Abstract
In tagged customer approach, an arbitrary message/customer is picked as the tagged message/customer and its passage through the network (closed queuing, with finite steady-state distribution) is tracked. By this method, the problem of computing the response time distribution of the tagged customer is transformed into time to absorption distribution of a finite-state, continuous time Markov chain (CTMC), conditioned on the state of the system upon entry. Using the arrival theorem of Sevcik and Mitrani [8], distribution of the other customers in the network at the instant of arrival of tagged customer can be established. This allows obtaining the unconditional response time distribution.
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Verma, A.K., Ajit, S., Kumar, M. (2011). Response-Time Models and Timeliness Hazard Rate. In: Dependability of Networked Computer-based Systems. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-318-3_6
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DOI: https://doi.org/10.1007/978-0-85729-318-3_6
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