Performance analysis of a threshold-based discrete-time queue using maximum entropy

The provision of guaranteed QoS for various Internet traffic types has become a challenging problem for researchers. New Internet applications, mostly multimedia-based, require differentiated treatments under certain QoS constraints. Due to a rapid increase in these new services, Internet routers are facing serious traffic congestion problems. This paper presents an approximate analytical performance model in a discrete-time queue, based on closed form expressions using queue threshold, to control the congestion caused by the bursty Internet traffic. The methodology of maximum entropy (ME) has been used to characterize closed form expressions for the state and blocking probabilities. A discrete-time GGeo/GGeo/1/{N1, N2} censored queue with finite capacity, N2, external compound Bernoulli traffic process and generalised geometric transmission times under a first come first serve (FCFS) rule and arrival first (AF) buffer management policy has been used for the solution process. To satisfy the low delay along with high throughput, a threshold, N1, has been incorporated to slow the arrival process from mean arrival rate k1 to k2 once the instantaneous queue length has been reached, otherwise the source operates normally. This creates an implicit feedback from the queue to the arrival process. The system can be potentially used as a model for congestion control based on the Random Early Detection (RED) mechanism. Typical numerical experiments have been included to show the credibility of ME solution against simulation for various performance measures and to demonstrate the performance evaluation of the proposed analytical model.

[1]  Irfan-Ullah Awan,et al.  MEM for arbitrary closed queueing networks with RS-blocking and multiple job classes , 1998, Ann. Oper. Res..

[2]  M. Tribus.  Rational descriptions, decisions, and designs , 1969 .

[3]  Richard J. Gibbens,et al.  Distributed connection acceptance control for a connectionless network , 1999 .

[4]  Steven H. Low,et al.  An enhanced random early marking algorithm for Internet flow control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[5]  D. Lapsley,et al.  Random early marking for Internet congestion control , 1999, Seamless Interconnection for Universal Services. Global Telecommunications Conference. GLOBECOM'99. (Cat. No.99CH37042).

[6]  Demetres D. Kouvatsos,et al.  A Universal Maximum Entropy Algorithm for General Multiple Class Open Networks with Mixed Service Disciplines , 1989 .

[7]  Demetres D. Kouvatsos,et al.  GGeo-Type Approximations for General Discrete-Time Queueing Systems , 1993, Modelling and Evaluation of ATM Networks.

[8]  Demetres D. Kouvatsos,et al.  ME-Based Approximations for General Discrete-Time Queueing Models , 1994, Perform. Evaluation.

[9]  A. Mokhtar,et al.  A random early discard framework for congestion control in ATM networks , 1999, IEEE ATM Workshop '99 Proceedings (Cat. No. 99TH8462).

[10]  Irfan-Ullah Awan,et al.  A cost-effective approximation for SRD traffic in arbitrary multi-buffered networks , 2000, Comput. Networks.

[11]  Ahmed Mokhtar,et al.  Stochastic approach for modeling random early detection gateways in TCP/IP networks , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[12]  QUTdN QeO,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

[13]  Demetres D. Kouvatsos,et al.  Maximum entropy and the G/G/1/N queue , 1986, Acta Informatica.

[14]  Marcel F. Neuts,et al.  Congestion Detection in ATM Networks , 1998, Perform. Evaluation.

[15]  Irfan-Ullah Awan,et al.  Entropy maximisation and open queueing networks with priorities and blocking , 2003, Perform. Evaluation.

[16]  Ahmed Mokhtar,et al.  Stochastic modeling of random early detection gateways in TCP networks , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[17]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[18]  Irfan-Ullah Awan,et al.  Analysis of Discrete Time Queueing Networks under Buffer Threshold Scheme , 2007, 2007 16th International Conference on Computer Communications and Networks.

[19]  R. Srikant,et al.  A time scale decomposition approach to adaptive ECN marking , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[20]  Martin May,et al.  Analytic evaluation of RED performance , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[21]  B. Barden.  Recommendations on queue management and congestion avoidance in the Internet , 1998 .

[22]  D. Potier,et al.  Modelling Techniques and Tools for Performance Analysis , 1985 .

[23]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[24]  Donald F. Towsley,et al.  On designing improved controllers for AQM routers supporting TCP flows , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[25]  Peter G. Harrison,et al.  Modelling techniques and tools for computer performance evaluation , 2003, Perform. Evaluation.

[26]  Demetres D. Kouvatsos,et al.  Approximate Analysis of Discrete-Time Networks with or without Blocking , 1993, Data Communication Networks and their Performance.

[27]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[28]  Demetres D. Kouvatsos,et al.  Entropy maximisation and queueing network models , 1994, Ann. Oper. Res..