A. Erramilli and L. J. Forys, "Oscillations and Chaos in a Flow Model of A Switching System," IEEE Journal on Selected Areas in Communication, Vol. 9, No. 2, pp. 171-178, Feb. 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of Electrical and Computer Engineering and the Institute for Systems Research University of Maryland College Park, MD 20742 USA priya, abed eng.umd.edu Abstract This paper analyzes the dynamics of the interaction of two queues carrying traffic with different priorities as proposed in [1] with changing operating conditions. It is shown that certain nonlinear instabilities can arise in the system as the amount of incoming traffic changes beyond a thresh hold. Appearance of multiple equillibria is shown to occur in a natural way due to border collision. We present an interesting ....

....We present an interesting nonlinear version of this model and show that nonlinear model retains most of the oscillatory and irregular behavior of the original system. Finally, we propose a new dynamic control strategy and illustrate that it performs better than the original control proposed in [1]. I Introduction Dynamics of traffic at both arriving and departure ports is of interest for many technologies including tele phone, computer networks and manufacturing [1, 3, 5] The connection between system dynamics and performance has also been of crucial importance. Traditionally, these ....

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A. Erramilli and L. J. Forys, "Oscillations and Chaos in a Flow Model of A Switching System," IEEE Journal on Selected Areas in Communication, Vol. 9, No. 2, pp. 171-178, Feb. 1991.

....The mechanism that creates this synchronization is related to the startup of the routers. However, in general, in network related phenomena, synchronization is only a real problem when there are forces driving the system toward synchronization, which is not the case here. For example, see [16] [17] where synchronization occurs as a result of the dynamics of the system pushing it towards 0 0.5 1 1.5 time (in period=1800 seconds) a) 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 time (in periods=2015 seconds) b) a) IOS 11 (b) IOS 12 Fig. 8. Number of routers whose LSAs were received within ....

Ashok Erramilli and Leonard J. Forys, "Oscillations and Chaos in a Flow Model of a Switching System," IEEE J. Selected Areas in Communications, vol. 9, no. 2, pp. 171--178, February 1991.

....are non symmetric, and with long tails. This is captured well with a Gamma Distribution (at least better than, say, a Normal Distribution, which was found to be inadequate) Possible reasons for the large tail include a First Come FirstServed (FCFS) scheduling and a systematic batching of traffic [6]. Perhaps a more critical question is, why is the tail so large, even in lightly loaded segments, and what can be done to prevent it. If the reason is FCFS scheduling, the solution lies in using a different scheduling discipline, e.g. Fair Queueing [5] if, however, it is due to some form of ....

....question is, why is the tail so large, even in lightly loaded segments, and what can be done to prevent it. If the reason is FCFS scheduling, the solution lies in using a different scheduling discipline, e.g. Fair Queueing [5] if, however, it is due to some form of traffic synchronization [6], or perhaps something else, a more serious investigation would be required to prevent it from occurring. 29 200 400 600 800 1000 (a) Shape rs. Time ol Day (Cross Country) 1200 1400 200 400 600 800 1000 1200 1400 (b) Scale rs. Time ol Day (Cross Country) 500 1000 1500 2000 (c) Shape rs. ....

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Erramilli, A. and L.J. Forys, "Oscillations and chaos in a flow model of a switching system," IEEE Journal on Selected Areas in Communications, pp 171-178, February, 1991.

....point to oscillatory behavior and finally to a chaotic state. A glimpse at the history of network congestion control reveals significant attempts to control congestion in the general network and telephony literature. Congestion and synchronization in tandem telephone queues have been studied in [15] using a piecewise affine model. A similar model has been applied to the dynamics of choke packets in a LAN to explain synchronization and sustained oscillations [16] These models indeed explain qualitative changes in the operation of a network or that of a network component as parameters cross ....

....to the dynamics of choke packets in a LAN to explain synchronization and sustained oscillations [16] These models indeed explain qualitative changes in the operation of a network or that of a network component as parameters cross critical values. In contrast to the deterministic setting of [15] and [16] multistability or emergence of pseudo stable states has been reported in a stochastic setting in [14] The paper discusses the qualitative changes in the stochastic behavior of the network due to parameter change, which may lead to degradation in network performance. There have been ....

