The superposition of periodic cell arrival streams in an ATM multiplexer

James Roberts, Jorma Virtamo

Research output: Contribution to journalArticleScientificpeer-review

88 Citations (Scopus)


The authors consider the queue arising in a multiservice network using ATM (asynchronous transfer mode) when a superposition of periodic streams of constant-length cells is multiplexed on a high-speed link. An exact closed formula is derived for the queue length distribution in the case where all streams have the same period, and tight upper and lower bounds are obtained on this distribution when the periods are different. Numerical results confirm that the use of a Poisson approximation (i.e. the M/D/1 queue) can lead to a significant overestimation of buffer requirements, particularly in the case of heavy loads. Buffer requirements for a mixture of different period streams can be accurately estimated from the upper bound on the queue length distribution. For given load, requirements increase with the number of long-period (i.e. low-bit rate) sources. The results are deduced from a novel characterization of the single-server constant service time queue, which should be useful in other applications.
Original languageEnglish
Pages (from-to)298-303
JournalIEEE Transactions on Communications
Issue number2
Publication statusPublished - 1991
MoE publication typeA1 Journal article-refereed


Dive into the research topics of 'The superposition of periodic cell arrival streams in an ATM multiplexer'. Together they form a unique fingerprint.

Cite this