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We present a decision support model for patient-centered precision surveillance that assists clinicians and patients for the whole disease prospect to provide a single operational framework of whole type 2 diabetic person care management while introducing experts in the loop modeling that facilitates data collection. Based on real-world data, the scientific computation shall be adopted with experts’ experiences for providing the patient health education and accessing complication risks thereby easily delineating disease pathways. A decision tree technique is used to build a single framework consisting of every possible diabetes complication in the decision process. Coping with the complex medical system for the prevention of diabetes and diabetic complications, a patient-centered framework gives the patient interactive, transparent and useful information for better communication in the decision process that includes experts’ experience as well as the value of the prediction generated from population-based data.

We consider an M/G/1 Markovian feedback queue with multi-class customers. We derive functional equations for the stationary distribution of the queue size and the total response time. A system of linear equations is also derived for the moments of the queue size and the total response time distributions. The mean and the variance of the queue size and the total response time can be computed by solving the system of linear equations. By using the Markovian feedback queue with multi-class customers, we also investigate the M/PH/1 weighted round-robin queue. Numerical examples are given to show that moments of the queue sizes and of the total response times can be easily computed for the weighted round-robin queue. As the service quantum shrinks to zero, the moments of the queue sizes and the total response times converge to some limits which should be the moments of the corresponding discriminatory processor sharing queue.

This paper studies a supply chain configuration (SCC) problem for a green product family in consideration of guaranteed service time and emission constraints. Several alternative options can be employed to implement the functions of each stage and safety inventory is adopted to satisfy stochastic demands. An SCC model is formulated to optimize the service time and option selection decisions to minimize the overall cost of the supply chain. The structural properties of the model are addressed and the problem is decomposed into two subproblems, namely, the service time decision problem and option selection problem. For the service time decision problem, the structural properties of the supply chain network is carefully studied, based on which a spanning tree-based algorithm (STA) is presented to solve the problem optimally. For the option selection problem that is proven to be NP-hard, a particle swarm optimization algorithm (PSO) is adopted to efficiently solve the problem. Consequently, a hybrid algorithm (STA+PSO) is developed to solve the SCC model. The numerical results show that the hybrid algorithm can efficiently and effectively solve the SCC model. The emission constraints on green products have significant effects on the supply chain cost and the emissions of the products; while the guaranteed service time also remarkably influences the supply chain configuration. (C) 2017 Elsevier B.V. All rights reserved.

Progressions of chronic diseases can be modeled as Markov processes. Frequently, the model parameters are concluded based on distinct short-term clinical studies because of the difficulty of observing the entire progression process in one clinical study. Though this piece-by-piece approach provides a global picture to the disease progression process, it could lead to unrealistic results under in-depth analysis. For instance, without careful calibration, patients’ life expectancy computed from the model might be longer than that of the general population. Such results usually arise from that the effect of population mortality is not sensible or not well included in these short-term clinical studies. For chronic diseases with which patients may experience a long chain of successive states, this inaccuracy is more obvious. Beck and Pauker propose that the population mortality may be integrated into a disease progression model in their work. Their method provides a solution to the aforementioned difficulty. However, their approach to integrate the population mortality into the model implicitly assumes that the population mortality solely affects the transition probabilities for transitions to the death state and for self-transitions remaining in the initial states. They do not explain why only these two types of transitions are affected by the imposed population mortality. From realistic situations, no matter what state transitions patients experience, they are all under the risk of death caused by population mortality. Based on this observation, a new modeling approach is proposed in this study. The proposed approach assumes that population mortality independently affects all state transitions of a Markov model. This extends Beck and Pauker’s idea and makes their method more reasonable. The proposed approach is applied to disease progression analysis of chronic hepatitis B virus (HBV) infection and considered for further applications. Specifically, with the natural history of chronic HBV infection originally described by a coarse Markov model a new model is developed by calibrating the coarse model with the proposed method. Numerical results show that the new model can obtain realistic estimates to patients’ life expectancy and survival probabilities. Meanwhile, the concept of first hitting time can find its interesting application in deriving the probabilities for patients’ first experiencing critical medical status during a specified duration. This delivers valuable information to chronic HBV patients. The model’s possible extensions such as its application to different countries and taking patients’ risk factors into account are also discussed for future study.

