1.
Parallel fluid queues with constant inflows and simultaneous random reductions - Kella, Offer; Miyazawa, Masakiyo
We consider I fluid queues in parallel. Each fluid queue has a deterministic inflow
with a constant rate. At a random instant subject to a Poisson process, random amounts
of fluids are simultaneously reduced. The requested amounts for the reduction are
subject to a general I-dimensional distribution. The queues with inventories that
are smaller than the requests are emptied. Stochastic upper bounds are considered for
the stationary distribution of the joint buffer contents. Our major interest is in
finding exponential product-form bounds, which turn out to have the appropriate decay
rates with respect to certain linear combinations of buffer contents.
2.
On the stability of a batch clearing system with Poisson arrivals and subadditive service times - Aldous, David; Miyazawa, Masakiyo; Rolski, Tomasz
We study a service system in which, in each service period, the
server performs the current set B of tasks as a batch, taking
time s(B), where the function s(.) is subadditive. A
natural definition of `traffic intensity under congestion' in this
setting is ? := limt??t-1Es (all tasks arriving during time [0,t]).
We show that ? > 1 and a finite mean of individual service times are
necessary and sufficient to imply stability of the system. A key observation
is that the numbers of arrivals during successive service periods form a
Markov chain {An}, enabling us to apply classical regenerative
techniques and to express the stationary distribution of...
3.
The size order of the state vector of a continuous-time homogeneous Markov system with fixed size - Kipouridis, I.; Tsaklidis, G.
The variation of the state vectors
p(t) = (pi(t)) of a
continuous-time homogeneous Markov system with fixed size is examined.
A specific time t0 after which the size order of the elements
pi(t) becomes stable provides a criterion of the system's
convergence rate. A method is developed to find t0 and a quickly
evaluated lower bound for t0. This method is based on the geometric
characteristics and the volumes of the attainable structures. Moreover,
a condition concerning the selection of starting vectors p(0) is
given so that the vector functions p(t) retain the same size
order for every time greater than a given time t.
4.
Some optimal stopping problems with nontrivial boundaries for pricing exotic options - Guo, Xin; Shepp, Larry
We solve the following three optimal stopping problems for different kinds of
options, based on the Black-Scholes model of stock fluctuations. (i) The
perpetual lookback American option for the running maximum of the stock price
during the life of the option. This problem is more difficult than the
closely related one for the Russian option, and we show that for a class of
utility functions the free boundary is governed by a nonlinear ordinary
differential equation. (ii) A new type of stock option, for a company, where
the company provides a guaranteed minimum as an added incentive in case the
market appreciation of the stock is low, thereby...
5.
On some distributional properties of a first-order nonnegative bilinear time series model - Zhang, Zhiqiang; Tong, Howell
We study a simple first-order nonnegative bilinear time-series model and give
conditions under which the model is stationary. The probability density function of
the stationary distribution (when it exists) is found. We also discuss the tail
behaviour of the stationary distribution and calculate the probability density
function by a numerical method. Simulation is used to check the calculation.
6.
On the optimal stopping values induced by general dependence structures - Müller, Alfred; Rüschendorf, Ludger
The optimal stopping value of random variables X1,...,Xn depends on
the joint distribution function of the random variables and hence on their
marginals as well as on their dependence structure. The maximal and
minimal values of the optimal stopping problem is determined within the
class of all joint distributions with fixed marginals F1,...,Fn.
They correspond to some sort of strong negative or positive
dependence of the random variables. Any value inbetween these two
extremes is attained for some dependence structures. The determination of
the minimal value is based on some new ordering results for probability
measures, in particular on lattice properties of stochastic orderings. We
also identify properties of dependence...
7.
On the existence of the stable birth-type distribution in a general branching process cell cycle model with unequal cell division - Alexandersson, Marina
We use multi-type branching process theory to construct a cell
population model, general enough to include a large class of such
models, and we use an abstract version of the Perron-Frobenius
theorem to prove the existence of the stable birth-type
distribution. The generality of the model implies that a stable
birth-size distribution exists in most size-structured cell cycle
models. By adding the assumption of a critical size that each cell
has to pass before division, called the nonoverlapping case, we
get an explicit analytical expression for the stable birth-type
distribution.
8.
On the convergence to stationarity of birth-death processes - Coolen-Schrijner, Pauline; Van Doorn, Erik A.
Taking up a recent proposal by Stadje and Parthasarathy in the setting of the
many-server Poisson queue, we consider the integral
?0?[limu??E(X(u))-E(X(t))]dt
as a measure of the speed of convergence towards
stationarity of the process {X(t) , t?0}, and evaluate the integral explicitly
in terms of the parameters of the process in the case that {X(t) , t?0} is an
ergodic birth-death process on {0,1,....} starting in 0. We also discuss the
discrete-time counterpart of this result, and examine some specific examples.
9.
Time dependent analysis of multivariate marked renewal processes - Dshalalow, Jewgeni H.
