Advanced wireless networks 4g technologies phần 4 ppsx

JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 EFFECTIVE LINK LAYER CAPACITY 243 0 500 1000 1500 2000 2500 3000 3500 20 22 24 26 28 30 32 Rate (cells/ms) Bucket size (cells) 0.1 0.01 0.001 0.0001 Figure 8.3 Shaping probability curves for nonsmooth mode. 0 500 1000 1500 2000 2500 3000 3500 20 22 24 26 28 30 32 Rate (cells/ms) B (cells) 0.1 0.01 0.001 0.0001 Figure 8.4 Shaping probability curves for smooth mode. 8.2 EFFECTIVE LINK LAYER CAPACITY In the previous section we discussed the problem of effective characterization of the traffic source in terms of the parameters which are used to negotiate with the network a certain level of QoS. Similarly, on the network side, to enable the efficient support of quality of service (QoS) in 4G wireless networks, it is essential to model a wireless channel in terms of connection-level QoS metrics such as data rate, delay and delay-violation probability. The traditional wireless channel models, i.e. physical-layer channel models, do not explicitly characterize a wireless channel in terms of these QoS metrics. In this section, we discuss a link-layer channel model referred to as effective capacity (EC) [11]. In this approach, a wireless link is modeled by two EC functions, the probability of nonempty buffer and the QoS exponent of a connection. Then, a simple and efficient algorithm to estimate these EC functions is discussed. The advantage of the EC link-layer modeling and estimation is ease JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 244 EFFECTIVE CAPACITY of translation into QoS guarantees, such as delay bounds and hence, efficiency in admission control and resource reservation. Conventional channel models, discussed in Chapter 3, directly characterize the fluctua- tions in the amplitude of a radio signal. These models will be referred to as physical-layer channel models, to distinguish them from the link-layer channel model discussed in this section. Physical-layer channel models provide a quick estimate of the physical-layer per- formance of wireless communications systems (e.g. symbol error rate vs SNR). However, physical-layer channel models cannot be easily translated into complex link-layer QoS guarantees for a connection, such as bounds on delay. The reason is that these complex QoS requirements need an analysis of the queueing behavior of the connection, which cannot be extracted from physical-layer models. Thus, it is hard to use physical-layer models in QoS support mechanisms, such as admission control and resource reservation. For these reasons, it was proposed to move the channel model up the protocol stack from the physical layer to the link layer. The resulting model is referred to as EC link model because it captures a generalized link-level capacity notion of the fading channel. Figure 8.5 illustrates the difference between the conventional physical-layer and link-layer model. For simplicity, the ‘physical-layer channel’ will be called the ‘physical channel’ and ‘link-layer channel’ will be referred to as the ‘link’. 8.2.1 Link-layer channel model 4G wireless systems will need to handle increasingly diverse multimedia traffic, which are expected to be primarily packet-switched. The key difference between circuit switching and packet switching, from a link-layer design viewpoint, is that packet switching requires queueing analysisof thelink. Thus,it becomesimportant tocharacterize theeffect ofthe data traffic pattern, as well as the channel behavior, on the performance of the communication system. QoS guarantees have been heavily researched in the wired networks [e.g. ATM and Internet protocol (IP) networks]. These guarantees rely on the queueing model shown in Demodulator Channel decoder Network access device Data sink Wireless channel Modulator Channel encoder Network access device Data source Receiver Received SNR Physical-layer channel Transmitter Link-layer channel Instantaneous channel capacity