A New Approximation for Multiserver Waiting Time, for Layered Queueing Systems

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  • Performance models must solve quickly even for large systems, to be useful in searching for changes that might give improvements. Thus, efficient solution is important, and is stressed in the Layered Queueing Network Solver (LQNS). This thesis introduces two approximations that approximate the queue states by binomial probabilities, to estimate the waiting time for multiservers (such as multi-threaded tasks or multi-core CPUs). Accuracy and speed of convergence were evaluated for one and for multiple classes of customers. The binomial approximations are compared with the "Rolia-Franks" approximation which is a relatively fast approximation that is currently used in the LQNS model-solving tool. One of the approximations (called the "Arrival-Theorem Binomial", or AB) is better, with smaller error in most cases. A novel approach for dealing with multiple classes is also evaluated, and a case study is included in which the AB approximation is combined with an LQNS solution.

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  • Copyright © 2022 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
Date Created
  • 2022


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