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

Vinayak K Gedam, Suresh B Pathare
2015 Statistics, Optimization and Information Computing  
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 byr 1 andr 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
more » ... l simulation study is conducted in order to demonstrate performance of the proposed estimatorr 1 andr 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. Guntur [15], Mooney and Duval [21], Young [27], Rubin [24], Miller [20]. Gedam and Pathare [12, 13, 14, 22] have studied the nonparametric statistical estimation approaches of various queueing network models. Chu and Ke [3] examined the statistical behavior of the mean response time for the M/G/1 queueing system using bootstrapping simulation. Chu and Ke [2] studied the interval estimation of mean response time for the G/M/1 queueing system using empirical Laplace function approach. Chu and Ke [4] developed a data based recurrence relation to compute a sequence mean response times and constructed confidence intervals of mean response times for the G/G/1 queueing system using simulation. This motivates us to develop the nonparametric statistical inferences of mean response time for a queueing network model. Consider the two-stage open queueing network shown in Figure 1 .
doi:10.19139/soic.v3i3.79 fatcat:mompevg3uzgsfk2v5f7fjsdkia