In this paper, we investigate the nonhomogeneity of state space for solving retrial queues through the performance of the M/M/S retrial system with impatient customers and S servers that is modeled under quasi-birth-and-death processes with level-dependent transient rates. We derive the analytic solution of multiserver retrial queues with orbit and develop an efficient method to solve this type of systems effectively. The methods proposed are based on nonhomogeneity of the state space although this queueing model was tackled by many researchers before. Under a weaker assumption in this paper, we study and provide the exact expression based on an eigenvector approach. Constructing an efficient algorithm for the stationary probability distribution by the determination of required eigenvalues with a specific accuracy, we develop streamlined matrices of state-balanced equations with the efficient implementation for computation of the performance measures.

Purpose – The purpose of this paper is to develop a novel model of a call center that must treat calls with distinctly different service depending on whether they orginate from VIP or regular customers. VIP calls must be responded to immediately but regular calls can be routed to a retrial queue if the operators are busy. Design/methodology/approach – This study’s proposed model can easily reveal the optimal arrangement of operators while minimizing computational time and without losing any precision of the performance measure when dealing with a call center with more operators. Findings – Based on the results of the comparison between the exact method and the proposed approximation method, the approach shows that the larger the number of operators or inbound calls, the smaller the error between the two methods. Originality/value – This investigation presents a computational method and management cost function intended to identify the optimal number of operators for a call center. Because of computational limitations, many operators could not be easily analyzed using the exact method. For the manager of a call center, the sooner the optimal solution is found, the faster business strategies are deployed. This study develops an approximation method and compares it with the exact method.

Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman's analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas' model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas' work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman's work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work.

In a content-delivery system, connections are viewed as resources for sending files. However, the growing business needs of large-scale networks require an effective content-delivery service for transferring files. Since connections are sparse resources, prioritizing connections is essential for efficiently delivering urgent files and regular files based on various business priorities. This study presents a loss function as a performance index for a content-delivery service. The proposed loss function was applied to a sample content-delivery system to derive the average number of regular files in the retry group, the probability of failure to transfer a regular file in the first attempt, and the probability of failure to transmit urgent files. Additionally, the loss was associated with the decreased number of reserve connections under regular hours and peak hours. The experimental results show that the proposed model finds the optimal number of reserve connections for sending high- and low-priority files,...

This paper studies a multiple-server queueing model under the assumptions of renewal arrival processes and limited buffer size. An approximation for the loss probability and the asymptotic behavior are studied under the heavy traffic conditions. We present an asymptotic analysis of the loss probability when both the arrival rate and number of servers approach infinity. In illustrative examples, the loss probabilities are estimated with heavy traffic under three common distributions of inter-arrival times: exponential, deterministic and Erlang-r distributions, respectively.

Motivated by the waiting lines between the U.S.–Canadian border crossings, we investigate a security-check system with both security and customer service goals. In such a system, every customer has to be inspected by the first-stage inspector, but only a proportion of customers need to go through the second stage for further inspection. This “further inspection proportion,” affecting both security screening and the system congestion, becomes a key decision variable for the security-check system. Using a stylized two-stage queueing model, we established the convexity of the expected waiting cost function. With such a property, the optimal further inspection proportion can be determined to achieve the balance of the two goals and the service capacities can be classified into “security-favorable,” “security-unfavorable,” or “security-infeasible” categories. A specific capacity category implies if the security and customer service goals are consistent or in conflict. In addition, we have verified that the properties discovered in the stylized model also hold approximately in a more general multiserver setting. Numerical results are presented to demonstrate the accuracy and robustness of the approximations and the practical value of the model. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

In this paper, an M/G/1 queue with exponentially working vacations is analyzed. This queueing system is modeled as a two-dimensional embedded Markov chain which has an M/G/1-type transition probability matrix. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. Then, based on the classical vacation decomposition in the M/G/1 queue, we derive a conditional stochastic decomposition result. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by analyzing the semi-Markov process. Furthermore, we provide the stationary waiting time and busy period analysis. Finally, several special cases and numerical examples are presented.