log(1 + SNR) Demodulator Channel decoder Network access device Data sink Wireless channel Modulator Channel encoder Network access device Data source Receiver Received SNR Physical-layer channel Transmitter Link-layer channel Instantaneous channel capacity log(1 + SNR) Figure 8.5 Packet-based wireless communication system. JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 EFFECTIVE LINK LAYER CAPACITY 245 Data source Rate μ A(t) B Queue Q(t) Capacity S(t) Channel Data source Rate μ A(t) Queue Q(t) Capacity S(t) Channel Figure 8.6 Queueing system model. Figure 8.6 and studied in Chapter 6. This figure shows that the source traffic and the network service are matched using a first-in first-out buffer (queue). Thus, the queue prevents loss of packets that could occur when the source rate is more than the service rate, at the expense of increasing the delay. Queueing analysis, which is needed to design appropriate admis- sion control and resource reservation algorithms, requires source traffic characterization and service characterization. The most widely used approach for traffic characterization is to require that the amount of data (i.e. bits as a function of time t) produced by a source conform to an upper bound, called the traffic envelope, (t). The service characteriza- tion for guaranteed service is a guarantee of a minimum service (i.e. bits communicated as a function of time) level, specified by a service curve SC (t)[12]. Functions (t) and (t) are specified in terms of certain traffic and service parameters, respectively. Ex- amples include the UPC parameters, discussed in the previous section, used in ATM for traffic characterization, and the traffic specification (T-SPEC) and the service specification (R-SPEC) fields used with the resource reservation protocol [12] in IP networks. A traffic envelope (t) characterizes the source behavior in the following manner: over any window of size t, the amount of actual source traffic A(t) does not exceed (t) (see Figure 8.7). For example, the UPC parameters, discussed in Section 8.1, specifies (t)by (t) = min  λ (s) p t,λ (s) s t + σ (s)  (8.18) where λ (s) p is the peak data rate, λ (s) s the sustainable rate, and σ (s) = B s the leaky-bucket size [12]. As shown in Figure 8.7, the curve (t) consists of two segments: the first segment has a slope equal to the peak source data rate λ (s) p , while the second has a slope equal to the sustainable rate λ (s) s , with λ (s) s <λ (s) p . σ (s) is the y-axis intercept of the second segment. (t) has the property that A(t) ≤ (t) for any time t. Just as (t) upper bounds the source traffic, a network SC (t) lower bounds the actual service S(t) that a source will receive. (t) has the property that (t) ≤ S(t) for any time t. Both (t) and (t) are negotiated during the admission control and resource reservation phase. An example of a network SC is the R-SPEC curve used for guaranteed service in IP networks (t) = max  λ (c) s (t − σ (c) ), 0  =  λ (c) s (t − σ (c) )  + (8.19) where λ (c) s is the constant service rate, and σ (c) the delay (due to propagation delay, link sharing, and so on). This curve is illustrated in Figure 8.7. (t) consists of two segments; JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 246 EFFECTIVE CAPACITY l s (s) Γ(t) Q(t) D(t) s(c) s(s) l s (c) Ψ(t) S(t) Time t Actual channel service Number of bits A(t) Time t Actual channel service Number of bits l p (S) Actual source traffic t Figure 8.7 Traffic and service characterization. (Reproduced by permission of IEEE [11].) the horizontal segment indicates that no packet is being serviced due to propagation delay, etc., for a time interval equal to the delay σ (c) , while the second segment has a slope equal to the service rate λ (c) s . In the figure, the horizontal difference between A(t) and S(t), denoted D(τ ), is the delay experienced by a packet arriving at time τ , and the vertical difference between the two curves, denoted by Q(τ ), is the queue length built