| P. H. Bauer, M. L. Sichitiu, and K. Premaratne, "On the nature of the time-variant communication delays," in Proc. of the IASTED Conference on Modeling, Identification and Control, (Innsbruck, Austria), pp. 792--797, Feb. 2001. |
.... # . 2.2 The forward and backward delays The system under investigation is shown in Figure 2. The controller SP(z) is transmitting data to a queue (modeled here as an ideal bu er) The data undergoes a time variant delay that needs to be modeled using a Variable Bit Rate (VBR) interface (see [7]) The length of the queue at the switch y(n) is fed back to the controller and also encounters a timevariant delay. We assume that the controller always uses the most recently available sample and thus an Hold Freshest Sample (HFS) 7] interface is appropriate. The input u(n) represents the ....
....to be modeled using a Variable Bit Rate (VBR) interface (see [7] The length of the queue at the switch y(n) is fed back to the controller and also encounters a timevariant delay. We assume that the controller always uses the most recently available sample and thus an Hold Freshest Sample (HFS) [7] interface is appropriate. The input u(n) represents the desired bu er occupancy level. At equilibrium, we have y(n) u(n) F 1 t (n) B R 1 y(n) network plant side controller side SP(z) Figure 2: Network Embedded Control System 2.3 Problem formulation In the light of the previous results ....
P. H. Bauer, M. L. Sichitiu, and K. Premaratne, \On the nature of the time-variant communication delays," in ##### ## ### ###### ####### ############### ############# ### #######, (Innsbruck, Austria), pp. 792-797, Feb. 2001.
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P. H. Bauer, M. L. Sichitiu, and K. Premaratne, "On the nature of the time-variant communication delays," in Proc. of the IASTED Conference on Modeling, Identification and Control, (Innsbruck, Austria), pp. 792--797, Feb. 2001.
....The source adjusts its transmission rate to the one specified in the most recent received RM cell and continues to transmit at that rate until another RM cell arrives. Since the source holds the same rate until it receives fresh information, we will call this the Hold Freshest Sample (HFS) [5] delay interface model. Congested zl (n) Return I e(n) RM Cells 2(n) I cz(n) e) Figure 3: HFS model for the communication link: tapped delay line with varying tap positions Figure 3 depicts the HFS model for the return path. We denote with z(n) the rate computed at the congested node at ....
....switch at every time instant n. Which switch is turned on is determined by the age of the last received RM cell. Thus if we have e(n) z(n r(n) then: c U (n) 0 otherwise (1) Notice that by HFS definition the coefficients c U (n) can not vary arbitrarily from one time instant to another [5]: the delay r(n) is restricted by r(n 1) r(n) 1, and hence we have: j(n) i k(n i) 0 V j i (2) In other words the used sample from the time variant delay output ages with time, but not faster. 2.2 The Variable Bit Rate Model On the forward path we need to quantify the number of ....
P.H. Bauer, M. L. Sichitiu, and K. Premaratne, "On the nature of the time-variant communication delays," Proc. of the IASTED Conference on Modeling, Identification and Control, Innsbruck, Austria, pp. 792-797, Feb. 2001.
....on and o# exactly one switch at every time instant n. Which switch is turned on is determined by the age of the last received RM cell. Thus, if we have r(n) b(n #(n) then: 3 (1) Notice that by HFS definition, the coe#cients # j (n) cannot vary arbitrarily from one time instant to another [14]: the integer delay #(n) is restricted by #(n 1)# #(n) 1, and hence we have: # j (n) 1# #k (n 1) 0 #k j 1 (2) Therefore, a sample that was available at time instant n will be held (reused) at time instant n 1, if no fresher sample has arrived at time n 1. Hence, the held sample ages by ....
....the two delays is di#erent. For example, the HFS delay cannot increase by more than one per time step (due to the holding action) while the VBR delay cannot decrease by more than one per time step (in order to assure that packet order is maintained) For detailed derivations of these bounds see [14, 17], or [15, 16] The model shown in Figure 4 is a macroscopic model for the delays and their e#ects on the data rates. The delays can be viewed as the compounded delays generated in individual queues from the source to the switch, but other delay e#ects can also be modeled by this method. 2.3 ....
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P. H. Bauer, M. L. Sichitiu, and K. Premaratne, "On the nature of the time-variant communication delays," in Proc. of the IASTED Conference on Modeling, Identification and Control, (Innsbruck, Austria), pp. 792--797, Feb. 2001. 14
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