Seung Hyun Yoon

Batch arrival queue with N -policy and single vacation

Abstract We consider an M x / G /1 queueing system with N -policy and single vacation. As soon as the system becomes empty, the server leaves the system for a vacation of random length V . When he returns from the vacation, if the system size is greater than or equal to predetermined value N (threshold), he beings to serve the customers. If not, the server waits in the system until the system size reaches or exceeds N . We derive the system size distribution and show that the system size distribution decomposes into two random variables one of which is the system size of ordinary M x / G /1 queue. The interpretation of the other random variable will also be provided. We also derive the queue waiting time distribution of an arbitrary customer. Finally we develop a procedure to find the optimal stationary operating policy under a linear cost structure.

Queue length and waiting time analysis of a batch arrival queue with bilevel control

Abstract Scope and Purpose —This paper concerns the analysis of a production system in which an early set-up and N -policy are employed. We model the system by M x /M/1 queue with bilevel control and obtain the queue length and waiting time distributions. In general, with more than two control policies mixed up, obtaining the waiting time distribution is extremely complicated due to the dependencies between the random variables involved. The methodology employed in this paper can be extended to other batch arrival queueing system with more complicated control policies. We consider an M x /M /1 queue with bilevel control. As soon as the system empties, the server becomes idle until m or more customers accumulate, at which time the server starts a set-up. After the set-up, if N or more customers are in the system ( N ⩾ m ) the server immediately start serving the customers in FCFS fashion. If less than N customers are in the system after the set-up, the server remains dormant in the system and wait until N or more customers accumulate. We derive the distributions of the number of customers in the system and the waiting time.

An analysis of multiple-class vacation queues with individual thresholds

This study examines a multiple-class M/G/1 queue with multiple thresholds. Each class of customer arrives according to an independent Poisson process, and each class has its own threshold. The idle server is reactivated as soon as any one of the thresholds is reached. Both FCFS and non-preemptive priority cases are considered. The Laplace-Stieltjes transform of the waiting time distribution function and the mean waiting time for each class of customers are derived.

A continuous approximation for batch arrival queues with threshold

In this paper, the system size of batch arrival queues with threshold is approximated by a diffusion process and the accuracy is evaluated. Firstly, the busy period process is approximated by a diffusion process with an instantaneous return boundary. Secondly, the idle period process is approximated by applying the renewal theory. Then we combine the two approximations to derive the system size distribution at an arbitrary time point. The accuracy of the approximation is evaluated for a number of interarrival and service time distributions.

A recursive method for Bernoulli arrival queues and its application to partial buffer sharing in ATM

Abstract In this research, we first develop a recursive method to compute the state probabilities of Geo/G/1/K discrete-time queueing system directly from the system equations. Then, we model the partial buffer sharing scheme of ATM buffer control mechanism by Geo1, Geo2/G/1/K+1 queue and apply the recursive method to obtain the steady-state probabilities and loss probabilities. Scope and purpose Most results in queueing theory are given in the form of transforms. We need to invert the transform solution to obtain probabilities and various performance measures. This is a big burden not only to researchers but also to practitioners. In this research, we develop a recursive method for discrete-time finite queueing systems which enables us to compute the state probabilities not by inverting the transform solution, but directly from the system equations. The developed recursive method is simple enough (even though somewhat tedious) to implement in analyzing many discrete-time finite queueing systems with Bernoulli arrivals.

Continuous approximations of the machine repair system

This paper considers two diffusion approximations to the queueing systems with finite calling population, with special emphasis on the machine repair problem. We consider two boundary policies: the elementary return boundary (ERB) and the instantaneous return boundary (IRB). We obtain approximate solutions to the probability distribution of the number of inoperative machines for each of the boundary policies.

Start-up class models in multiple-class queues with N -policy

In this paper, we consider multiple‐class queueing systems with N‐policy in which the idle server starts service as soon as the number of customers in the “start‐up class” reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems.

A Mathematical Programming Approach for Cloud Service Brokerage

Cloud computing is fast becoming the wave of the future for both home and business computing. Because of this growing acceptance, we can expect an explosion of diverse cloud service providers in the coming years. However, the cloud is not a single entity, rather it is a set of many disconnected islands of application (SaaS), infrastructure (IaaS), and different platform (PaaS) services. Cloud brokering mechanisms are essential to transform the heterogeneous cloud market into a commodity-like service. Cloud service brokers (CSBs) are the new form of business entities to help to aggregate the scattered set of cloud services and make conveniently available to their diverse users. CSBs can reserve a certain percentage of their clients’ (users’) demand and satisfy the remaining portion in an on-demand basis. In doing so, they need to minimize cost of both reserved and on-demand instances as well as the distance of a link between the cloud service provider (CSP) and the user. The study proposes a reservation approach with a mixed integer model to optimizes the cloud service cost and quality.

Resource and Network Routing Optimization in Smart Nodes Environment

ABSTRACTIn this research, we dealt with an optimization problem which aims to minimize total cost of resources usage and network routing in a smart node environment. Toward this, we briefly introduced technology trends in smart nodes, methods in resource optimization fields, economic effects of smart network and content delivery (or distribution) network (CDN). Moreover, based on CDN we proposed and implemented a mathematical (mixed integer) programming model to combine replica placement and requests distribution problem (RPRDP) and routing problem. Computational result of an example on RPRDP+Routing problem is also provided. Key words : CDN, Resource Usage, RPRDP, Smart Node, Network Routing요 약본 연구에서는 네트워크 총 비용 최소화의 관점에서 스마트 노드 자원사용과 네트워크 트래픽 경로를 함께 결정하는 최 적화 문제를 고려하였다. 이를 위해, 스마트 노드의 기술 추세와 자원 최적화에 대한 분석방법 , 스마트 네트워크의 경제적 효과와 CDN에 대해 살펴보았다. CDN에 대한 분석을 기반으로 혼합정수계획법 모형을 제안하였으며 , 이는 기존에 알려진 복제위치선정과 고객요청 분배문제 (RPRDP)와 경로 결정문제가 결합된 형태로 볼 수 있다. 제안된 혼합정수계획법 모형을 구현하고 그 결과를 소개함으로써 제안된 모형의 유효성을 밝혔다 .주요어 : 콘텐츠전송네트워크, 자원사용량, RPRDP, 스마트노드, 네트워크 라우팅

An empirical study on a web server queueing system and traffic generation by simulation

In this study, we first analyze the log data of the web-server system at a Korean company and confirm strong self-similarities that have been reported in a wide range of internet data. Then, we propose a simulation approach to generate arrivals of web page requests based on the conventional familiar probability distributions. We also present a forecasting model to generate future arrivals and test the validity of our approach through real data. Finally, we present our software tool that we developed to analyze web log data.