Chapter 4Standard Queues

4.1 Introduction of Queues (General Birth and Death Process)

In this book, words such as “queue,” “waiting line,” and “congestion” are used interchangeably. Although a queueing model could be deterministic, queueing theory is an application of stochastic processes, that is, mathematical theory and analysis of waiting lines and delays while waiting in a line or queue for obtaining service from a system.

The basic queueing models, as described later, are examples of birth and death processes. In other words, we consider the stochastic behavior of processes arising in connection with services in cases where random fluctuations occur. The idea is to predict fluctuating demands from observational data, which will ultimately enable an enterprise to provide adequate service with tolerable waiting times for its clients. The art of queueing theory is to construct a model that is simple to carry out mathematical analysis, but containing sufficient details so that its performance measures may reflect the behavior of the real system. Thus, queueing theory is considered as a branch of operations research, because the results are often used when making business decisions about the resources needed to provide a service. The reader may refer to Haghighi and Mishev (2014) for some examples. Recently, expressions such as Q-nomy's queue management system has been used to “organize waiting lines by providing visitors with an easy ordering method based on “first-in-first-out,” ...

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