Simulation Modelling of the Addition of Servers in Queueing Systems


Published: 2020-04-29

Page: 70-77

Mihir Dash *

Alliance University, Bangalore, India.

*Author to whom correspondence should be addressed.


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.

How to Cite

Dash, M. (2020). Simulation Modelling of the Addition of Servers in Queueing Systems. Asian Journal of Pure and Applied Mathematics, 2(1), 70–77. Retrieved from


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Gross D, Harris CM. Fundamentals of queueing theory. Third Ed. John Wiley & Sons, New York; 1998.

Chao X, Scott C. Several results on the design of queueing systems. Operations Research. 2000;48(6):965-970.

Scheller-Wolf A. Necessary and sufficient conditions for delay moments in FIFO multiserver queues with an application comparing slow servers with one fast one. Operations Research. 2003;51(5):748-758.

Morse P. Queues, inventories and maintenance. John Wiley and Sons; 1958.

Stidham S. On the optimality of single-server queueing systems. Operations Research. 1970;18(4):708-732.

Brumelle SL. Some inequalities for parallel-server queues. Operations Research. 1971;19:402-413.

Reiman MI, Simon B. Open queueing systems in light traffic. Mathematics of Operations Research. 1989;14(1):26-59.

Iglehart DL, Whitt W. Multiple channel queues in heavy traffic I. Advances in Applied Probability. 1970;2:150-177.

Hillier FS. Economic models for industrial waiting line problems. Management Science. 1963;10(1):119-130.

Beckman MJ. Making the customers wait: The optimal number of servers in a queueing system. Operations-Research-Spektrum. 1994;16(2):77-79.

Little JDC. A proof for the queuing formula: L = λW. Operations Research. 1961;9(3):383-387.

Dash M. A model for waiting times for non-stationary queueing systems. Journal of Management and Science. 2016;1(1):68-71.