The objective of the study was to analyse the improvement in operating characteristics of an M./M/1 queueing system with the addition of a server, as a function of the utilisation rate λ/µ. The study has applied a simulation model for M/M/1 and M/M/2 systems using the same generated set of random inputs to examine the impact of the addition of servers in queueing systems. The improvement in system length ΔL was analysed using four proposed models: ln(ΔL) as linear and quadratic functions of λ/µ, and as linear and quadratic functions of ln(λ/µ). The Chow test was used to examine structural breaks at λ/µ = 1 and λ/µ = 2.
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Keywords: M/M/1 and M/M/2 queueing systems, simulation, utilization rate λ/µ, Chow test, structural breaks
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