# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
A calculus for network delay. I: Network elements in isolation. (English) Zbl 0712.94028
Summary: A calculus is developed in this paper (Part I) and the sequel (Part II; reviewed below (see Zbl 0712.94029)) for obtaining bounds on delay and buffering requirements in a communication network operating in a packet switched mode under a fixed routing strategy. The theory we develop is different from traditional approaches to analyzing delay because the model we use to describe the entry of data into the network is nonprobabilistic: We suppose that the data stream entered into the network by any given user satisfies “burstiness constraints”. A data stream is said to satisfy a burstiness constraint if the quantity of data from the stream contained in any interval of time is less than a value that depends on the length of the interval. Several network elements are defined that can be used as building blocks to model a wide variety of communication networks. Each type of network element is analyzed by assuming that the traffic entering it satisfies burstiness constraints. Under this assumption bounds are obtained on delay and buffering requirements for the network element, burstiness constraints satisfied by the traffic that exits the element are derived.

##### MSC:
 94C99 Circuits, networks