Soon Seok Lee

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.

Overview of ITU-T NGN QoS Control

This article presents an overview of standards activities defining the QoS control architecture. Several standards bodies define the QoS control architectures based on their scope of work. This article first reviews the QoS control architectures defined in the standards bodies such as Cable Lab, DSL Forum, MSF, ETSI, and ITU-T. ITU-T NGN architecture provides the generic framework to cover the results of each standards body. Other architectures focus on solving specific problems. We explain in more detail the ITU-T QoS control architecture defined in resource and admission control functions (RACF) and discuss future standards developments.

Operating characteristics of MX/G/1 queue with N-policy

We consider aMX/G/1 queueing system withN-policy. The server is turned off as soon as the system empties. When the queue length reaches or exceeds a predetermined valueN (threshold), the server is turned on and begins to serve the customers. We place our emphasis on understanding the operational characteristics of the queueing system. One of our findings is that the system size is the sum of two independent random variables: one has thePGF of the stationary system size of theMX/G/1 queueing system withoutN-policy and the other one has the probability generating function ∑j=0N=1 πjzj/∑j=0N=1 πj, in which πj is the probability that the system state stays atj before reaching or exceedingN during an idle period. Using this interpretation of the system size distribution, we determine the optimal thresholdN under a linear cost structure.

A FIXED-SIZE BATCH SERVICE QUEUE WITH VACATIONS

The paper deals with batch service queues with vacations in which customers arrive according to a Poisson process. Decomposition method is used to derive the queue length distributions both for single and multiple vacation cases. The authors look at other decomposition techniques and discuss some related open problems.

DiffProbe: one way delay measurement for asynchronous network and control mechanism in BcN architecture

Recently NGN standard organizations provide significant effort to implement the QoS guaranteed service in the IP based packet switching network. The NGN architecture assumes the admission control for all the premium service and monitoring the service performance to meet the QoS requirement. In Korea, broadband convergence network (BcN) architecture has been developed. BcN strategy is delivering NGN solution by converging different types of services. The service reliability and performance of BcN is maintained by OAM over virtual switched path (VSP). However, no clear solution for monitoring the delay performance network is available for asynchronous packet switching network. This paper presents the BcN architecture and introduces the performance monitoring and control algorithm for packet switching network. First part of the paper presents BcN architecture in both transport and control plane. The second part introduces a delay measurement algorithm designed for BcN network called DiffProbe (differentiated probe). DiffProbe is OAM based delay measurement algorithm that can be used for delay measurement in asynchronous transport network where the clock synchronization is not available. Network control strategy using DiffProbe is also presented. Based on the simulation result, DiffProbe captures the delay dynamics in high load condition

On a batch service queue with single vacation

Abstract We consider a batch service queuering system with a single-vacation policy. The server leaves for a vacation as soon as the system empties. If more than B customers are present when the server returns from a vacation, the first B customers are taken into service. if fewer than B customers are present, all waiting customers go into service. If the server finds no customers, the server waits idle for the first customer to arrive. We assume that late arrivals are not allowed to join the ongoing service. We derive the queue size distribution at random points, the system size at departure points, queue waiting time distribution, and other performance measures.

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.

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.

Performance Monitoring for Multimedia Traffic using Differentiated Probe (DiffProbe)

Guaranteeing end-to-end QoS for multimedia traffic in the IP transport network is a challenging issue. Monitoring the one way delay of the multimedia traffic is necessary but no clear solution for the performance monitoring in the core network exists. In the previous work, we introduced an one-way delay monitoring mechanism called DiffProbe. We introduced the basic concept and the implementation details in the MPLS core network. In this paper, we provided an analytical model of the scheme and investigated the performance of the proposed delay measurement mechanism. We evaluate the accuracy of the delay measurement mechanism and the efficiency of the control mechanism with the simulation. The numerical result shows that our proposed algorithm captures the delay performance of the real traffic when the traffic load is high.

Server unavailability reduces mean waiting time in some batch service queuing systems

Abstract This article shows that in some queuing systems server unavailability is sometimes beneficial both to the system owner and to the customers. To be more specific, mean queue size and mean waiting time may decrease even in the presence of server vacations. To this end, we first derive the probability generating function of the batch service M/GB/1 system with multiple vacations. We, then consider the case of exponential service and vacation times and show that under some parameter combinations, mean queue size decreases even in the presence of server vacations. We discuss the implications of this phenomenon.