up at time τ , due to packets that have not been served yet. As discussed in Chapter 4, providing QoS guarantees over wireless channels requires accurate models of their time-varying capacity, and effective utilization of these models for QoS support. The simplicity of the SCs discussed earlier motivates us to define the time-varying capacity of a wireless channel as in Equation (8.19). Specifically, we hope to lower bound the channel service using two parameters: the channel sustainable rate λ (c) s , and the maximum fade duration σ (c) . Parameters λ (c) s and σ (c) are meant to bein a statistical sense. The maximumfade duration σ (c) is a parameter that relates the delay constraint to the channel service. It determines the probability sup t Pr { S(t) <(t) } . We will see later that σ (c) is specified by the source with σ (c) = D max , where D is the delay bound required by the source. However, physical-layer wireless channel modelsdo not explicitly characterize thechan- nel intermsof suchlink-layer QoSmetricsas datarate, delayanddelay-violation probability. For this reason, we are forced to look for alternative channel models. A problemthat surfaces isthat a wirelesschannel has acapacity that variesrandomly with time. Thus, an attempt to provide a strict lower bound [i.e. the deterministic SC (t), used in IP networks] will most likely result in extremely conservative guarantees. For example, in a Rayleigh or Ricean fading channel, the only lower bound that can be deterministically guaranteed is a capacity of zero. The capacity here is meant to be delay-limited capacity, which is the maximum rate achievable with a prescribed delay bound (see Hanly and Tse [13] for details). This conservative guarantee is clearly useless in practice. Therefore, the concept of deterministic SC (t) is extended to a statistical version, specified as the pair { (t),ε } . The statistical SC { (t),ε } specifies that the service provided by the channel, denoted ˜ S(t), willalways satisfythe property thatsup t Pr  ˜ S(t) <(t)  ≤ ε. In other words, ε is the probability that the wireless channel will not be able to support the pledged SC JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 EFFECTIVE LINK LAYER CAPACITY 247 (t), referred to as the outage probability. For most practical values of ε,anonzero SC (t) can be guaranteed. 8.2.2 Effective capacity model of wireless channels From the previous discussion we can see that for the QoS control we need to calculate an SC (t) such that, for a given ε>0, the following probability bound on the channel service ˜ S(t) is satisfied: sup t Pr  ˜ S(t) <(t)  ≤ ε and (t) =  λ (c) s (t − σ (c) )  + (8.20) The statistical SC specification requires that we relate its parameters {λ (c) s ,σ (c) ,ε} to the fading wireless channel, which at the first sight seems to be a hard problem. At this point, the idea that the SC (t)isadual of the traffic envelope (t) is used [11]. A number of papers exist on the so-called theory of effective bandwidth [14], which models the statistical behavior of traffic. In particular, the theory shows that the relation sup t Pr { Q(t) ≥ B } ≤ ε is satisfied forlarge B, by choosingtwo parameters(whichare functionsofthe channelrater) that depend on the actual data traffic, namely, the probability of nonempty buffer, and the effective bandwidth of the source. Thus, a source model defined by these two functions fully characterizes the source from a QoS viewpoint. The duality between Equation (8.20) and sup t Pr { Q(t) ≥ B } ≤ ε indicates that it may be possible to adapt the theory of effective bandwidth to SC characterization. This adaptation will point to a new channel model, which will be referred to as the effective capacity (EC) link model. Thus, the EC link model can be thought of as the dual of the effective bandwidth source model, which is commonly used in networking. 