Traffic Management for the Available Bit Rate (ABR) Service in ...
Traffic Management for the Available Bit Rate (ABR) Service in ... Traffic Management for the Available Bit Rate (ABR) Service in ...
Transmitted Cell Rate Link Utilization 180 160 140 120 100 80 60 40 20 TCR for S1 TCR for S4 0 0 5000 10000 15000 Time in micro-seconds 120 100 (a) Transmitted Cell Rates 80 60 40 20 Link Utilization of Sw1-Sw2 link Link utilization of Sw2-Sw3 link 0 0 5000 10000 15000 Time in micro-seconds (c) Link Utilization Queue Length 140 120 100 80 60 40 20 Cells in Q to Sw1-Sw2 link Cells in Q to Sw1-Sw2 link 0 0 5000 10000 15000 20000 Time in micro-seconds (b) Queue Lengths Figure 5.23: Simulation results for the upstream bottleneck con guration with packet train workload. 137
5.8 Proof: Fairness Algorithm Improves Fairness In this section we analytically prove two claims about the simple fairness (TUB) algorithm: C1. Once inside TUB, the fairness algorithm keeps the link in TUB. C2. With the fairness algorithm, the link converges towards fair operation. Our proof methodology is similar to that used in Chiu and Jain (1989)[19], where it was proven that multiplicative decrease and additive increase are necessary and su cient for achieving e ciency and fairness for the DECbit scheme. Consider two sources sharing a link of unit bandwidth. Let x = Input rate of source 1 y = input rate of source 2 z = Load level of the link = x + y U = Target utilization = Half-width of the target utilization band s = Fair share rate = U/2 When x + y = U, the link is operating e ciently. This is shown graphically by the straight line marked \E ciency line" in Figure 5.24(a). When x = y, the resource allocation is fair. This represents the straight line marked \Fairness line" in the gure. The ideal goal of the load adjustment algorithm is to bring the resource allocations from any point inthetwo dimensional space to the point marked \Goal" at the intersection of the e ciency and fairness line. When the network is operating in a region close to the e ciency line, we consider the network to be operating e ciently. This region is bounded by the lines corre- sponding to x + y = U(1 ; ) and x + y = U(1 + ) are in Figure 5.24(a). The quadrangular region bounded by these two lines and the x and y axes is the e cient operation zone also called the target utilization band (TUB). The TUB is described 138
- Page 113 and 114: A combination of several ideas in a
- Page 115 and 116: 4.13 SP-EPRCA scheme The SP-EPRCA s
- Page 117 and 118: RTD and shuts o the source (for sta
- Page 119 and 120: 4.14.1 Common Drawbacks Though the
- Page 121 and 122: The ATM Tra c Management standard a
- Page 123 and 124: 5.1.1 Control-Cell Format The contr
- Page 125 and 126: The last two elds are used in the b
- Page 127 and 128: Figure 5.3: Flow chart for updating
- Page 129 and 130: LAF in cell Max(LAF in cell, z) The
- Page 131 and 132: the time of departure (instant mark
- Page 133 and 134: the steady state. The system operat
- Page 135 and 136: 5.2.3 Use Measured Rather Than Decl
- Page 137 and 138: said about the maximum queue length
- Page 139 and 140: The key problem with some unipolar
- Page 141 and 142: Figure 5.6: Space time diagram show
- Page 143 and 144: As noted, these heuristics do not g
- Page 145 and 146: Transmitted Cell Rate ABR Queue Len
- Page 147 and 148: 4. The RM cell contains a timestamp
- Page 149 and 150: 1. The source o ered average cell r
- Page 151 and 152: Transmitted Cell Rate Link Utilizat
- Page 153 and 154: Transmitted Cell Rate Link Utilizat
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- Page 157 and 158: Figure 5.17: The parking lot fairne
- Page 159 and 160: Figure 5.19: Network con guration w
- Page 161 and 162: Transmitted Cell Rate Link Utilizat
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- Page 167 and 168: Region 2: y s and x s and U(1 + ) x
- Page 169 and 170: eing divided into eight non-overlap
- Page 171 and 172: Proof for Region 2 Triangular regio
- Page 173 and 174: have: and y 0 = y(1 ; ) z x + y 0 =
- Page 175 and 176: The OSU scheme is, therefore, incom
- Page 177 and 178: workloads, where input load and cap
- Page 179 and 180: (a) Regions used to prove Claim C1
- Page 181 and 182: 6.1 The Basic ERICA Algorithm The s
- Page 183 and 184: A ow chart of the basic algorithm i
- Page 185 and 186: efore competing sources can receive
- Page 187 and 188: that the latest CCR information is
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- Page 197 and 198: level of control. These parameters
- Page 199 and 200: 6.14 ERICA+: Queue Length as a Seco
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- Page 205 and 206: Figure 6.4: Linear functions for ER
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Transmitted Cell <strong>Rate</strong><br />
L<strong>in</strong>k Utilization<br />
180<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
20<br />
TCR <strong>for</strong> S1<br />
TCR <strong>for</strong> S4<br />
0<br />
0 5000 10000 15000<br />
Time <strong>in</strong> micro-seconds<br />
120<br />
100<br />
(a) Transmitted Cell <strong>Rate</strong>s<br />
80<br />
60<br />
40<br />
20<br />
L<strong>in</strong>k Utilization of Sw1-Sw2 l<strong>in</strong>k<br />
L<strong>in</strong>k utilization of Sw2-Sw3 l<strong>in</strong>k<br />
0<br />
0 5000 10000 15000<br />
Time <strong>in</strong> micro-seconds<br />
(c) L<strong>in</strong>k Utilization<br />
Queue Length<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
20<br />
Cells <strong>in</strong> Q to Sw1-Sw2 l<strong>in</strong>k<br />
Cells <strong>in</strong> Q to Sw1-Sw2 l<strong>in</strong>k<br />
0<br />
0 5000 10000 15000 20000<br />
Time <strong>in</strong> micro-seconds<br />
(b) Queue Lengths<br />
Figure 5.23: Simulation results <strong>for</strong> <strong>the</strong> upstream bottleneck con guration with packet<br />
tra<strong>in</strong> workload.<br />
137
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