Analyzing a degenerate buffer with general inter-arrival and service times in discrete time

Abstract In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity. Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design.

[1]  Dieter Fiems,et al.  A performance model for an asynchronous optical buffer , 2005, Perform. Evaluation.

[2]  Raul C. Almeida,et al.  A generic-traffic optical buffer modeling for asynchronous optical switching networks , 2005, IEEE Communications Letters.

[3]  Herwig Bruneel,et al.  Discrete-time models for communication systems including ATM , 1992 .

[4]  Ivan Atencia,et al.  A Discrete-Time Geo/G/1 Retrial Queue with General Retrial Times , 2004, Queueing Syst. Theory Appl..

[5]  QiaoChunming,et al.  Optical burst switching (OBS) - a new paradigm for an optical Internet , 1999 .

[6]  Masayuki Murata,et al.  Ultrafast photonic label switch for asynchronous packets of variable length , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[7]  Marc Moeneclaey,et al.  Queueing analysis of a single-wavelength Fiber-Delay-Line buffer , 2006, Telecommun. Syst..

[8]  W. Rogiest,et al.  Optical buffers, batch arrivals and synchronization , 2006, 2006 2nd Conference on Next Generation Internet Design and Engineering, 2006. NGI '06..

[9]  Franco Callegati,et al.  Optical buffers for variable length packets , 2000, IEEE Communications Letters.

[10]  V. Klimenok,et al.  On the Modification of Rouche's Theorem for the Queueing Theory Problems , 2001, Queueing Syst. Theory Appl..

[11]  Raul C. Almeida,et al.  Optical buffer modelling for performance evaluation considering any packet inter-arrival time distribution , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[12]  Franco Callegati Approximate Modeling of Optical Buffers for Variable Length Packets , 2004, Photonic Network Communications.

[13]  Herwig Bruneel,et al.  Analysis of a single-wavelength optical buffer , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[14]  Jesús R. Artalejo,et al.  A classified bibliography of research on retrial queues: Progress in 1990–1999 , 1999 .

[15]  L. Lakatos On a simple discrete cyclic-waiting queueing problem , 1998 .

[16]  Chunming Qiao,et al.  Optical burst switching (OBS) - a new paradigm for an Optical Internet^{1} , 1999, J. High Speed Networks.