8.2.2.1 Effective bandwidth The stochastic behavior of a source traffic can be modeled asymptotically by its effective bandwidth. Consider an arrival process { A(t), t ≥ 0 } , where A(t) represents the amount of source data (in bits) over the time interval [0, t). Assume that the asymptotic log-moment generating function of A(t), defined as (u) = lim t→∞ 1 t log E  e uA(t)  (8.21) exists for all u ≥ 0. Then, the effective bandwidth function of A(t) is defined as [11, 14] α(u) = (u) u , ∀u ≥ 0. (8.22) This becomes more evident if we assume the constant traffic A(t) = A so that Equation (8.21) gives (u) = lim t→∞ 1 t log E  e uA(t)  = lim t→∞ 1 t log E  e uA  = lim t→∞ uA t = u lim t→∞ A t = uα(u) (8.21a) Consider now a queue of infinite buffer size served by a channel of constant service rate r, such as an AWGN channel. Owing to the possible mismatch between A(t) and S(t), the JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 248 EFFECTIVE CAPACITY queue length Q(t) could be nonzero. As already discussed in Section 8.1 [analogous to Equation (8.5)] or by using the theory of large deviations [14] , it can be shown that the probability of Q(t) exceeding a threshold B satisfies sup t Pr { Q(t) ≥ B } ∼ e −θ B (r)B as B →∞ (8.23) where f (x) ≈ g(x) means that lim x→∞ f (x)/g(x) = 1. For smaller values of B, the fol- lowing approximation, analogous to Equation (8.3), is more accurate [15]: sup t Pr { Q(t) ≥ B } ≈ γ (r)e −θ B (r)B (8.24) where both γ (r) and θ B (r) are functions of channel capacity r. According to the theory, γ (r) = Pr { Q(t) ≥ 0 } is the probability that the buffer is nonempty for randomly chosen time t, while the QoS exponent θ B is the solution of α(θ B ) = r. Thus, the pair of functions {γ (r),θ B (r)}model the source. Note that θ B (r) is simply the inverse function corresponding to the effective bandwidth function α(u). If the quantity of interest is the delay D(t) experienced by a source packet arriving at time t, then with same reasoning the probability of D(t) exceeding a delay bound D max satisfies sup t Pr { D(t) ≥ D max } ≈ γ (r)e −θ(r)D max (8.25) where θ(r) = θ B (r) ×r [16]. Thus, the key point is that for a source modeled by the pair {γ (r),θ(r)}, which has a communication delay bound of D max , and can tolerate a delay- bound violation probability of at most ε, the effective bandwidth concept shows that the constant channel capacity should be at least r, where r is the solution to ε = γ (r)e −θ(r)D max . In terms of the traffic envelope (t) (Figure 8.7), the slope λ (s) s = r and σ (s) = rD max . In Section 8.1 a simple and efficient algorithm to estimate the source model functions γ (r) and θ(r) was discussed. In the following section, we use the duality between traffic modeling {γ (r),θ(r)}, and channel modeling to present an EC link model, specified by a pair of functions {γ (c) (μ),θ (c) (μ)}. The intention is to use {γ (c) (μ),θ (c) (μ)}as the channel duals of the source functions {γ (r),θ(r)}. Just as the constant channel rate r is used in source traffic modeling, we use the constant source traffic rate μ in modeling the channel. Furthermore, we adapt the source estimation algorithm from Section 8.1 to estimate the link model parameters {γ (c) (μ),θ (c) (μ)}. 8.2.2.2 Effective capacity link model Let r(t) be the instantaneous channel capacity at time t. Define ˜ S(t) =  t 0 r(τ)dτ, which is the service provided by the channel. Note that the channel service ˜ S(t) is different from the actual service S(t) received by the source; ˜ S(t) only depends on the instantaneous channel capacity and thus is independentof the arrival A(t). Paralleling the development of Equation (8.21) and (8.22) we assume that  (c) (−u) = lim t→∞ 1 t log E  e −u ˜ S(t)  (8.26) JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 EFFECTIVE LINK LAYER CAPACITY 249 exists for all u ≥ 0. This assumption is valid, for example, for a stationary Markov-fading process r(t). Then, the EC function of r(t) is defined as α (c) (u) = − (c) (−u) u , ∀u ≥ 0 (8.27) Consider a queue of infinite buffer size supplied by a data source of constant data rate