Refined parametric decomposition approximation of queueing networks
Abstract
For general queueing networks, the exact performance measures such as average waiting time in queue are not available in closed form. Even though these performance measures can be estimated by simulation, a good approximation can sometimes be obtained quickly by decomposition methods. The key feature of the decomposition approach is the analysis of each station in isolation. In many methods, the departure process from each station is approximated as a renewal process by the stationary interval method. However, it is known that the stationary interval method significantly underestimates the average waiting time at bottleneck stations in some cases. This is known as the “heavy traffic bottleneck phenomenon”, and is caused by the cumulative effect of many small autocorrelations among successive interarrival times not captured by the stationary interval approximation method. These small autocorrelations can be characterized by the index of dispersion for intervals (IDI) sequence of the interarrival times. This research analyzes IDI's of interarrival times under various situations and presents a refined queueing network analyzer, RQNA, that takes account of the heavy traffic bottleneck phenomenon using the IDI. The RQNA is different from previous decomposition approximations in the sense that each arrival process is approximated as a non-renewal process and that two different levels of correlations are taken into account. First, the correlations among successive interarrival times of an arrival process are approximated in terms of the IDI. A refined queueing formula is proposed for the approximation of the IDI for the interdeparture times. Second, the correlation among arrival processes is modeled by the innovations method developed by O'Cinneide and Muralidharan. The innovations method is designed to keep track of the correlations among split streams in open queueing networks. The RQNA is a synthesis of the refined queueing formula and the innovations method. Our implementation of RQNA shows a significant improvement in approximation of average waiting time at the bottleneck station and indicates that the heavy traffic bottleneck phenomenon in quite many open queueing networks can be resolved by our approach.
Degree
Ph.D.
Advisors
O'Cinneide, Purdue University.
Subject Area
Industrial engineering|Operations research|Management
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