Effective bandwidths at multi-class queues

Consider a queue which serves traffic from a number of distinct sources and which is required to deliver a performance guarantee, expressed in terms of the mean delay or the probability the delay exceeds a threshold. For various simple models we show that an effective bandwidth can be associated with each source, and that the queue can deliver its performance guarantee by limiting the sources served so that their effective bandwidths sum to less than the capacity of the queue.

[1]  S. Ross.  Bounds on the delay distribution in GI/G/1 queues , 1974, Journal of Applied Probability.

[2]  Arne Jensen,et al.  The life and works of A. K. Erlang , 1960 .

[3]  F. Kelly.  Routing in circuit-switched networks: optimization, shadow prices and decentralization , 1988, Advances in Applied Probability.

[4]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[5]  Walter L. Smith.  On the distribution of queueing times , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[7]  J. Kingman.  Inequalities in the Theory of Queues , 1970 .

[8]  Zbigniew Dziong,et al.  Admission Control and Routing in ATM Networks , 1990, Comput. Networks ISDN Syst..

[9]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[10]  S. Zachary,et al.  Loss networks , 2009, 0903.0640.

[11]  F. Kelly.  The throughput of a series of buffers , 1982, Advances in Applied Probability.

[12]  W. Whitt,et al.  Blocking when service is required from several facilities simultaneously , 1985, AT&T Technical Journal.

[13]  Richard J. Gibbens,et al.  Dynamic Routing in Fully Connected Networks , 1990 .

[14]  T. R. Griffiths.  Analysis of a connection acceptance strategy for asynchronous transfer mode networks , 1990, [Proceedings] GLOBECOM '90: IEEE Global Telecommunications Conference and Exhibition.

[15]  Joseph Y. Hui.  Resource allocation for broadband networks , 1988, IEEE J. Sel. Areas Commun..

[16]  P. Billingsley,et al.  Probability and Measure , 1980 .

[17]  Joseph Yu Hui,et al.  Switching and Traffic Theory for Integrated Broadband Networks , 1990 .