μ (see Figure 8.6). The theory of effective bandwidth can be easily adapted to this case. The difference is that, whereas in the previous case the source rate was variable while the channel capacity was constant, now the source rate is constant while the channel capacity is variable. Similar to Equation (8.25), it can be shown that the probability of D(t) exceeding a delay bound D max satisfies sup t Pr { D(t) ≥ D max } ≈ γ (c) (μ)e −θ (c) (μ)D max (8.28) where {γ (c) (μ),θ (c) (μ)} are functions of source rate μ. This approximation is accurate for large D max , but we will see later in the simulation results, that this approximation is also accurate even for smaller values of D max . For a given source rate μ, γ (c) (μ) = Pr { Q(t) ≥ 0 } is again the probability that the buffer is nonempty at a randomly chosen time t, while the QoS exponent θ (c) (μ) is defined as θ(μ) = μα −1 (μ), where α −1 (·) is the inverse function of α (c) (u). Thus, the pair of functions {γ (c) (μ),θ (c) (μ)} model the link. So, if a link that is modeled by the pair {γ (c) (μ),θ (c) (μ)}is used, a source that requires a communication delay bound of D max , and can tolerate a delay-bound violation probability of at most ε, needs to limit its data rate to a maximum of μ, where μ is the solution to ε = γ (c) (μ)e −θ (c) (μ)D max . In termsof the SC (t) shownin Figure 8.7, thechannel sustainable rate λ (c) s = μ and σ (c) = D max . If the channel-fading process r(t) is stationary and ergodic, then a simple algorithm to estimate the functions {γ (c) (μ),θ (c) (μ)} is similar to the one described in Section 8.1. Paralleling Equation (8.7) we have γ (c) (μ) θ (c) (μ) = E [ D(t) ] = τ s (μ) + E [ Q(t) ] μ (8.29) γ (c) (μ) = Pr { D(t) > 0 } (8.30) where τ s (μ) is the average remaining service time of a packet being served. Note that τ s (μ) is zero for a fluid model (assuming infinitesimal packet size). Now, the delay D(t) is the sum of the delay incurred due to the packet already in service, and the delay in waiting for the queue Q(t) to clear which results in Equation (8.29), using Little’s theorem. Substituting D max = 0 in Equation (2.28) results in Equation (3.30). As in Section 8.1, solving Equation (8.29) for θ (c) (μ) gives similarly to Equation (8.8a) θ (c) (μ) = γ (c) (μ) ×μ μ ×τ s (μ) + E [ Q(t) ] (8.31) According to Equation (8.30) and (8.31) , as in Section 8.1, the functions γ and θ can be estimated by estimating Pr { D(t) > 0 } ,τ s (μ), and E [ Q(t) ] . The latter can be estimated by taking a number of samples, say N, over an interval of length T , and recording the following quantities at the nth sampling epoch: S n the indicator of whether a packets is in service (S n ∈ { 0, 1 } ), Q n the number of bits in the queue (excluding the packet in service), JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 250 EFFECTIVE CAPACITY and T n the remaining service time of the packet in service (if there is one in service). Based on the same measurements, as in Section 8.1, ˆγ = N  n=1 S n /N ˆ q = N  n=1 Q n /N ˆτ s = N  n=1 T n /N are computed and then, from Equation (8.31), we have ˆ θ = ˆγ ×μ μ × ˆτ s + ˆ q (8.32) These parameters are used to predict the QoS by approximating Equation (8.28) with sup t Pr { D(t) ≥ D max } ≈ ˆγ e − ˆ θ D max (8.33) If the ultimate objective of EC link modeling is to compute an appropriate SC (t), then, given the delay-bound D max and the target delay-bound violation probability ε of a connec- tion, we can find (t) ={σ (c) ,λ (c) s } by setting σ (c) = D max , solving Equation (8.33) for μ and setting λ (c) s = μ. 8.2.3 Physical layer vs link-layer channel model In Jack’s model of a Rayleigh flat-fading channel, the Doppler spectrum S( f )isgivenas S( f ) = 1.5 π f m  1 − ( F/ f m ) 2 (8.34) where f m is the maximum Doppler frequency, f c is the carrier frequency, and F = f − f c . Below we show how to calculate the EC for this channel [11]. Denote a sequence of N measurements of the channel gain, spaced at a time