Capacity and queueing in communication systems in .NET Deploy Code 39 Full ASCII in .NET Capacity and queueing in communication systems

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2.3 Capacity and queueing in communication systems using visual studio .net toget barcode 39 with web,windows application bar code The single server queue can 3 of 9 for .NET describe the ow of customers through a bank. A very different application is a communication model in which packets are sent through a communication channel to a receiver.

The service rate is equal to the rate at which packets can be sent through the channel. This is limited due to noise, as well as interference from other users. Factors that contribute to delay again include arrival rates, service rates, and variability.

Consider the queueing model in which data arrives for transmission in the form of xed-length packets A = (A(1), A(2), . . .

). The arrival process is i.i.

d., with nite mean = E[A(t)]. Once a packet arrives for transmission, the data in that packet is queued until it can be coded and sent via the input sequence X.

The basic additive white Gaussian noise (AWGN) channel with real-valued input sequence X and output sequence Y is described by Y (t) = X(t) + N (t), t 0,. where N is independent of X. It is assumed that the noise N is i.i.

d. and Gaussian with zero mean and variance 2 , and that the input sequence is subject to the average 2 2 power constraint E[X(t)2 ] X for all t, where X is a nite constant. The maximum rate at which data can be transmitted is given by Shannon s formula,.

2 X bits per time-slot. (2. visual .

net Code 39 13) N 2 This model describes a version of the single server queue in which the arrival rate 2 is and the maximal service rate is = C 2 ( X ). Any achievable transmission N 2 rate R < C 2 ( X ) can be interpreted as R = where [0, 1] is the allocation N rate. However, there is one important difference between the communication model and standard queueing models.

To implement the allocation rule 1, so that data is 2 sent at rate R C 2 ( X ), it is necessary to use a coding scheme consisting of very N long block lengths. In a sense then, the variability of the service process increases with the mean allocation rate . Nevertheless, as long as a strict bound on is enforced, this system can be described reasonably accurately using a GI/G/1 or CRW model.

2 C 2 ( X ) = 1 2. log2 1 + 2.4 Multiple-access communication Consider the multiple-access system illustrated in Figure 2.4, where two users transmit to a single receiver. The two users share a single channel which is corrupted by additive.

Control Techniques for Complex Networks Draft copy April 22, 2007. A2 X2 Figure 2.4: Multiple-access communication system with two users and a single receiver. (C 2 +P2 (P1 ), C 2 (P2 )). (C 2 (P1 ), C 2 +P1 (P2 )). Channel Capacity Region: Static Model Channel Capacity Region: Time-Varying Model Figure 2.5: Achievable rates Code 39 Extended for .NET in two multidimensional communication models.

white Gaussian noise (AWGN). The output of the system seen at the receiver is given by Y (t) = X1 (t) + X2 (t) + N (t), (2.14) where N is again i.

i.d. Gaussian, and independent of the two inputs {X 1 , X 2 }.

It is 2 assumed that user i is subject to the average power constraint E[Xi (t)2 ] Xi for all t. This is known as the ALOHA model when the two users send data independently [7, 336, 47]. Stability of ALOHA systems based on queueing models and channel coding theory is addressed in [14, 405, 354].

The queueing system associated with the ALOHA model has two buffers that receive arriving packets of data modeled as the i.i.d.

sequences Ai = (Ai (1), Ai (2), . . .

), with nite nite mean i = E[Ai (t)], i = 1, 2. Data at queue i is stored in its respective queue until it is coded and sent to the receiver using the respective input sequence X i . The set of all possible data rates is given by the Cover-Wyner region U illustrated at left in Figure 2.

5. Any pair (R1 , R2 ) U within this region can be achieved through independent coding schemes at the two buffers. Additional information, such as knowledge of the state of the other users queue, or joint-coding of data, does not improve the achievable rate region (see [354].

) The capacity region U depends critically on the channel model statistics. If, for example, the noise N is not Gaussian then there is in general no closed-form expression for U. In wireless communication systems there is typically random fading, so that the model (2.

14) is re ned through the introduction of fading processes {Gi : i = 1, 2}, Y (t) = G1 (t)X1 (t) + G1 (t)X2 (t) + N (t). (2.15) Again, the capacity region is not known except in very special circumstances.

Shown at right in Figure 2.5 is the form of U that might be expected in a fading environment..

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