Mathematical Methods for Construction of Queueing Modelsto the English edition Many processes that describe the operation of engineering, economic, organiza tional, and other systems are represented as sequences of operations performed on material, information, or other types of flows. Typical examples are processes of connection of telephone users, data transmission and processing, calculation at multi user computer centers, and queueing at service centers. The models studied by the theory of service systems, or queueing theory, are used to describe such processes. The more pessimistic term "queueing theory" is used more often in the non-Soviet literature. Random arrivals (requests for service), probability distributions defining queueing processes (distributions of service times and acceptable waiting times), and structure parameters (customer priorities, parameters that delimit acceptable queues, parameters that define paths of customers, etc.) are characteristic com ponents of queueing models. Typical output characteristics of queueing models are the probability distributions of queue lengths, waiting times, lengths of busy periods, and so forth. |
Contents
Substantive Formulation of the Problem | 4 |
Simplification and Approximation of Probability Models | 8 |
The Concept of Characterization as a General Mathematical Schema | 17 |
Copyright | |
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Mathematical Methods for Construction of Queueing Models Vladimir Kalashnikov No preview available - 2013 |
Common terms and phrases
analogous approximation characterization problem compound metric construction COROLLARY d₁ defined by equation definition distance distributed random variables distribution functions estimate example exponentially distributed finite following bound formulate fulfilled function f ideal metric identically distributed inequality input data input flow intervals Laplace-Stieltjes transform lemma Let us consider Let us define Let us note Let us write Lévy metric Lévy-Prokhorov metric LM(X Markov chain measure metric space minimal metric notation obtain output data P₁ parameter perturbed model probability metric proof quantity quasimetric quasimetric space queueing models queueing theory random variables right side S. T. Rachev Section semi-Markov process sequence simple metric stability of characterization subset theorem tion unperturbed V. M. Zolotarev V. V. Kalashnikov valid values vector weak convergence μα μη