interval δ apart, by x = [ x 0 , x 1 , ···, x N−1 ] , where { x n , n ∈ [ 0, N − 1 ] } are the complex-valued Gaussian distributed channel gains( | x n | are, therefore, Rayleighdistributed). For simplicity, the constant noise variance will be included in the definition of x n . The measurement x n is a realization of a random variable sequence denoted by X n , which can be written as the vector X = [ X 0 , X 1 , ···, X N−1 ] . The pdf of a random vector X for the Rayleigh-fading channel is f X (X) = 1 π N det(R) e −xR −1 x H (8.35) where R is the covariance matrix of the random vector X, det(R) the determinant of matrix R, and x H the conjugate transpose (Hermitan) of x. To calculate the EC, we start with E[e −u ˜ S(t) ] = E  exp  −u  t 0 r(τ)dτ  (a) ≈  exp  −u  N−1  n=0 δ × r(τ n )  f x (x)dx JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 EFFECTIVE LINK LAYER CAPACITY 251 (b) ≈  exp  −u  N−1  n=0 δ log(1 +|x n | 2 )  f x (x)dx (8.36) (c) ≈  exp  −u  N−1  n=0 δ log(1 +|x n | 2 )  . 1 π N det(R) e −xR −1 x H dx where (a) approximates the integral by a sum, (b) is the Shannon result for channel capacity (i.e. γ (τ n ) = log(1 + | x n | 2 ), and (c) is from Equation (8.35). This gives the EC, Equation (8.27), as α (c) (u) = −1 u lim t→∞ log  exp  −u  N−1  n=0 δ log(1 +|x n | 2 )  . 1 π N det(R) e −xR −1 x H dx (8.37) Using the approximation (a) log(1 + | x n | 2 ) ≈ | x n | 2 for low SNR [11], Equation (8.37) can be further simplified as E[e −u ˜ S(t) ] (a) ≈  exp  −uδ  N−1  n=0 |x n | 2  . 1 π N det(R) e −xR −1 x H dx (b) =  e −uδ||x|| 2 1 π N det(R) e −xR −1 x H dx (b) = 1 π N det(R)  e −x(R −1 +uδI)x H dx (8.38) = 1 π N det(R) × π N det  (R −1 + uδI) −1  = 1 det(uδR + I) where approximation (b) is due to the definition of the norm of the vector x, and (c) the relation  x  2 = xx H (I is identity matrix). Reference [11] considers three cases of interest for Equation (8.38). 8.2.3.1 High mobility scenario In the extreme high mobility (HM) case there is no correlation between the channel samples and we have R = rI, where r = E | x n | 2 is the average channel capacity. From Equation (8.38), we have E[e −u ˜ S(t) ] ≈ 1 det(uδR + I) = 1 (urδ +1) N = 1 (urt/N + 1) N (8.39) where δ t/N. As the number of samples N →∞,wehave lim N→∞ E[e −u ˜ S(t) ] ≈ lim N→∞ (urt/N + 1) −N = e −urt (8.40) Thus, in the limiting case, the Rayleigh-fading channel reduces to an AWGN channel. Note that this result would not apply at high SNRs because of the concavity of the log(·) function. JWBK083-08 JWBK083-Glisic February 23, 2006 3:53 Char Count= 0 252 EFFECTIVE CAPACITY 8.2.3.2 Stationary scenario In this case all the samples are fully correlated, R = [R ij ] = [r]. In other words all elements of R are the same and Equation (8.38) now gives E[e −u ˜ S(t) ] ≈ 1 det(uδR + I) = 1 urδN + 1 = 1 ur × t N × N + 1 = 1 1 +urt (8.41) 8.2.3.3 General case Denote the eigenvalues of matrix R by {λ n , n ∈ [ 0, N − 1 ] }. Since R is symmetric, we have R = UDU H , where U is a unitary matrix, U H is its Hermitian, and the diagonal matrix D = diag ( λ 0 ,λ 1 , ···,λ N−1 ) . From Equation (8.38), we have E[e −u ˜ S(t) ] ≈ 1 det(uδR + I) = 1 det(uδUDU H + UU H ) = 1 det[U diag (uδλ 0 + 1, uδλ 1 + 1, ,uδλ N−1 + 1)U H ] = 1  n (uδλ n + 1) = exp  −  n log(uδλ n + 1)  (8.42) We now use the calculated E[e −u ˜ S(t) ]toget  (c) (−u) = lim t→∞ 1 t log E[e −u ˜ S(t) ] (a) ≈ lim t→∞ 1 t log exp  −  n log(uδλ n + 1)  (b) = lim  f →0 − f  n log  u λ n B w + 1  (c) = −  log(uS( f ) + 1) d f (8.43) where (a) follows from Equation (8.42), (b) follows from the fact that the frequency interval  f = 1/t and the bandwidth B w = 1/δ, and (c) from the fact thatthe power spectral density S( f ) = λ n /B w and that the limit of a sum becomes an integral. This gives the EC, Equation (8.27), as α (c) (u) =  log(uS( f ) + 1)d f u (8.44) Thus, the Dopplerspectrum allows us to calculate α (c) (u). The EC function,Equation (8.44), can be used to guarantee QoS using Equation (8.28). One should