Many software applications have been developed on client-server and web-based architectures, with client software installed in numerous clerks' devices spread over the whole of Taiwan along the hierarchical organization of large-scaled service companies. The damage for a large-scaled service company would be caused by an inconsistent system, in which client software fails to receive updated content causing loss of emergency calls and possibility of recovery. Therefore, a reliable content-delivering service is needed for such a large-scaled service company to ensure system consistency whenever a disaster occurs. This study analyses the error situations of a proposed content-delivering service that has been implemented in a large-scaled company in Taiwan. Moreover, its disaster avoidance mechanism provides a reliability model with the waiting-time distribution of disconnected links. The proposed disaster avoidance mechanism prevents damage from terminating operations of a company caused by disasters, such as earthquakes, tsunamis, nuclear plant explosions or wars. Empirical results demonstrate that the proposed design run on 19 servers distributes content with less than 3.4 content-delivery failures per million hours.

In this paper, we study a Ck/Cm/1/N open queueing system with finite capacity. We investigate the property which shows that a product of the Laplace Stieltjes Transforms of interarrival and service times distributions satisfies an equation of a simple form. According to this equation, we present that the stationary probabilities on the unboundary states can be written as a linear combination of vector product-forms. Each component of these products is expressed in terms of roots of an associated characteristic polynomial. As a result, we carry out an algorithm for solving stationary probabilities in Ck/Cm/1/N systems, which is independent of N, hence greatly reducing the computational complexity.

This retrospective cohort study investigated the progression risk of sequential complication in Asian type 2 diabetes (T2D) patients using the Taiwan Pay-for-Performance Diabetes Registry and claim data from November 2003 to February 2009. 226,310 adult T2D patients without complication were followed from diagnosis to complications, including myocardial infarction (MI), other ischemic heart disease (IHD), congestive heart failure (CHF), stroke, chronic kidney disease (CKD), retinopathy, amputation, death or to the end of study. Cumulative incidences (CIs) of first and second complications were analyzed in 30 and 4 years using the cumulative incidence competing risk method. IHD (29.8%), CKD (24.5%) and stroke (16.0%) are the most common first complications. The further development of T2D complications depends on a patient’s existing complication profiles. Patients who initially developed cardiovascular complications had a higher risk (9.2% to 24.4%) of developing IHD or CKD, respectively. All-cause mortality was the most likely consequence for patients with a prior MI (12.0%), so as stroke in patients with a prior MI (10.8%) or IHD (8.9%). Patients with CKD had higher risk of developing IHD (16.3%), stroke (8.9%) and all-cause mortality (8.7%) than end-stage renal disease (4.0%). Following an amputation, patients had a considerable risk of all-cause mortality (42.1%).

Our goal is to study which conditions of the output process of a queue preserve the Increasing Failure Rate (IFR) property in the interdeparture time. We found that the interdeparture time does not always preserve the IFR property, even if the interarrival time and service time are both Erlang distributions with IFR. We give a theoretical analysis and present numerical results of E"m/E"k/1 queues. We show, by numerical examples, that the interdeparture time of E"m/E"k/1 retains the IFR property if m>=k.

In this note, we study anEk/Em/1 queueing model where interarrival and service times are Erlang distributions with parametersk andm respectively. We prove that the roots of the characteristic polynomial associated with Erlang distributions are simple if the arrival and service rates are real. Based on this result, a general solution space of vectors for stationary probabilities is easily constructed.

The departure process of a single queue has been studied since the 1960s. Due to its inherent complexity, closed form solutions for the distribution of the departure process are nearly intractable. In this study, kernel type estimators of the density of interdeparture time in a GI/G/1 queue are studied. Uniform strong consistency of the estimators in a GI/G/1 queue and their rates of convergence are obtained. The stochastic processes are shown to satisfy the strong mixing condition with random instants of sampling. With the analysis presented, we provide a novel analytic tool for studying the departure process in a general queueing model.

We consider a queueing system with two stations in series. Assume the service time distributions are general at one station and a finite mixture of Erlang distributions at the other. Exogenous customers should snatch tokens at a token buffer of finite capacity in order to enter the system. Customers are lost if there are no tokens available in the token buffer while they arrive. To obtain the stationary probability distribution of number of customers in the system, we construct an embedded Markov chain at the departure times. The solution is solved analytically and its analysis is extended to semi-Markovian representation of performance measures in queueing networks. A formula of the loss probability is derived to describe the probability of an arriving customer who finds no token in the token buffer, by which the throughput and the optimal number of tokens are also studied.

Understanding the behavior of an idle time of a limited resource is the key to increase productivity in service operations. When the system consists of nonexponential properties of time distributions it becomes difficult to provide results for the general case. We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a GI/G/1 queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The expected error bound under this approach is identified. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., cycle time or interdeparture time distributions. Numerical examples are given to illustrate these results.

