Asian Journal of Pure and Applied Mathematics 2(1): 70-77, 2020; Article no.AJPAM.189 _____________________________________ *Corresponding author: E-mail: mihirda@rediffmail.com; Simulation Modelling of the Addition of Servers in Queueing Systems Mihir Dash 1* 1 Alliance University, Bangalore, India. Author’s contribution The sole author designed, analysed, interpreted and prepared the manuscript. Received: 21 February 2020 Accepted: 27 April 2020 Published: 29 April 2020 _______________________________________________________________________________ Abstract 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. Keywords: M/M/1 and M/M/2 queueing systems; simulation; utilization rate λ/µ; Chow test ; structural breaks. 1 Introduction The operating characteristics of queueing systems have been studied extensively, particularly for stationary queueing systems (Gross and Harris, [1]). The most important determinant of the operating characteristics of queueing systems is the utilisation rate λ/µ, that is, the ratio of the arrival rate λ and the service rate µ. This parameter is used in practice to take decisions about several service arrangements, particularly the number of channels/servers. The improvement in operating characteristics of queueing systems when additional servers are introduced has been studied by several authors. Chao and Scott [2] showed that the mean waiting time in a queueing system decreases with each addition of a server, reaching a minimum only in the limiting case of an infinite number of servers. Scheller-Wolf [3] showed that the tail of the stationary delay distribution is significantly reduced by increasing the number of servers under highly variable service demand distributions. Several authors have proposed conditions under which a single server is optimal: Morse [4] for the M/M/k/FCFS Original Research Article