Queuing theory

As it is impossible to discuss them all, a number of cases has been compiled in Table 42.1 with reference to relevant literature in which the cases are discussed by queuing theory or are simulated (see Section 42.4). 

In Section 42.2 we have discussed that queuing theory may provide a good qualitative picture of the behaviour of queues in an analytical laboratory. However the analytical process is too complex to obtain good quantitative predictions. As this was also true for queuing problems in other fields, another branch of Operations Research, called Discrete Event Simulation emerged. The basic principle of discrete event simulation is to generate sample arrivals. Each sample is characterized by a number of descriptors, e.g. one of those descriptors is the analysis time. In the jargon of simulation software, a sample is an object, with a number of attributes (e.g. analysis time) and associated values (e.g. 30 min). Other objects are e.g. instruments and analysts. A possible attribute is a list of the analytical... 

A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern Ltd., New Delhi, 1978 H. M. Srivastava and B. R. K. Kashyap, Special Functions in Queuing Theory and Related Stochastic Processes Academic Press, New York, 1982. 

The term Markov chain frequently appears in this chapter. This term is named after the Russian mathematician Andre Markov (1856-1922). The Markov theory is widely applied in many fields, including the analysis of stock-markets, traffic flows, queuing theories (e.g. modelling a telephone customer service hotline), reliability theories (e.g. modelling the time for a component to wear out) and many other systems involving random processes. 

Discrete event simulation is based on queuing theory, which is the mathematical study of waiting in lines or queues. 

Robertazzi, T. 1994. Computer networks and systems Queuing theory and performance evaluation. New York Springer-Verlag. 

R.E. Matick, T. J. Heller, M. Ignatowski. Analytical analysis of finite cache penalty and cycles per instruction of a multiprocessor memory hierarchy using miss rates and queuing theory. IBM J. Research Development, Vol. 45, No. 6, Nov. 2001, pp. 819 - 842. 

Hale, J. (1988), Queuing Theory in the Emergency Department, in Proceedings of the 1988 Annual Healthcare Systems Conference, vol. 1, AHA, pp. 1-7. 

Ortiz, A., and Etter, G. (1990), Simulation Modeling vs. Queuing Theory, in Proceedings of the 1990 Annual Healthcare Information and Management Systems Conference, AHA, pp. 349-357. Roberts, S. D., and English, W. L., Eds. (1981), Survey of the Application of Simulation to Healthcare, Simulation Series, Vol. 10, No. 1, Society for Computer Simulation, La JoUa, CA. 

Unnecessary work and delay encountered in indirect and expense work are meiinly due to queues. Workers need to stand in line at the tool crib, the stockroom, or the fax machine, photocopy machine, or some other equipment. Through the application of queuing theory, analysts may be able to determine the waiting time incurred in such activities as well as determine the optimum number of service facilities to improve service quality. 

Queueing networks, 2163-2170 decomposition methods, 2167-2170 general product-form networks, 2165-2167 Jackson networks, 2164-2165 Queuing theory, 128... 

Queuing theory models are used for describing the relationships between logistic parameters. 

First, a summary of an availability analysis model is presented. Based on queuing theory resources, the details of this model were described in a previous article (Pizzo Cugnasca, 2006). In addition, some specific degradation characteristics were considered, representing computer systems operations in airspace... 

Availability analysis of computer systems with queuing theory models... 

This section proposes an abstract model of risk recovery based on concepts borrowed from queuing theory and reliability engineering (Bilsel and Ravindran, 2012). In queuing theory, it is customary to model a system using a Poisson process and assume Exponential inter-arrival times. Similar methods are used in reliability engineering, especially for modeling the reliability... 

In contrast to the continuous models, the discrete models consider the processes at the level of individual structural elements, e.g. individual fibres, threads or loops, or individual stages of the process. In these models the processes are modelled as a series of states where the transition from one state to another happens with a probability. The underpinning theories for these models are theory of Markov processes (Kemeny and Snell, 1960), queuing theory (Gross et nf, 2008), and finite automata theory (Anderson, 2006 Hopcroft et al., 2007). 

Grishanov S, Siewe F and Cassidy T (2011), An apphcation of queuing theory to modelling of melange yarns. Part II A method of estimating the fibre migration probabUities and a yarn structure simulation algorithm , Text Res /, 81(8), 798-818. 

Siewe F, Grishanov S, Cassidy T and Banyard G (2009), An appUcation of queuing theory to modelling of melange yarns. Part I A queuing model of melange yarn structure . Text Res J, 79(16), 1467-1485. 

The Poisson distribution, denoted by p(A), is a discrete distribution used to model the occurrence of independent events in a given time interval or space. It is the result of taking the binomial distribution and extending the number of trials to infinity. The Poisson distribution is encountered in reliability engineering to model the time occurrences of failure and used in queuing theory to model the behaviour of a queue. Useful properties of the Poisson distribution are summarised in Table 2.6. 

Transportation Research, Part B Methodological (0191-2615). Scope Development and solution to problems, particularly those such as traffic flow, analysis of transportation networks, and queuing theory that require mathematical analysis. 

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