Yoshiaki Shikata

Multi-Server Loss System with T-Limited Service for Traffic Control in Information Networks

To handle more phone and personal computer users in such a natural disaster as terribly strong earthquake, a traffic control has been previously proposed by limiting the individual call holding time. This traffic control mechanism leads to our T-limited service. By T-limited service, we mean that the service time is limited to a threshold T. The call whose service time reaches T is assumed to be lost. For evaluating the traffic control performance, we present multi-server loss systems with T-limited service. Without any retrial queues, we analyze a Poisson input and general service time loss system to derive the steady-state distribution of the number of calls in the system. With a retrial queue, assuming further that the call sojourn time at the retrial queue is exponentially distributed and that the T-limited service time is also exponentially distributed, we propose an approximation for the steady-state distribution of the number of calls in the system. Our approximation accuracy is validated by a simulation result.

A single-server queueing system with modified service mechanism

We consider a single-server GI/G/1 queueing system with modified service mechanism. By modified service mechanism, we mean that the service time distribution (H0) for the customers arriving to find the system idle may be different from the service time distribution (H1) for the customers arriving to find the system busy. We present qualitative relationships among the performance measures in the system. Approximating the virtual waiting time process via the diffusion process and combining the qualitative relationships, we propose a new approximate formula for the mean performance measures. For special cases, our approximation is seen to be consistent with the previously-obtained exact results for the M/G/1 queueing system with modified service mechanism, and it is further seen to be consistent with the previously-proposed approximate results for the GI/GI/1 queueing system with standard ( H0 = H1 ) service mechanism.

Diffusion Approximation for a Web-Server System with Proxy Servers

It is an important and urgent Operations Research (OR) issue to evaluate the delay in a web-server system handling internet commerce real-time services. Usually, proxy servers in differently-located sites enable us to shorten the web-server access delay in order to guarantee the quality of real-time application services. However, there exists almost no literature on the queueing analyses for the web-server system with proxy servers. The goal of this paper is to provide a queueing analysis for the web-server system. We derive the statistics of the individual output processes from the proxy servers. Regarding the unfinished workload in the web-server system with input as a diffusion process, we derive a mean-delay explicit formula.

Routing strategy of a prioritized limited multi-server processor-sharing system

In this work, routing strategies of an arriving request to a server in a prioritized limited multi-server processor-sharing (PS) system are studied in order to optimize a given performance criterion. In this system, an arriving request enters the dispatcher, which routes this request to each server according to a predetermined strategy. In the prioritized limited PS server, a high-priority request is allocated a service ratio that is m (called the priority ratio) times greater than that of a low-priority request. Moreover, the sum of the number of the requests receiving service is restricted to a fixed value. The arriving request which cannot receive service will be queued (waiting system) or rejected (loss system). In this server, at the arrival (or departure) of a request, the extension (or shortening) of the remaining sojourn time of each request that is receiving service can be calculated using the number of requests and priority ratio. Employing a simulation program to execute these events and calculations enables us to analyze the performance of this system, such as the loss probability, mean sojourn time, and mean waiting time. Based on the evaluation results, the most suitable routing strategy for the loss or waiting system is clarified.

Approximate Formula of Delay-Time Variance in Renewal-Input General-Service-Time Single-Server Queueing System

Approximate formulas of the variance of the waiting-time (also called as delay-time variance) in a renewal-input general-service-time single-server (GI/GI/1) system play an important role in practical applications of the queueing theory. However, there exists almost no literature on the approximate formulas of the delay-time variance in the GI/GI/1 system. The goal of this paper is to present an approximate formula for the delay-time variance. Our approach is based on the combination of a higher-moment relationship between the unfinished work and the waiting time, and the diffusion process approximation for the unfinished work. To derive the former relationship, we apply Miyazawa’s rate conservation law for the stationary point process. Our approximate formula is shown to converge to the exact result for the Poisson-input system as traffic intensity goes to the unity. The accuracy of our approximation is validated by simulation results.