The paper examines multivariate delayed marked renewal processes,
of which one component is formed by a delayed compound Poisson
process observed at epochs of some point process. In addition, the
values of these observations (and other components) are watched
when crossing their respective thresholds and the value of the
original Poisson process at any moment of time, past the first
passage time, is the objective of this investigation. The results
(which are imperative for classes of semiregenerative processes)
are given in closed analytical forms and illustrated on various
stochastic models.
10.
Combinatorial techniques for M/G/1-type queues - Mercankosk, G.; Nair, G. M.; Soet, W. J.
The application of the generalised ballot theorem to queueing
theory leads to elegant results for the simple M/G/1 queue. It
is thought that such results are not possible for more general
M/G/1-type queues. We, however, derive a batch ballot theorem
which can be applied to derive the first passage distribution
matrix, G, for the general M/G/1-type queue.
11.
The coupon subset collection problem - Adler, Ilan; Ross, Sheldon M.
The coupon subset collection problem is a generalization of the
classical coupon collecting problem, in that rather than collecting
individual coupons we obtain, at each time point, a random subset of
coupons. The problem of interest is to determine the expected number of
subsets needed until each coupon is contained in at least one of these
subsets. We provide bounds on this number, give efficient simulation
procedures for estimating it, and then apply our results to a
reliability problem.
12.
A note on stochastic comparisons of excess lifetimes of renewal processes - Belzunce, Félix; Ortega, Eva M.; Ruiz, José M.
In this paper we provide new results about stochastic comparisons
of the excess lifetime at different times of a renewal process
when the interarrival times belong to several ageing classes. We
also provide a preservation result for the new better than used in
the Laplace transform order ageing class for series systems.
13.
A new discrete distribution arising in a model of DNA replication - Cowan, Richard
During DNA replication, small fragments of DNA are formed. These have been observed
experimentally and the mechanism of their formation modelled mathematically. Using the
stochastic model of Cowan and Chiu (1992), (1994), we find the probability
distribution of the number of fragments. A new discrete distribution arises. The work
has interest as an application of the recent theory on quasirenewal equations in Piau
14.
A stochastic covariate failure model for assessing system reliability - Ebrahimi, Nader
Many failure mechanisms can be traced to an underlying deterioration
process, and stochastically changing covariates may influence this
process. In this paper we propose an alternative model for assessing a
system's reliability. The proposed model expresses the failure time of
a system in terms of a deterioration process and covariates. When it is
possible to measure deterioration as well as covariates, our model
provides more information than failure time for the purpose of
assessing and improving system reliability. We give several properties
of our proposed model and also provide an example.
15.
On the total time spent in records by a discrete uniform sequence - Grübel, Rudolf; Reimers, Anke
We consider the sum Sd of record values in a sequence of independent
random variables that
are uniformly distributed on 1,...,d. This sum can be interpreted as the
total amount
of time spent in record lifetimes in the standard renewal theoretic setup. We
investigate
the distributional limit of Sd and some related quantities
as d??. Some explicit
values are given for d=6, a case that can be interpreted as a simple game
of chance.
16.
A reconsideration of Lotka's extinction probability using a bisexual branching process - Hull, David M.
It is generally recognized that Alfred Lotka made the first application of
standard
Galton-Watson branching process theory to calculate an extinction
probability in a
specific population (using asexual reproduction). This note applies bisexual
Galton-Watson branching process theory to the calculation of an extinction
probability from
Lotka's data, yielding a somewhat higher value.
17.
On hitting times for compound Poisson dams with exponential jumps and linear release rate - Kella, Offer; Stadje, Wolfgang
For a compound Poisson dam with exponential jumps and linear release rate (shot-noise
process), we compute the Laplace-Stieltjes transform (LST) and the mean of the
hitting time of some positive level given that the process starts from some given
positive level. The solution for the LST is in terms of confluent hypergeometric
functions of the first and second kinds (Kummer functions).
18.
Some peculiarities of exponential random variables - Litvak, Nelly
In this paper we utilize a particular transformation of i.i.d.
exponential random variables to derive two distributional
identities. Throughout the analysis we discover some peculiar
properties of exponentials. We also discuss possible
generalizations and applications of the results.
19.
On the stationary workload distribution of work-conserving single-server queues: a general formula via stochastic intensity - Miyoshi, Naoto
It is well known that a simple closed-form formula exists for the stationary
distribution of the workload in M/GI/1 queues. In this paper, we extend
this to the general stationary framework. Namely, we consider a
work-conserving single-server queueing system, where the sequence of
customers' arrival epochs and their service times is described as a general
stationary marked point process, and we derive a closed-form formula for the
stationary workload distribution. The key to our proof is two-fold: one is
the Palm-martingale calculus, that is, the connection between the notion of
Palm probability and that of stochastic intensity. The other is the
preemptive-resume last-come, first-served discipline.
20.
Rates of convergence for products of random stochastic 2 × 2 matrices - Neininger, Ralph
Products of independent identically distributed random stochastic
2 × 2 matrices are known to converge in distribution under a trivial condition.
Rates for this convergence are estimated in terms of the minimal Lp-metrics and the Kolmogoroff metric and applications to convergence
rates of related interval splitting procedures are discussed.
1.