keep inmindthat theECfunction, Equation(8.44),is validonly foraRayleigh flat-fading channel, at low SNR. At high SNR, the EC for a Rayleigh-fading channel is specified by the complicated integral in Equation (8.37). To the best of our knowledge, a closed-form solution toEquation (8.37) does not exist. Itis clear that anumerical calculation of EC is also very difficult, because the integral has a high dimension. Thus, it is difficult to extract QoS metrics from a physical-layer channel model, even for a Rayleigh flat-fading channel. The extraction may not even be possible for more general fading channels. In contrast, the EC link model that was described in this section can be easily translated into QoS metrics for a connection, and we have shown a simple estimation algorithm to estimate the EC model functions. [...]... 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(satellite links), lossy links (wireless networks) and asymmetric paths (hybrid satellite networks) are becoming widely embedded in the Internet Many works have studied by experimentation [1], analytical modeling [2] and simulation [3, 4, 12, 17, 18] the performance of TCP in this new environment Most of these works have focused on a particular environment (satellite networks, mobile networks, etc.) They have... bandwidth asymmetry TCP is a reliable window-based ACK-clocked flow control protocol It uses an additiveincrease multiplicative-decrease strategy for changing its window as a function of network Advanced Wireless Networks: 4G Technologies C 2006 John Wiley & Sons, Ltd Savo G Glisic 260 ADAPTIVE TCP LAYER conditions Starting from one packet, or a larger value as we will see later, the window is increased by one... bandwidth to convey ACKs without being disturbed This is almost true with the so-called symmetric networks where the forward and the reverse directions have the same bandwidth However, some of today’s networks (e.g direct broadcast satellite, 4G cellular networks and asymmetric digital subscriber loop networks) tend to increase capacity in the forward direction, whereas a low-speed channel is used... K=3 Reno: K=3 OldTahoe 0 .4 0.3 0.2 0.1 0.0 10 –3 10 –2 10 –1 Packet error probability Figure 9 .4 Throughput of versions of TCP vs packet-loss probability; λ = 5μ; K is the fast-retransmit threshold (Reproduced by permission of IEEE [13].) 9.3 TCP FOR MOBILE CELLULAR NETWORKS Many papers have been written proposing methods for improving TCP performance over a wireless link [ 14 24] Most of these papers... 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Whitt, Asymptotics for steady-state tail probabilities in structured Markov queueing models, Stochastic Models, vol 10, 19 94, pp 99– 143 [ 24] D.P Heyman and T.V Lakshman, What are the implications of long-range dependence for VBR-video traffic engineering? IEEE/ACM Trans Networking, vol 4, 1996, pp 301–317 [25] W Whitt, Tail probabilities with statistical multiplexing and effective bandwidths in multi-class... bandwidth of general Markovian traffic sources and admission control of high speed networks, IEEE/ACM Trans Networking, vol 1, 1993, pp 323–329 [28] A.K Parekh and R.G Gallager, A generalized processor sharing approach to flow control in integrated services networks: The singlenode case, IEEE/ACM Trans Networking, vol 1, 1993, pp 344 –357 [29] B.L Mark and G Ramamurthy, UPC-based traffic descriptors for ATM: . (QoS) in 4G wireless networks, it is essential to model a wireless channel in terms of connection-level QoS metrics such as data rate, delay and delay-violation probability. The traditional wireless. multiplicative-decrease strategy for changing its window as a function of network Advanced Wireless Networks: 4G Technologies Savo G. Glisic C  2006 John Wiley & Sons, Ltd. 259 JWBK083-09. capacity: a wireless link model for support of quality of service, IEEE Trans. Wireless Commun., vol. 2, no. 4, 2003, pp. 630– 643 . [12] R. Guerin and V. Peris, Quality-of-service in packet networks: