A saturated tree network of polling stations with flow control

We consider a saturated tree network with flow control. The network consists of two layers of polling stations, all of which use the random polling service discipline. We obtain the equilibrium distribution of the network using a Markov chain approach. This equilibrium distribution can be used to efficiently compute the division of throughput over packets from different sources. Our study shows that this throughput division is determined by an interaction between the flow control limits, buffer sizes, and the service discipline parameters. A numerical study provides more insight in this interaction. The study is motivated by networks on chips where multiple masters share a single slave, operating under flow control.

[1]  Jacques Resing,et al.  Reduction of a polling network to a single node , 2008, Queueing Syst. Theory Appl..

[2]  Mario Gerla,et al.  Flow Control: A Comparative Survey , 1980, IEEE Trans. Commun..

[3]  P Paul Beekhuizen,et al.  Performance analysis of networks on chips , 2010 .

[4]  J. G. Dai,et al.  Stabilizing Queueing Networks with Setups , 2004, Math. Oper. Res..

[5]  M. Reiser,et al.  A Queueing Network Analysis of Computer Communication Networks with Window Flow Control , 1979, IEEE Trans. Commun..

[6]  Otis B. Jennings.  Heavy-Traffic Limits of Queueing Networks with Polling Stations: Brownian Motion in a Wedge , 2008, Math. Oper. Res..

[7]  Kees G. W. Goossens,et al.  An efficient on-chip network interface offering guaranteed services, shared-memory abstraction, and flexible network configuration , 2004, Proceedings Design, Automation and Test in Europe Conference and Exhibition.

[8]  I. Olkin,et al.  Probability in the Engineering and Informational Sciences , 2013 .

[9]  U. Yechiali,et al.  Polling systems with permanent and transient jobs , 1999 .

[10]  Thomas Bonald,et al.  Window flow control in FIFO networks with cross traffic , 1999, Queueing Syst. Theory Appl..

[11]  Lawrence M. Wein,et al.  Heavy Traffic Analysis of Polling Systems in Tandem , 2011, Oper. Res..

[12]  Leonard Kleinrock,et al.  The Analysis of Random Polling Systems , 1988, Oper. Res..

[13]  Uri Yechiali,et al.  Polling in a Closed Network , 1994 .

[14]  Marco Ajmone Marsan,et al.  A detailed and accurate closed queueing network model of many interacting 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).

[15]  Dimitris Bertsimas,et al.  Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part I, the Single-Station Case , 1999 .

[16]  Dee Denteneer,et al.  End-to-end delays in polling tree networks , 2008, VALUETOOLS.

[17]  W. Dally,et al.  Route packets, not wires: on-chip interconnection networks , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[18]  Uri Yechiali,et al.  Closed polling models with failing nodes , 2000, Queueing Syst. Theory Appl..