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== Abstract ==

Consider a node in a communication network with n outgoing links grouped into k trunks of n1 ...., nk links respectively. n1+...+nk = n. Calls arrive in a Poisson stream of rate ? The state of the node is specified by the number of idle links in each trunk. A policy is a rule by which a call, finding the node in some state, is assigned to one of the available links in one of the available outgoing trunks. The links are assumed to have exponential holding times with mean 1/µ which are independent, and are independent of the arrival process. Further, a call assigned to trunk ?, 1 ?? ?k is immediately lost with probability (1--??)--this feature models the nature of the links and the congestion downstream of the node along that route. A call is said to be blocked if all the outgoing links are busy when it arrives. It is known that the blocking probability is independent of the assignment policy. We give an explicit closed form formula for the blocking probability Pb = 1/?n1j1 = 0 .. ?nkjk = 0 [n1, j1] ... [nk, jk](j1 + ... + jk)! (µ/?1)j1 ... (µ/?k)jk where ?1 = ?1 . ? ..., ?k = ?k . ?. This generalizes the well-known Erlang formula of traffic engineering.

== Original document ==

The different versions of the original document can be found in:

* [http://www.eecs.berkeley.edu/~ananth/1987-1989/Erlang_QUESTA.pdf http://www.eecs.berkeley.edu/~ananth/1987-1989/Erlang_QUESTA.pdf]

* [http://xplorestaging.ieee.org/ielx5/4048220/4048221/04048683.pdf?arnumber=4048683 http://xplorestaging.ieee.org/ielx5/4048220/4048221/04048683.pdf?arnumber=4048683],
: [http://dx.doi.org/10.1109/cdc.1985.268519 http://dx.doi.org/10.1109/cdc.1985.268519]

* [http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000004048683 http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000004048683],
: [https://ieeexplore.ieee.org/document/4048683 https://ieeexplore.ieee.org/document/4048683],
: [https://academic.microsoft.com/#/detail/2023193343 https://academic.microsoft.com/#/detail/2023193343]

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Gopinath Anantharam 2008a - Revision history

Scipediacontent: Scipediacontent moved page Draft Content 283572860 to Gopinath Anantharam 2008a

Scipediacontent: Created page with " == Abstract == Consider a node in a communication network with n outgoing links grouped into k trunks of n1 ...., nk links respectively. n1+...+nk = n. Calls arrive in a Poi..."