Estimation Approaches of Mean Response Time for a Two Stage Open Queueing Network Model

Vinayak K Gedam,Suresh B Pathare

doi:10.19139/soic.v3i3.79

Vinayak K Gedam, Suresh B Pathare

Open Access

https://doi.org/10.19139/soic.v3i3.79

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Abstract

In the analysis of queueing network models, the response time plays an important role in studying the various characteristics. In this paper data based recurrence relation is used to compute a sequence of response time. The sample means from those response times, denoted by $\hat {r_1} $ and $ \hat {r_2}$ are used to estimate true mean response time $r_1$ and $r_2$. Further we construct some confidence intervals for mean response time $r_1$ and $r_2$ of a two stage open queueing network model. A numerical simulation study is conducted in order to demonstrate performance of the proposed estimator $ \hat {r_1} $ and $ \hat {r_2}$ and bootstrap confidence intervals of $ r_1$ and $r_2$. Also we investigate the accuracy of the different confidence intervals by calculating the coverage percentage, average length, relative coverage and relative average length.

Highlights

The response time is defined as the time spent by a customer from arrival until it departs
The statistical inference in queueing networks are rarely found in the literature and the work of related problems in the past mainly concentrates on only parametric statistical inference, in which the distribution of population is with a known form
The coverage percentages, average lengths, relative coverage’s and relative average lengths of mean response time ri, i = 1, 2 based on simulation study for queuing network models for different interval estimation approaches are shown in Tables 4 to 6 for large sample and Tables 7 to 9 for small sample

Summary

Introduction

The response time is defined as the time spent by a customer from arrival until it departs. Chu and Ke [2] studied the interval estimation of mean response time for the G/M/1 queueing system using empirical Laplace function approach. Let (Xij, Yij, i = 1, 2, j = 1, 2, · · · , n) be a random sample drawn from (Xi, Yi, i = 1, 2) represents inter-arrival times and service times for jth customer at ith node of a queueing network. Using CAN estimators ri, i = 1, 2 and its associated approximate variances σi2/n, i = 1, 2, we construct confidence intervals for mean response times ri, i = 1, 2 of a distribution-free two-stage open queueing network. As sample size is small, using the student t-distribution we construct confidence intervals for mean response times ri, i = 1, 2 of a two-stage open queueing network. 9. Bias-corrected and accelerated bootstrap(BCaB) Confidence Intervals for mean response times.

10. Simulation Study

11. Conclusions