Second order properties of queues are important in design and analysis of service systems. In this paper we show that the blocking probability of M/M/C/N queue is increasing directionally convex in (λ,−μ), where λ is arrival rate and μ is service rate. To illustrate the usefulness of this result we consider a heterogeneous queueing system with non-stationary arrival and service processes. The arrival and service rates alternate between two levels (λ1,μ1) and (λ2,μ2), spending an exponentially distributed amount of time with rate cαi in level i, ie1,2. When the system is in state i, the arrival rate is λi and the service rate is μi. Applying the increasing directional convexity result we show that the blocking probability is decreasing in c, extending a result of Fond and Ross [7] for the case CeNe1.

This study developed a parallel algorithm to efficiently solve linear programming models. The proposed algorithm utilizes the Dantzig-Wolfe Decomposition Principle and can be easily implemented in a general distributed computing environment. The analytical performance of the well-known method, including the speedup upper bound and lower bound limits, was derived. Numerical experiments are also provided in order to verify the complexity of the proposed algorithm. The empirical results demonstrate that the speedup of this parallel algorithm approaches linearity, which means that it can take full advantage of the distributed computing power as the size of the problem increases.

We study the problem of optimally controlling a multiserver queueing system. Customers arrive in a Poisson fashion and join a single queue, served by N servers, S 1,S 2,… , S N. The servers have different rates. The service times at each server are independent and exponentially distributed. The objective is to determine the policy which minimizes the average number of customers in the system. We show that any optimal, nonpreemptive policy is of threshold type, i.e., it assigns a customer to server S i, if this server is the fastest server available and the number of customers in the queue is m i or more. The threshold m i may depend on the condition of other (slower) servers at the decision instant. In order to establish the results, we reformulate the optimal control problem as a linear program and use a novel argument based on the structure of the constraint matrix.

Queues that involve waiting as a model for analyzing the possible delay have been studied for past several decades. The average total time spent in the system and the average total time spent in queue are two of the most fundamental quantities describing a queueing system's behavior. In addition, there are other important factors that will affect the delay as well. For example, the environment in which queue waiting occurs plays a fundamental role in a customer's perceived and/or actual cost of participating in that system. In this paper, we study a queueing model that takes the waiting environment into account. We present a very simple solution procedure to solve the steady-state probability in this model with the required measurement.

By geometric viewpoint in search directions of linear programming problems (LP), there are two major approaches: the simplex method and the interior-point algorithm originated from Karmarkar's approach. Many of their variants developed both in theory and applications are still in progress. Roughly speaking, the main difference among them is that the simplex method is devoted for each the exact optimal solution while Karmarkar-based method is computationally fast in approaching to the neighborhood of the optimal solution, but it becomes slow near the optimal point. By the separating hyperplane theorem, we know that the optimal solution of a linear programming problem would locate at the boundary point. However, Karmarkar's algorithm is claimed as an interior-point approach which takes a solution trajectory path through the interior of the feasible region. On the other hand, these algorithms will coincide the zig-zag situation following the trajectory path before attaining the optimal point meanwhi...

We propose an optimal schedule for multiple classes of arrivals in a queueing system consisting of queues in tandem. The arrival process for each class is Poisson with different rates, and the service times are constant. A theoretical result is presented by Linear Programming of sample-path arguments, together with duality theory. The approach shows a powerful analytical tool which facilities the procedure in analysis of optimization in queueing control problems and a possibility of future study in other similar problems.

The departure process of a queueing system has been studied since the 1960s. Due to its inherent complexity, closed form solutions for the distribution of the departure process are nearly intractable. In this paper, we derive a closed form expression for the distribution of interdeparture time in a GI / G /1 queueing model. Without loss of generality, we consider an embedded Markov chain in a general K M / G /1 queueing system, in which the interarrival time distribution is Coxian and service time distribution is general. Closed form solutions of the equilibrium distribution are derived for this model and the Laplace–Stieltjes transform (LST) of the distribution of interdeparture times is presented. An algorithmic computing procedure is given and numerical examples are provided to illustrate the results. With the analysis presented, we provide a novel analytic tool for studying the departure process in a general queueing model.

