Abstract: In this paper, the joint optimization of the
economic manufacturing quantity (EMQ), safety stock level,
and condition-based maintenance (CBM) is presented for a partially
observable, deteriorating system subject to random failure. The
demand is stochastic and it is described by a Poisson process.
The stochastic model is developed and the optimization problem
is formulated in the semi-Markov decision process framework. A
modification of the policy iteration algorithm is developed to find
the optimal policy. A numerical example is presented to compare
the optimal policy with the policy considering zero safety stock.
Abstract: This work assesses the performance of an analytical
model framework to generate daily flow duration curves, FDCs,
based on climatic characteristics of the catchments and on their
streamflow recession coefficients. According to the analytical model
framework, precipitation is considered to be a stochastic process,
modeled as a marked Poisson process, and recession is considered
to be deterministic, with parameters that can be computed based
on different models. The analytical model framework was tested
for three case studies with different hydrological regimes located in
Switzerland: pluvial, snow-dominated and glacier. For that purpose,
five time intervals were analyzed (the four meteorological seasons
and the civil year) and two developments of the model were tested:
one considering a linear recession model and the other adopting
a nonlinear recession model. Those developments were combined
with recession coefficients obtained from two different approaches:
forward and inverse estimation. The performance of the analytical
framework when considering forward parameter estimation is poor in
comparison with the inverse estimation for both, linear and nonlinear
models. For the pluvial catchment, the inverse estimation shows
exceptional good results, especially for the nonlinear model, clearing
suggesting that the model has the ability to describe FDCs. For
the snow-dominated and glacier catchments the seasonal results are
better than the annual ones suggesting that the model can describe
streamflows in those conditions and that future efforts should focus
on improving and combining seasonal curves instead of considering
single annual ones.
Abstract: Understanding the statistics of non-isotropic scattering multipath channels that fade randomly with respect to time, frequency, and space in a mobile environment is very crucial for the accurate detection of received signals in wireless and cellular communication systems. In this paper, we derive stochastic models for the probability density function (PDF) of the shift in the carrier frequency caused by the Doppler Effect on the received illuminating signal in the presence of a dominant line of sight. Our derivation is based on a generalized Clarke’s and a two-wave partially developed scattering models, where the statistical distribution of the frequency shift is shown to be consistent with the power spectral density of the Doppler shifted signal.
Abstract: This article considers the problem of evaluating
infinite-time (or finite-time) ruin probability under a given compound
Poisson surplus process by approximating the claim size distribution
by a finite mixture exponential, say Hyperexponential, distribution. It
restates the infinite-time (or finite-time) ruin probability as a solvable
ordinary differential equation (or a partial differential equation).
Application of our findings has been given through a simulation study.
Abstract: We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.
Abstract: Fading noise degrades the performance of cellular
communication, most notably in femto- and pico-cells in 3G and 4G
systems. When the wireless channel consists of a small number of
scattering paths, the statistics of fading noise is not analytically
tractable and poses a serious challenge to developing closed
canonical forms that can be analysed and used in the design of
efficient and optimal receivers. In this context, noise is multiplicative
and is referred to as stochastically local fading. In many analytical
investigation of multiplicative noise, the exponential or Gamma
statistics are invoked. More recent advances by the author of this
paper utilized a Poisson modulated-weighted generalized Laguerre
polynomials with controlling parameters and uncorrelated noise
assumptions. In this paper, we investigate the statistics of multidiversity
stochastically local area fading channel when the channel
consists of randomly distributed Rayleigh and Rician scattering
centers with a coherent Nakagami-distributed line of sight component
and an underlying doubly stochastic Poisson process driven by a
lognormal intensity. These combined statistics form a unifying triply
stochastic filtered marked Poisson point process model.
Abstract: Extensive rainfall disaggregation approaches have been developed and applied in climate change impact studies such as flood risk assessment and urban storm water management.In this study, five rainfall models that were capable ofdisaggregating daily rainfall data into hourly one were investigated for the rainfall record in theChangi Airport, Singapore. The objectives of this study were (i) to study the temporal characteristics of hourly rainfall in Singapore, and (ii) to evaluate the performance of variousdisaggregation models. The used models included: (i) Rectangular pulse Poisson model (RPPM), (ii) Bartlett-Lewis Rectangular pulse model (BLRPM), (iii) Bartlett-Lewis model with 2 cell types (BL2C), (iv) Bartlett-Lewis Rectangular with cell depth distribution dependent on duration (BLRD), and (v) Neyman-Scott Rectangular pulse model (NSRPM). All of these models werefitted using hourly rainfall data ranging from 1980 to 2005 (which was obtained from Changimeteorological station).The study results indicated that the weight scheme of inversely proportional variance could deliver more accurateoutputs for fitting rainfall patterns in tropical areas, and BLRPM performedrelatively better than other disaggregation models.
