CONGESTION CONTROL Connection Oriented Network

96 CONGESTION CONTROL IN ATM NETWORKS There are various approximations that can be used to compute quickly the equivalent bandwidth of a source. A commonly used approximation is based on the assumption that the source is an interrupted fluid process IFP. IFP is characterized by the triplet R, r, b, where R is its peak bit rate; r the fraction of time the source is active, defined as the ratio of the mean length of the on period divided by the sum of the mean on and off periods; and b the mean duration of the on period. Assume that the source feeds a finite-capacity queue with a constant service time, and let K be the size of the queue expressed in bits. The service time is equal to the time it takes to transmit out a cell. Then, the equivalent bandwidth e is given by the expression: e = a − K + a − K 2 + 4Kar 2a R, 4.1 where a = b1 − rR ln1ε. The equivalent bandwidth of a source is used in statistical bandwidth allocation in the same way that the peak bit rate is used in nonstatistical bandwidth allocation. For instance, let us consider an output link of a non-blocking switch with output buffering, and let us assume that it has a transmission speed of 25 Mbps and its associated buffer has a capacity of 200 cells. Assume that no connections are currently routed through the link. The first setup request that arrives is for a connection that requires an equivalent bandwidth of 5 Mbps. The connection is accepted and the link has now 20 Mbps available. The second setup request arrives during the time that the first connection is still up and is for a connection that requires 10 Mbps. The connection is accepted and 10 Mbps are reserved, leaving 10 Mbps free. If the next setup request is for a connection that requires more than 10 Mbps and arrives while the first two connections are still active, then the new connection is rejected. This method of simply adding up the equivalent bandwidth requested by each connec- tion can lead to underutilization of the link. That is, more bandwidth might be allocated for all of the connections than it is necessary. The following approximation for the equivalent bandwidth of N sources corrects the over-allocation problem: c = min ρ + σ − 2 lnε − ln 2π , N i= 1 e i , 4.2 where ρ is the average bit rate of all of the sources, e i is the equivalent bandwidth of the ith source, calculated using the expression 4.1, and σ is the sum of the standard deviation of the bit rate of all of the sources and is equal to: σ = N i= 1 r i R i − r i . When a new setup request arrives, the equivalent bandwidth for all of the existing con- nections, and the new one is calculated using the expression 4.2. The new connection is accepted if the resulting bandwidth c is less than the link’s capacity. Below is a numerical example that demonstrates how the maximum number of con- nections admitted using the above expressions for the equivalent bandwidth varies with the buffer size K, the cell loss rate ε, and the fraction of time the source is active r. Con- sider a link that has a transmission speed of C equal to 150 Mbps and a buffer capacity