalization of continuous‐time processed
defined by

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,
to the case of f being a distribution. We give a necessary and sufficient
condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes.
In addition, we investigate a generalization to processes with stationary increments.
Selections of set‐valued stochastic processes
Authors: Michta Mariusz , Rybiński Longin E.
Published: March 2007

We show that ℱt‐adapted, set‐valued stochastic processes satisfying mild
continuity conditions admit, ℱt‐adapted, stochastically continuous selections.
On a class of multivalued variational inequalities
Authors: Noor Muhammad Aslam
Published: March 2007

In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These
variational inequalities include as special cases, the previously known
classes of variational inequalities. Using projection techniques, we show
that multivalued variational inequalities are equivalent to fixed point problems and Wiener‐Hopf equations. These alternate formulations are used
to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to
study the existence of a solution of multivalued variational inequalities
and suggest a novel iterative algorithm. In addition, we have shown that
the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.
Oscillation of the solutions of a class of impulsive differential equations with a deviating argument
Authors: Bainov D. D. , Dimitrova Margarita B. , Dishliev Angel B.
Published: March 2007

Sufficient conditions are found for oscillation of all solutions of a class of
impulsive differential equations with deviating argument.
Second method of Lyapunov for stability of linear impulsive differential‐difference equations with variable impulsive perturbations
Authors: Bainov D. D. , Stamova I. M. , Vatsala A. S.
Published: March 2007

The present work is devoted to the study of stability of the zero solution to linear impulsive differential‐difference equations with variable impulsive perturbations. With the aid of piecewise continuous auxiliary functions, which are generalizations of the classical Lyapunov′s functions, sufficient conditions are found for the uniform stability and uniform asymptotical stability of the zero solution to equations under consideration.
Nonlinear filtering and optimal quality control
Authors: Beneš Václav E.
Published: March 2007

Some stochastic models of optimal decision processes in quality control problems are formulated, analyzed, and solved. It is assumed that costs, positive or negative, are assigned to various events in a simple manufacturing
model, such as processing an item, producing a saleable item, discarding
an item for salvage, selling a “lemon”, etc. and models are described by
giving a sequence of events, some of which are decisions to process, to
abandon, to accept, to restart, …. All the models have the rather unrealistic classical information pattern of cumulative data. The object is then to
find optimal procedures for minimizing the total cost incurred, first in dealing with a single item, and second, in operating until an item first passes
all the tests. The policies that appear as optimal depend on such matters
as whether a conditional probability given certain data exceeds a ratio of
prices, and on more complex functionals of the conditional expectations in
the problem. Special “sufficient” classes of policies are discerned, which reduce the decision problem to finding one number.
Sojourn times for the Brownian motion
Authors: Takács Lajos
Published: March 2007

In this paper explicit formulas are given for the distribution function, the
density function and the moments of the sojourn time for the reflecting
Brownian motion process.
A heavy‐traffic theorem for the GI/G/1 queue with a Pareto‐type service time distribution
Authors: Cohen J. W.
Published: March 2007

For the GI/G/1 queueing model with traffic load a < 1, service time
distribution B(t) and interarrival time distribution A(t), whenever for
t → ∞

urn:x-wiley:20903332:media:ista149413:ista149413-math-0001

,
and

urn:x-wiley:20903332:media:ista149413:ista149413-math-0002

,
converges in distribution for a↑1. Here w is distributed as the
stationary waiting time distribution. The L.‐S. transform of the limiting
distribution is derived and an asymptotic series for its tail probabilities is
obtained. The theorem actually proved in the text concerns a slightly
more general asymptotic behavior of 1 − B(t), t → ∞, than mentioned
above.
Moment estimation of customer loss rates from transactional data
Authors: Daley D. J. , Servi L. D.
Published: March 2007

Moment estimators are proposed for the arrival and customer loss rates of
a many‐server queueing system with a Poisson arrival process with customer loss via balking or reneging. These estimators are based on the lengths
{Sj1} of the initial inter‐departure intervals of the busy periods j = 1, …, M observed in a dataset consisting of service starting and finishing
times and encompassing both busy and idle periods of the process, and
whether those busy periods are of length 1 or >1. The estimators are
compared with maximum likelihood and parametric model‐based estimators found previously.
Verifying cell loss requirements in high‐speed communication networks
Authors: Fendick Kerry W. , Whitt Ward
Published: March 2007

