# Queuing Theory and Constant Service Time Model Essay

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Updated: Aug 16th, 2020

## Introduction

The queuing theory refers to a formal study of queues in operations management that is based on the fields of mathematics such as statistics and probability theory. The theory is used when proposing different models for use in the description of queues, as well as the process behind the queues (Gross, 2008). As such, queuing theory is very useful in the service industry because it helps organizations in such industries to improve their service delivery to customers.

According to Gross (2008), organizations that apply the queuing theory in their operations are likely to have several advantages. For example, the queuing theory offers the concerned organization with a model, which can determine the pattern in which customers use to arrive.

Through such a platform, organizations know the suitable number of services points to install. Secondly, queuing theory helps the management of any organization to create balance in a situation where they are faced with a dilemma to optimize either the service costs or the waiting costs. Additionally, the queuing theory is suitable for any service industry because it offers the organization a platform to understand better the concept of waiting lines. Such understanding helps organizations to establish suitable and quality service for which customers can tolerate waiting.

Despite the advantages above, queuing theory has several limitations for any service organization. First, most of the models that are available for organizations to use are quite complex, making it hard for the management to understand their use. As such, the models are very uncertain considering that there are different types of theoretical probability distributions and parameters applied in any model.

Secondly, the use of queuing theory makes it hard for the management to analyze the probability distribution of outcomes in comparison to the actual outcomes. For example, for a multichannel queuing, such analysis may not be beneficial considering that the departure from one queue is likely to lead to the arrival of another queue.

Thirdly, it is hard for organizations to match the observations of the time intervals to the mathematical distributions. As such, most of the theoretical models, such as the Poisson distribution, do not apply to real business situations (Gross, 2008).

## Constant Service Time Model

The constant service time model refers to a constant distribution whereby an organization follows a fixed cycle to process equipment or customers (Roongrat, 2011). This type of model has several benefits for any organization. For example, organizations making use of this model can incorporate the Poisson process, which allows the organization to analyze the stationary waiting time. The incorporation of the stationary time waiting for distribution helps the concerned organization to analyze the queue length distribution easily.

Thus, using a constant time service model, organizations are in a position to determine both the distribution probability and the actual distribution in any situation.

Roongrat (2011) asserted that the use of constant service time model allows an organization to work with actual probabilities because the rates applied, in this case, are always certain. Additionally, the average length of a queue, the average waiting time in a queue as well as the average customers in a system can be determined easily. Usually, the values for the queue length, waiting time in queue, and the average customers in a system are halved in the constant time service model. For this reason, an organization can plan their service delivery effectively.

## References

Gross, D. (2008). Fundamentals of queuing theory. John Wiley & Sons.

Roongrat, C. (2011). Constant service time queuing model. London: Sage.

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IvyPanda. (2020) 'Queuing Theory and Constant Service Time Model'. 16 August.