Abstract
Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Altman, F. Baccelli and J.-C. Bolot, Discrete time analysis of adaptive rate control mechanisms, Preprint (1995).
E. Altman and T. Basar, Optimal rate control for high speed telecommunication network, Preprint (August 1995).
D. Artiges, Analysis of the ARB (Adaptive Rate Based) congestion avoidance algorithm, Proc. IEEE CDC (1996) 2899–2904.
A. Arulambalam, X. Chen and N. Ansari, Allocating fare rates for available bit rate service in ATM networks, IEEE Comm. Magazine 34 (1996) 92–100.
S. Asmussen, Applied Probability and Queues (Wiley, New York, 1987).
ATM traffic management specification version 4.0, ATM Forum (April 1996).
B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer, Nonlinear Parametric Optimization (Birkhauser, Basel, 1983).
S. Bhatnagar and V. Sharma, Optimal control of a feed-back queue via stochastic approximations, to be presented at IEEE Conf. GLOBECOM '98 (1998).
P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
F. Bonomi and K.W. Fendick, The rate based flow control framework for the available bit rate ATM service, IEEE Network (March/April 1995) 25–39.
F. Bonomi, D. Mitra and J.B. Seery, Adaptive algorithms for feedback-based flow control in high speed wide-area ATM networks, IEEE JSAC 13 (1995) 1267–1282.
A.A. Borovkov, Stochastic Processes in Queueing Theory (Springer, New York, 1976).
A.A. Borovkov and S.A. Utev, Estimates for distribution of sums stopped at Markov times, Theory Probab. Appl. 38 (1993) 214–225.
A. Brandt, P. Franken and B. Lisek, Stochastic Stationary Models (Wiley, New York, 1990).
D.M. Chiu and R. Jain, Analysis of the increase and decrease algorithms for congestion avoidance in computer networks, in: Computer Networks and ISDN Systems, Vol. 17 (1989) pp. 1–84.
B.W. Conolly and C. Langaris, On a new Formula for the transient state probabilities for M/M/1 queues and computational implications, J. Appl. Probab. 30 (1993) 237–246.
S.N. Ethier and T.G. Kurtz, Markov Processes, Characterization and Convergence (Wiley, New York, 1986).
K.W. Fendick and M.A. Rodrigues, Asymptotic analysis of adaptive rate control for diverse sources with delayed feedback, IEEE Trans. Inform. Theory 40 (1994) 2008–2025.
K.W. Fendick, M.A. Rodrigues and A. Weiss, Analysis of a rate based feedback control strategy for long haul data transport, Performance Evaluation 16 (1992) 67–84.
A. Gut, Stopped Random Walks (Springer, New York, 1988).
V.V. Kalashnikov, Mathematical Methods in Queueing Theory (Kluwer, Dordrecht, 1994).
K. Kawahara, Y. Oie and H. Miyahara, Performance analysis of reactive congestion control for ATM networks, IEEE JSAC 13 (1995) 651–660.
S. Keshav, A control theoretic approach to flow control, in: Proc. ACM SIGCOMM '91 (1991) pp. 3–15.
A. Kolarov and G. Ramamurthy, A control theoretic approach to the design of closed loop rate based flow control for high speed ATM networks, Preprint (1997).
A. Mukherjee and J.C. Strikwerda, Analysis of dynamic congestion control protocols — A Fokker-Plank approximation, in: Proc. ACM SIGCOMM '91 (1991) pp. 159–169.
R.S. Pazhyannur and R. Agarwal, Feedback based flow control of B-ISDN/ATM networks, IEEE JSAC 13 (1995) 1252–1266.
W.A. Rosenkrantz, Some martingales associated with queueing and storage processes, Z. Wahr. 58 (1981) 205–222.
O.P. Sharma, Markovian Queues (Ellis Horwood, New York, 1990).
V. Sharma, Reliable estimation via simulation, Queueing Systems 19 (1995) 169–192.
V. Sharma, Some limit theorems for regenerative queues, to appear in Queueing Systems.
V. Sharma and R. Mazumdar, Stability and performance of some window and credit based flow controlled in the presence of background traffic, submitted.
S. Shenker, A theoretical analysis of feedback flow control, in: Proc. ACM SIGCOMM '90 (1990) pp. 156–165.
K.-Y. Siu and H.-Y. Tzeng, Intelligent congestion control for ABR service in ATM networks, in: Proc. ACM SIGCOMM '95 (1995) pp. 81–106.
V. Sumita, On conditional passage time of birth-death processes, J. Appl. Probab. 21 (1984) 10–21.
Y.T. Wang and B. Sengupta, Performance analysis of a feedback congestion control policy, in: Proc. ACM SIGCOMM '91 (1991) pp. 149–157.
N. Yin and M.G. Hluchyj, On closed-loop rate control for ATM cell relay networks, in: Proc. INFOCOM '94 (1994) pp. 99–108.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharma, V., Kuri, J. Stability and performance analysis of rate-based feedback flow controlled ATM networks. Queueing Systems 29, 129–159 (1998). https://doi.org/10.1023/A:1019127929282
Issue Date:
DOI: https://doi.org/10.1023/A:1019127929282