Abstract: The electrical substation components are often subject to degradation due to over-voltage or over-current, caused by a short circuit or a lightning. A particular interest is given to the circuit breaker, regarding the importance of its function and its dangerous failure. This component degrades gradually due to the use, and it is also subject to the shock process resulted from the stress of isolating the fault when a short circuit occurs in the system. In this paper, based on failure mechanisms developments, the wear out of the circuit breaker contacts is modeled. The aim of this work is to evaluate its reliability and consequently its residual lifetime. The shock process is based on two random variables such as: the arrival of shocks and their magnitudes. The arrival of shocks was modeled using homogeneous Poisson process (HPP). By simulation, the dates of short-circuit arrivals were generated accompanied with their magnitudes. The same principle of simulation is applied to the amount of cumulative wear out contacts. The objective reached is to find the formulation of the wear function depending on the number of solicitations of the circuit breaker.
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Abstract: In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.
Abstract: The use of buffer thresholds, blocking and adequate
service strategies are well-known techniques for computer networks
traffic congestion control. This motivates the study of series queues
with blocking, feedback (service under Head of Line (HoL) priority
discipline) and finite capacity buffers with thresholds. In this paper,
the external traffic is modelled using the Poisson process and the
service times have been modelled using the exponential distribution.
We consider a three-station network with two finite buffers, for
which a set of thresholds (tm1 and tm2) is defined. This computer
network behaves as follows. A task, which finishes its service at
station B, gets sent back to station A for re-processing with
probability o. When the number of tasks in the second buffer exceeds
a threshold tm2 and the number of task in the first buffer is less than
tm1, the fed back task is served under HoL priority discipline. In
opposite case, for fed backed tasks, “no two priority services in
succession" procedure (preventing a possible overflow in the first
buffer) is applied. Using an open Markovian queuing schema with
blocking, priority feedback service and thresholds, a closed form
cost-effective analytical solution is obtained. The model of servers
linked in series is very accurate. It is derived directly from a twodimensional
state graph and a set of steady-state equations, followed
by calculations of main measures of effectiveness. Consequently,
efficient expressions of the low computational cost are determined.
Based on numerical experiments and collected results we conclude
that the proposed model with blocking, feedback and thresholds can
provide accurate performance estimates of linked in series networks.
Abstract: This paper presents a computational methodology
based on matrix operations for a computer based solution to the
problem of performance analysis of software reliability models
(SRMs). A set of seven comparison criteria have been formulated to
rank various non-homogenous Poisson process software reliability
models proposed during the past 30 years to estimate software
reliability measures such as the number of remaining faults, software
failure rate, and software reliability. Selection of optimal SRM for
use in a particular case has been an area of interest for researchers in
the field of software reliability. Tools and techniques for software
reliability model selection found in the literature cannot be used with
high level of confidence as they use a limited number of model
selection criteria. A real data set of middle size software project from
published papers has been used for demonstration of matrix method.
The result of this study will be a ranking of SRMs based on the
Permanent value of the criteria matrix formed for each model based
on the comparison criteria. The software reliability model with
highest value of the Permanent is ranked at number – 1 and so on.
Abstract: Software Reliability is one of the key factors in the software development process. Software Reliability is estimated using reliability models based on Non Homogenous Poisson Process. In most of the literature the Software Reliability is predicted only in testing phase. So it leads to wrong decision-making concept. In this paper, two Software Reliability concepts, testing and operational phase are studied in detail. Using S-Shaped Software Reliability Growth Model (SRGM) and Exponential SRGM, the testing and operational reliability values are obtained. Finally two reliability values are compared and optimal release time is investigated.
Abstract: Software developed for a specific customer under contract
typically undergoes a period of testing by the customer before
acceptance. This is known as user acceptance testing and the process
can reveal both defects in the system and requests for changes to
the product. This paper uses nonhomogeneous Poisson processes to
model a real user acceptance data set from a recently developed
system. In particular a split Poisson process is shown to provide an
excellent fit to the data. The paper explains how this model can be
used to aid the allocation of resources through the accurate prediction
of occurrences both during the acceptance testing phase and before
this activity begins.
Abstract: A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.
Abstract: C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.