In high‐speed communication networks it is common to have requirements
of very small cell loss probabilities due to buffer overflow. Losses are measured to verify that the cell loss requirements are being met, but it is not
clear how to interpret such measurements. We propose methods for determining whether or not cell loss requirements are being met. A key idea is
to look at the stream of losses as successive clusters of losses. Often clusters of losses, rather than individual losses, should be regarded as the important “loss events”. Thus we propose modeling the cell loss process by a
batch Poisson stochastic process. Successive clusters of losses are assumed
to arrive according to a Poisson process. Within each cluster, cell losses
do not occur at a single time, but the distance between losses within a cluster should be negligible compared to the distance between clusters. Thus,
for the purpose of estimating the cell loss probability, we ignore the spaces
between successive cell losses in a cluster of losses. Asymptotic theory
suggests that the counting process of losses initiating clusters often should
be approximately a Poisson process even though the cell arrival process is
not nearly Poisson. The batch Poisson model is relatively easy to test statistically and fit; e.g., the batch‐size distribution and the batch arrival rate
can readily be estimated from cell loss data. Since batch (cluster) sizes
may be highly variable, it may be useful to focus on the number of
batches instead of the number of cells in a measurement interval. We also
propose a method for approximately determining the parameters of a special batch Poisson cell loss with geometric batch‐size distribution from a
queueing model of the buffer content. For this step, we use a reflected
Brownian motion (RBM) approximation of a G/D/1/C queueing model.
We also use the RBM model to estimate the input burstiness given the cell
loss rate. In addition, we use the RBM model to determine whether the
presence of losses should significantly affect the estimation of server utilization when both losses and utilizations are estimated from data. Overall,
our analysis can serve as a basis for determining required observation intervals in order to reach conclusions with a solid statistical basis. Thus our
analysis can help plan simulations as well as computer system measurements.
Some reflections on the Renewal‐theory paradox in queueing theory
Authors: Cooper Robert B. , Niu Shun-Chen , Srinivasan Mandyam M.
Published: March 2007

The classical renewal‐theory (waiting time, or inspection) paradox states
that the length of the renewal interval that covers a randomly‐selected
time epoch tends to be longer than an ordinary renewal interval. This
paradox manifests itself in numerous interesting ways in queueing theory,
a prime example being the celebrated Pollaczek‐Khintchine formula for the
mean waiting time in the M/G/1 queue. In this expository paper, we give
intuitive arguments that “explain” why the renewal‐theory paradox is ubiquitous in queueing theory, and why it sometimes produces anomalous results. In particular, we use these intuitive arguments to explain decomposition in vacation models, and to derive formulas that describe some recently‐discovered counterintuitive results for polling models, such as the reduction of waiting times as a consequence of forcing the server to set up
even when no work is waiting.
On certain random polygons of large areas
Authors: Kovalenko Igor N.
Published: March 2007

Consider the tesselation of a plane into convex random polygons
determined by a unit intensity Poissonian line process. Let M(A) be the
ergodic intensity of random polygons with areas exceeding a value A. A
two‐sided asymptotic bound

urn:x-wiley:20903332:media:ista535296:ista535296-math-0001

is established for large A, where c0 > 2.096, c1 > 6.36.
Multiserver queueing networks and the tandem queue model
Authors: Gall Pierre Le
Published: March 2007

Using a tandem queue model we evaluate the local “endogenous”
(= internal) queueing delay in single server and multiserver queueing networks. The new concept of the apparent overall upstream queueing delay(as perceived by the downstream network) allows us to analyze the distribution of this local queue by interpolating between the distributions of
the tandem queue (generated by a concentration tree) and the isolated
G/G/squeue. The interpolation coefficients depend on the proportion of
“premature departures”, typically interfering in the upstream stage and
leaving the considered path without being offered to the considered local
queue. On the other hand, local “exogenous” arrivals (from outside the
network) require the introduction of the “interference delay” concept.
Finally, in the case of single server queueing networks, we stress the need
to extend the capacities of the buffers, by considering the “worst case”
scenario and by using an “equivalent tandem queue” model.
Covariance and relaxation time in finite Markov chains
Authors: Keilson Julian
Published: March 2007