A. Erramilli, L. J. Forys, "Oscillations and Chaos in a Flow Model of A Switching System," IEEE Journal on Selected Areas in Communication, Vol. 9, No. 2, pp. 171-178, Feb. 1991.

....and telephony literature. Congestion and synchronization in tandem telephone queues have The authors are with the Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD 20742 USA. Email: abed isr.umd.edu. been studied in [15] using a piecewise affine model. A similar model has been applied to the dynamics of choke packets in a LAN to explain synchronization and sustained oscillations [16] These models indeed explain qualitative changes in the operation of a network or that of a network component as parameters cross ....

....to the dynamics of choke packets in a LAN to explain synchronization and sustained oscillations [16] These models indeed explain qualitative changes in the operation of a network or that of a network component as parameters cross critical values. In contrast to the deterministic setting of [15] and [16] multi stability or emergence of pseudo stable states has been reported in a stochastic setting in [14] The paper discusses the qualitative changes in the stochastic behavior of the network due to parameter change, which may lead to degradation in network performance. There have been ....

A. Erramilli, L. J. Forys, "Oscillations and Chaos in a Flow Model of A Switching System," IEEE Journal on Selected Areas in Communication, Vol. 9, No. 2, pp. 171-178, Feb. 1991.

....to shape application level traffic more aggressively [3] Alternatively, or additionally, self similar behavior could be a side effect of the network s own protocols, a possibility that has not received as much attention. This phenomenon has been observed in other kinds of communications systems [5], and there have been cases where researchers have observed protocols unintentionally causing rapid oscillations in traffic levels [8] or prolonging congestion [21] in a manner that might have this effect. If some protocols prolong burstiness to create or strengthen traffic self similarity, then ....

A. Erramilli and L. J. Forys, Oscillations and Chaos in a Flow Model of a Switching System, IEEE J. Selected Areas in Communications, vol. 9, no. 2, Feb. 1991, pp. 171-8.

....to similar conclusions [26, 4, 10] The existence of time delays also gives rise to oscillatory and other complicated behavior. Large amplitude periodic and chaotic oscillations, and their adverse effect on bandwidth utilization, have indeed been observed in a wide range of communication networks [17, 9, 27]. These difficulties led to the development of control mechanisms that explicitly take propagation delays into account. One such mechanism uses packet round trip delays as feedback information and a window adjustment algorithm derived from the asymptotic analysis of a queueing network with large ....

A. Erramilli, L. Forys, "Oscillations and chaos in a flow model of a switching system", IEEE JSAC, vol. 9, no. 2, pp. 171-178, February 1991.

....trajectories are on the attractor, they diverge from each other while remaining within the attractor. Interestingly, teletraffic systems under certain conditions have been known to exhibit chaotic behavior. For example, a flow model of a tandem switch in a circuit switched network was shown in [26] to exhibit sustained chaotic oscillations under a momentary overload. While such phenomena are an important connection between teletraffic systems and chaos, and are important in their own right, they are not the subject of our present inquiry. There is no direct connection between fractal sets ....

....invariant density is independent of the initial condition x 0 . Given that an initial condition corresponds to a distinct trajectory, this is equivalent to assuming ergodicity. This is a property of the underlying map. For example, the Traffic Synchronization Map studied by Erramilli and Forys [26], is not ergodic, and different initial conditions may lead to distinct attractors, or steady state solutions. The first step in analyzing the properties of the time series y n is to find the invariant density of the associated map. Numerical approaches to solving EQ (5) are based on ....

A. Erramilli and L.J. Forys, "Oscillations and Chaos in a Flow model of a Switching System", IEEE JSAC, April 1990.

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A. Erramilli and L. J. Forys, "Oscillations and chaos in a flow model of a switching system," IEEE Journal on Selected Areas in Communications, pp. 171-178, February 1991.

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