Queuing simulation is based on the idea of queuing theory thar stems from operations research and helps to analyse and model resource allocation and process duration for a variety of different applications.

**What is it?**

Queuing simulation as a mehod is used to analyze how systems with limited resources distribute those resources to elements waiting to be served, while waiting elements may exhibit discrete variability in demand, i.e. arrival times and require discrete processing time.

Queuing theory based analysis is regularly used for e.g. telecommunications, computer networks, predicting computer performance, traffic, call centres, etc.

Kleinrock describes it as: Any system in which arrivals place demands upon a finite capacity resource may be termed a queuing system. Different queuing models are possible; however, all follow the structure of:

- Arrival process
- Service process
- Number of servers

The arrival time and also the service process time can take different forms of probability distributions. Both can be either: Markov chain (M), deterministic (D), or arbitrary (G). Entry into the system is either in batch or bulk while servers are oriented either in parallel or in line. Commonly queuing models are described as M/M/1 or M/D/c models referring to the respective properties of the arrival process / services process / number of servers.

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Markov chain: In mathematics, a Markov chain is a stochastic process with the Markov property. Markov property means that, given the present state, future states are independent of the past states. In other words, the description of the present state fully captures all the information that could influence the future evolution of the process. Future states will be reached through a probabilistic process instead of a deterministic one.*

*Poisson distribution: In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.*

**How is it used?**

Queuing simulation is used to determine possible bottlenecks in resource allocation and enables a simulation of different usage stages and their consequences on waiting lines. It thereby makes it possible to estimate waiting times or optimize server utilization.

**What does it tell?**

Queuing simulation tells about the implications of service process configurations on the possibility of waiting lines and if and when those occur, how they develop over time (e.g. the implications of a red traffic light on a road for the flow or throughput of the traffic on the road). Its application in Workplace Management can be seen in the modelling of workspace usage over time. It can be used to optimize person/seat ratios and helps understanding the inherent limitations of such actions. It thereby enables Workplaces Managers to better leverage non-territorial workplace arrangements and help communicating utilization rate limitations to management.

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**Read more: **

Bhat, U.N. (2008) An Introduction to Queueing Theory: Modeling and Analysis in Applications (Statistics for Industry and Technology).

Daganzo, Carlos F. & Laval, Jorge A. (2003) Moving bottlenecks: a numerical method that converges in flows.

Fomundam S. & Herrmann J. (2007) A Survey of Queuing Theory Applications in Healthcare http://www.lib.umd.edu/drum/bitstream/1903/7222/1/tr_2007-24.pdf

Hlynka, M. (2009) Myron Hlynka's Queueing Theory Page, http://web2.uwindsor.ca/math/hlynka/queue.html

Kleinrock, L. (1975) Queueing Systems. Volume 1. Theory. Srivastava, H. M. & Kashyap, B. R. K. (1982) Special functions in queuing theory and related stochastic processes.