The relaxation time TREL of a finite ergodic Markov chain in continuous
time, i.e., the time to reach ergodicity from some initial state distribution,
is loosely given in the literature in terms of the eigenvalues λj of the infinitesimal generator . One uses TREL = θ−1 where . This paper establishes for the relaxation time θ−1 the theoretical solidity of the time reversible case. It does so by examining the
structure of the quadratic distance d(t) to ergodicity. It is shown that, for
any function f(j) defined for states j, the correlation function ρf(τ) has
the bound |ρf(τ)| ≤ exp[−π|τ|] and that this inequality is tight. The
argument is almost entirely in the real domain.
Performance limitations of parallel simulations
Authors: Chen Liang , Serfozo Richard F.
Published: March 2007

This study shows how the performance of a parallel simulation may be
affected by the structure of the system being simulated. We consider a
wide class of “linearly synchronous” simulations consisting of asynchronous and synchronous parallel simulations (or other distributed‐processing
systems), with conservative or optimistic protocols, in which the differences in the virtual times of the logical processes being simulated in real
time t are of the order o(t) as t tends to infinity. Using a random time
transformation idea, we show how a simulation′s processing rate in real
time is related to the throughput rates in virtual time of the system being
simulated. This relation is the basis for establishing upper bounds on
simulation processing rates. The bounds for the rates are tight and are
close to the actual rates as numerical experiments indicate. We use the
bounds to determine the maximum number of processors that a simulation
can effectively use. The bounds also give insight into efficient assignment
of processors to the logical processes in a simulation.
On intensities of modulated Cox measures
Authors: Dshalalow Jewgeni H.
Published: March 2007

In this paper we introduce and study functionals of the intensities of
random measures modulated by a stochastic process ξ, which occur in
applications to stochastic models and telecommunications. Modulation of a
random measure by ξ is specified for marked Cox measures. Particular
cases of modulation by ξ as semi‐Markov and semiregenerative processes
enabled us to obtain explicit formulas for the named intensities. Examples
in queueing (systems with state dependent parameters, Little′s and
Campbell′s formulas) demonstrate the use of the results.
Self‐similar processes in collective risk theory
Authors: Michna Zbigniew
Published: March 2007

Collective risk theory is concerned with random fluctuations of the total
assets and the risk reserve of an insurance company. In this paper we consider self‐similar, continuous processes with stationary increments for the
renewal model in risk theory. We construct a risk model which shows a
mechanism of long range dependence of claims. We approximate the risk
process by a self similar process with drift. The ruin probability within
finite time is estimated for fractional Brownian motion with drift. A
similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and
inventory models.
Moment computation in shift invariant spaces
Authors: Eubanks David A. , van Fleet Patrick J. , Wang Jianzhong
Published: March 2007

An algorithm is given for the computation of moments of f ∈ S, where S
is either a principal h‐shift invariant space or S is a finitely generated h‐shift invariant space. An error estimate for the rate of convergence of our
scheme is also presented. In so doing, we obtain a result for computing
inner products in these spaces. As corollaries, we derive Marsden‐type
identities for principal h‐shift invariant spaces and finitely generated h‐shift invariant spaces. Applications to wavelet/multiwavelet spaces are
presented.
Generalized stability of motion of impulsive Lurie‐Postnikov systems with structural perturbation
Authors: Martynyuk A. A. , Stavroulakis I. P.
Published: March 2007

This paper investigates the absolute stability on ℊs of the zero solution of
Lurie‐Postnikov systems with impulses and structural perturbation. A
number of absolutely stable on ℊs theorems of the Lyapunov type for
Lurie‐Postnikov systems are proved, extending and generalizing previous
work on the subject. These results are applied to some fourth‐order Lurie‐Postnikov type systems decomposed into two systems.
Semilinear integro‐differential equations with compact semigroups
Authors: Bahuguna D. , Srivastava S. K.
Published: March 2007

In this paper we study the local and global existence of mild solutions to a
class of integro‐differential equations in an arbitrary Banach space associated with the operators generating compact semigroups on the Banach
space.
Transformations of index set for Skorokhod integral with respect to Gaussian processes
Authors: Gawarecki Leszek
Published: March 2007

We consider a Gaussian process {Xt, t ∈ T} with an arbitrary index set T
and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution
for the time‐reversed equation and, to Ogawa line integral, give an analogue of the fundamental theorem of calculus.