Fujimoto et al., have proved that the tail of the joint queue length distribution in a two-stage tandem queueing system has the geometric decay property. We continue to investigate the properties of stationary distributions in this tandem queueing system. Under the same conditions proposed by them, it is further shown that the stationary probability of the saturated states in the PH/PH/c1 A' /PH/c2 queue has a linear combination of product-forms. The method of linear combination of product-forms is presented in a QBD process with a countable number of phases in each level. We show that each component of these products can be expressed in terms of roots of the associated characteristic polynomials which involve only the Laplace-Stieltjes transforms of the interarrival and service time distributions.

Client-server computing provides many corporations with the ability to build scalable, adaptive and cost-effective information systems. However, to design and implement an effective client-server system is not an easy job. The complexity due to the inherent heterogeneity in client-server platforms makes the performance evaluation an important issue. The main purpose of this paper is to provide an analytical model to evaluate the performance of a client-server system before it is implemented. It is shown in this paper that the Petri net model is a powerful technique used to study the client-server system performance. Besides using a numerical example to illustrate the solution procedure of the Petri net model, a case study is also given to show the applicability of the developed analytical model. This research concludes that, with the assistance of some software packages, the Petri nets are very useful tools for the information system manager to analyse a client-server system and to decide the appropriate ...

Supplemental Digital Content is available in the text, Congenital anomalies of the kidney and urinary tract (CAKUT) are 1 of the major factors in young adults needing renal replacement therapy, but there is little extensive assessment of their incidence and risk factors. This study aimed to evaluate trends in the incidence of and risk factors for CAKUT among all births in Taiwan. This population-based case–control study design was conducted using the Taiwan national births registry, which contains detailed information about maternal health and characteristics of newborns, supplied by health professionals. Of 1,603,794 newborns registered between 2004 and 2014, 668 infants were reported to have CAKUT. Newborns without congenital anomalies were matched with CAKUT cases by birth year, month, and Apgar score in a ratio of 5:1. Odds ratio (OR) and 95% confidence interval (CI) for developing CAKUT were calculated using a conditional multivariate logistic regression model. The incidence of CAKUT was approximately 4.2 per 10,000 births. The adjusted ORs for CAKUT in newborns associated with maternal age of 20 to 29 (OR, 2.18; 95% CI, 1.11–4.28), or 30 to 39 (OR, 2.29; 95% CI, 1.17–4.51), maternal gestational diabetes (OR, 2.22, 95% CI, 1.06–4.67), maternal thalassemia/hemochromatosis (OR, 2.67; 95% CI, 1.35–5.27), polyhydramnios or oligohydramnios (OR, 9.16; 95% CI, 5.46–15.37), birth parity >1 (OR, 0.27; 95% CI, 0.15–0.50), having a gestational age

Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death (QBD) with phase-type distribution normally are dependent on the structure of the queueing network. In this paper, a new computing scheme is developed for attaining stationary probabilities in queueing networks with multiple servers. This scheme provides a general approach of considering the complexity of computing algorithm. The result becomes more significant when a large matrix is involved in computation. The background theorem of this approach is proved and provided with an illustrative example in this paper.

Operations Research Society of Taiwan was organized and established in 2003 to provide more services for OR professions, as well as academia and industry. Its mission includes promoting the advancement and practice of OR in Taiwan, boosting worldwide recognition for the profession and launching new publications. International Journal of Operations Research (IJOR), as the institutional journal for global professionals, both stimulating reading and serving as a source for practitioners Keywords: ORSTW; INFORMS; IJOR; Taiwan Chapter

With the emerging popularity of multimedia applications, quality of service on Internet becomes an important issue. Random Early Detection (RED) is one of the most widely used adaptive queue management in the Internet. In this paper, we extend the basic concept and study an analytic model for RED queues with batch arrival and multiple servers. A Markovian approach is presented in order to study different quality metrics by RED parameters, such as batch sizes, dropping rates, etc. Numerical results obtained by simulation and analytic methods illustrate those performance measures of the proposed RED queue, such as average system/queue sizes, average sysetm/queue waiting time, average dropping probability.

