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Correlation functions in queueing theory
Journal of Applied Probability, 1972The object of this paper is to study the actual waiting time of a customer in aGI/G/1 queue. This is an important criterion from the viewpoint of both the customers and the efficient functioning of the counter. Suitable point processes in the product space of load and time parameters for any general inter-arrival and service time distributions are ...
R. Subramanian +2 more
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Annals of Operations Research, 1990
This paper presents a brief survey of research in the field of queueing theory carried out in the People's Republic of China from the late fifties until the present. Special attention is given to transient behaviour of queueing systems and heavy-traffic results.
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This paper presents a brief survey of research in the field of queueing theory carried out in the People's Republic of China from the late fifties until the present. Special attention is given to transient behaviour of queueing systems and heavy-traffic results.
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Introduction to Queueing Theory
1999A simple queueing system was first introduced in Chapter 1 as an example of a DES. We have since repeatedly used it to illustrate many of the ideas and techniques discussed thus far. In this chapter, we will take a more in-depth look at queueing systems.
Christos G. Cassandras +1 more
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1981
Queueing theory is a generic term for mathematical structures inspired by and descriptive of service systems with random features such as random delay, randomly arriving customers, etc.† Such systems can be classified in two ways: according to the structure and postulates which characterize the operation, on the one hand, and according to the random ...
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Queueing theory is a generic term for mathematical structures inspired by and descriptive of service systems with random features such as random delay, randomly arriving customers, etc.† Such systems can be classified in two ways: according to the structure and postulates which characterize the operation, on the one hand, and according to the random ...
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Renewal theory. Queueing theory
2009Queueing theory was founded by Danish scientist A. Erlang who worked for the Copenhagen Telephone Exchange for many years at the beginning of the twentieth century. The works of F. Pollaczek, A. Khinchin, L. Takacs, and also B. Gnedenko and his school had significant influence on the development of queueing theory.
Dmytro Gusak +4 more
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2011
Queuing theory models provide these benefits with at least two types of associated costs. First, users need to make a limiting set of assumptions about arrivals and service distributions. These assumptions might not apply to any reasonable approximation in some cases of interest. Making them could lead to inadvisable recommendations.
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Queuing theory models provide these benefits with at least two types of associated costs. First, users need to make a limiting set of assumptions about arrivals and service distributions. These assumptions might not apply to any reasonable approximation in some cases of interest. Making them could lead to inadvisable recommendations.
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Two results in the theory of queues
Journal of Applied Probability, 1970Summary In this paper it is shown that the distribution of the instant of service of a customer is symmetric as between the distributions of service and interarrival time. Also U(t), the expected number of departures in (0, t), is a delayed renewal function for the GI/M/1 queue.
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Sixty Years of Queueing Theory
Management Science, 1969Queueing Theory has been attacked on two fronts. Some theoreticians say that Queueing Theory is closed. Some practitioners feel that there is very little in it for use. In view of this, it seems that after six decades of development it is time for stock taking.
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On fluctuation problems in the theory of queues
Advances in Applied Probability, 1976This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions ...
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Journal of the Royal Statistical Society. Series A (General), 1973 Jonathan Rosenhead, E. Page
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