Hsing Luh

Analysis of the M/G/1 queue with exponentially working vacations--a matrix analytic approach

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.

Threshold control policies for heterogeneous server systems

Abstract. 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, S1,S2,… , SN. 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 Si, if this server is the fastest server available and the number of customers in the queue is mi or more. The threshold mi 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.

Modeling Security-Check Queues

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.

An effective approach for content delivery in an evolving intranet environment – a case study of the largest telecom company in taiwan

Being the dominant telecommunication company in Taiwan, ChungHwa Telecom Co., Ltd., CHT is her symbol listed on the New York Stock Exchange, provides major communication services to more than 23 million people living in Taiwan. CHT has vast number of software developed on client-server or web-based architectures with client software installed in more than ten thousand client computers spreading over the entire nation. Since telecommunication industry evolved in fast pace, the software functions are constantly changing. The changes have to be reflected in all client software before new services can be launched. Thus, the cost and time in distributing contents to client computers has become a major concern in CHT. To improve the efficiency of contents distribution, this research helps CHT develop new software to automatically distribute contents to client computers. To minimize the chance of system locks and balance contents distribution loading, in the new system, each dispatching server sends update contents to no more than three other servers. The contents are delivered with hybrid routing strategy that combines both fixed and adaptive routing strategies. With its low error rate and speedy distribution, the new system reduces the man-minutes per year required to manage the contents distribution of a client server system from 14,227.2 minutes to 1,144 minutes, namely reduces 92% of the time. The user satisfaction of the system was also found to be above 80% among six factors of the measurement designed by Bailey, et al. [1].

An efficient search direction for linear programming problems

In this paper, we present an auxiliary algorithm, in terms of the speed of obtaining the optimal solution, that is effective in helping the simplex method for commencing a better initial basic feasible solution. The idea of choosing a direction towards an optimal point presented in this paper is new and easily implemented. From our experiments, the algorithm will release a corner point of the feasible region within few iterative steps, independent of the starting point. The computational results show that after the auxiliary algorithm is adopted as phase I process, the simplex method consistently reduce the number of required iterations by about 40%.

A robust web-based approach for broadcasting downward messages in a large-scaled company

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.

Petri nets for performance modelling study of client-server systems

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 ...

Derivation of the N-step interdeparture time distribution in GI/G/1 queueing systems

Abstract 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.

Optimal services for content delivery based on business priority

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, and a manager can increase the service rate to ensure that losses are tolerable when delivering urgent files. Finally, the relative probabilities of blocked urgent files and blocked regular files are used as an indicator of efficiency in reserving connections.

Analysis of bandwidth allocation on end-to-end QoS networks under budget control

Abstract This paper considers the problem of bandwidth allocation on communication networks with multiple classes of traffic, where bandwidth is determined under the budget constraint. Due to the limited budget, there is a risk that the network service providers can not assert a 100% guaranteed availability for the stochastic traffic demand at all times. We derive the blocking probabilities of connections as a function of bandwidth, traffic demand and the available number of virtual paths based on the Erlang loss formula for all service classes. A revenue/profit function is studied through the monotonicity and convexity of the blocking probability and expected path occupancy. We present the optimality conditions and develop a solution algorithm for optimal bandwidth of revenue management schemes. The sensitivity analysis and three economic elasticity notions are also proposed to investigate the marginal revenue for a given traffic class by changing bandwidth, traffic demand and the number of virtual paths, respectively. By analysis of those monotone and convex properties, it significantly facilitates the operational process in the efficient design and provision of a core network under the budget constraint.