A content-delivering service within a large-scaled company in Taiwan has been proposed to use 40 servers to meet user requirements on the previous study. The managers of the case company want to use resources as few as possible. From previous study [19--21], we suggest them using 19 servers to deliver large files. However, because we need not only servers but also links to deliver content from the source to all destinations, we cannot discuss servers merely. Therefore, we must discuss about the reliability and cost of links that in previous study it discussed few about this matter. Since the important packets must be delivered on time, and the regular packets are flexible. Therefore, we need a proper design to make the important packets deliver to the destinations without mistake. The regular packets also need to be delivered to destinations, but they can resent to destinations until the urgent files are delivered completely. Therefore, the reliability design of links must consider following utilization: the system is used to deliver every kind of data securely, but the important packets must be delivered without delay. Therefore, this work models the reliability and cost of links to find the proper resource allocation that can help manager delivering urgent files and regular files.

The Peer-to-Peer (P2P) approaches utilize the passive means of delivering large amounts of content due to the ease of content delivery and small amount of effort required for file transmission and failure control by the file provider. However, P2P methods incur network congestion due to the large number of uncontrolled connections established by those retrieving content. Additionally, P2P methods potentially stop file providers from exchanging data with other devices because of congested outbound traffic. Therefore, existing P2P approaches are infeasible for large-scale organizations as a congested uncontrolled network is not ideal in a business environment. Related studies demonstrated that the active method for content can minimize outbound congestion for a provider but it needs the fault tolerance. This study presents a novel application called Enterprise Peer-to-Peer (EP2P), which integrates passive and active approaches. Using EP2P, the outbound traffic from a sender on an Intranet can be controlled efficiently, because the transmission between a provider and many receivers can be changed from passive to active on necessary. Therefore, we suggest organizations use EP2P for the delivery of content.

We propose a mathematical model for calculating blocking probabilities with optimal bandwidth allocation and QoS routing on multiclass communication networks. This scheme is performed by means of a two-phase procedure. The first step determines optimal paths under network constraints. The second step computes the blocking probability with predetermined optimal solutions. The blocking is due to the failure of meeting the demand of end-to-end paths for each class.

We present an integer programming approach to offer optimal bandwidth allocation and QoS routing for network management problems with heterogeneous service classes. The bandwidth allocation policy in such communication networks is determined in accordance with the proportionally fair rule, which can be expressed by utility functions of network users. The objective of this utility maximization scheme is to prepare a routing table for future user request. This routing table identifies the allocated bandwidth and the suitable end-to-end path under QoS guarantees for each user. We analyze the mathematical properties of the optimal bandwidth allocation and provide computational results to demonstrate the validity and efficiency of the proposed scheme.

We propose a precomputation-based scheme which offers Pareto optimal solutions to the network dimensioning problem. This scheme is performed by means of a two-phase procedure. The first phase precomputes paths for a wide range of possible constraints, while the second phase selects an adequate path through a simple procedure. That is, the first phase prepares a routing database which enables to identify a suitable path upon each connection request through the second phase. We propose a bandwidth allocation model with nonlinear utility functions. We focus on allocating resources with proportional fairness and finding a routing scheme on communication networks.

Downward communication is a popular push-based scheme to forward messages from headquarters to front-line staff in a large-scaled company. With the maturing intranet and web technology, broadcasting algorithms, including pull-based and push-based broadcasting algorithms, it is feasible to send downward messages through web-based design by sending packets on a network. To avoid losing messages due to the traditional push-based method, companies adopt a pull-based algorithm to build up the broadcasting system. However, although the pull-based method can ensure that a message is received, it has a critical problem, the network is always congested. The push-based method can avoid congesting the network, but it needs a specific robust design to ensure that the message reaches its destination. Hence, adopting only a pull-based or a push-based broadcasting algorithm is no longer feasible especially not for a large-scaled company with complex network architecture. To ensure that every receiver will read downward messages thereby reducing the consumption of network bandwidth, this work proposes a robust web-based push- and pull-based broadcasting system for sending downward messages. This proposed system was successfully applied to a large-scaled company for a one-year period.

We propose a precomputation-based scheme offering Pareto optimal solutions to the network optimization problem. This scheme precomputes bandwidth allocation (rate vector) and end-to-end paths with QoS guarantees. It prepares a routing database, identifying an optimal path upon each connection request. We propose a mixed-integer optimization model with nonlinear utility functions. The purpose of this work is to choose the optimal solutions and to provide decision makers a set of solutions satisfying users' preferences with fairness. It prepares for a proportionally fair treatment of all competing connections. Numerical results show that the proposed model can provide each connection with its fair share of the bandwidth which is proportional to the target rate.