The Entropy and Delay of Traffic Processes in Atm Networks

In this paper we discuss the application of some recent results obtained from studying the asymptotics and the entropy of flows in large queueing systems to the analysis of entropy variations of traffic processes in ATM networks. We argue that certain important queueing nodes/networks (e.g. ·/M/1, ·/GI/∞ nodes and Jackson networks) are entropy increasing in nature, in that the entropy of the arrival process to such a node/network is strictly less than the entropy of the departure process except when the arrival process is Poisson (which has maximum entropy). The entropy increasing nature of ·/GI/∞ queues is established for a class of input processes. Based on these entropy maximization results and with the aid of some simulations, we investigate the connection between the entropy and delay of ATM traffic processes, and examine the effectiveness of entropy as a measure of “burstiness” of traffic streams in ATM virtual circuits.

[1]  Hamid Ahmadi,et al.  Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks , 1991, IEEE J. Sel. Areas Commun..

[2]  Israel Cidon,et al.  Congestion control for high speed packet switched networks , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[3]  P. Moran,et al.  Reversibility and Stochastic Networks , 1980 .

[4]  Pravin Varaiya,et al.  The entropy of traffic streams in ATM virtual circuits , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[5]  Masayuki Murata,et al.  Analysis of Interdeparture Processes for Bursty Traffic in ATM Networks , 1991, IEEE J. Sel. Areas Commun..

[6]  Martin de Prycker,et al.  Asynchronous Transfer Mode, Solution for Broadband Isdn , 1991 .

[7]  Ward Whitt,et al.  Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data , 1986, IEEE J. Sel. Areas Commun..

[8]  Frank P. Kelly,et al.  Effective bandwidths at multi-class queues , 1991, Queueing Syst. Theory Appl..

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

[10]  San-qi Li,et al.  Traffic analysis in large-scale high-speed integrated networks: validation of nodal decomposition approach , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[11]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[12]  F. Baccelli,et al.  Palm Probabilities and Stationary Queues , 1987 .

[13]  Richard J. Gibbens,et al.  Effective bandwidths for the multi-type UAS channel , 1991, Queueing Syst. Theory Appl..

[14]  J. McFadden.  The Entropy of a Point Process , 1965 .

[15]  B. Prabhakar,et al.  On the Weak Convergence of Departures from an Infinite Series of $\cdot /M/ 1$ Queues , 1995 .

[16]  V. Anantharam.  Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$ , 1993 .

[17]  Debasis Mitra,et al.  Analysis and design of rate-based congestion control of high speed networks, I: stochastic fluid models, access regulation , 1991, Queueing Syst. Theory Appl..

[18]  J.-P. Coudreuse,et al.  Spacing cells protects and enhances utilization of ATM network links , 1992, IEEE Network.

[19]  Hirokazu Ohnishi,et al.  Flow control schemes and delay/loss tradeoff in ATM networks , 1988, IEEE J. Sel. Areas Commun..