CALL ADMISSION CONTROL CAC 95
This type of queueing structure is known as the ATM multiplexer. It represents a number of ATM sources feeding a finite-capacity queue, which is served by a server, i.e., the
output port. The service time is constant and is equal to the time it takes to transmit an ATM cell.
Let us assume that the QoS, expressed in cell loss rate, of the existing connections is satisfied. The question that arises is whether the cell loss rate will still be maintained if
the new connection is accepted. This can be answered by solving the ATM multiplexer queueing model with the existing connections and the new connection. However, the
solution to this problem is CPU intensive and it cannot be done in real-time. In view of this, a variety of different CAC algorithms have been proposed which do not require the
solution of such a queueing model.
Most of the CAC algorithms that have been proposed are based solely on the cell loss rate QoS parameter. That is, the decision to accept or reject a new connection is
based on whether the switch can provide the new connection with the requested cell loss rate without affecting the cell loss rate of the existing connections. No other QoS
parameters, such as peak-to-peak cell delay variation and the max CTD, are considered by these algorithms. A very popular example of this type of algorithm is the equivalent
bandwidth,
described below. CAC algorithms based on the cell transfer delay have also been proposed. In these
algorithms, the decision to accept or reject a new connection is based on a calculated absolute upper bound of the end-to-end delay of a cell. These algorithms are closely
associated with specific scheduling mechanisms, such as static priorities, early deadline first, and weighted fair queueing. Given that the same scheduling algorithm runs on all
of the switches in the path of a connection, it is possible to construct an upper bound of the end-to-end delay. If this is less than the requested end-to-end delay, then the new
connection is accepted.
Below, we examine the equivalent bandwidth scheme and then we present the ATM block transfer ABT
scheme used for bursty sources. In this scheme, bandwidth is allo- cated on demand and only for the duration of a burst. Finally, we present a scheme
for controlling the amount of traffic in an ATM network based on virtual path connec- tions VPC.
4.6.2 Equivalent Bandwidth
Let us consider a finite capacity queue served by a server at the rate of µ. This queue can be seen as representing an output port and its buffer in a non-blocking switch with
output buffering. Assume that this queue is fed by a single source, and let us calculate its equivalent bandwidth. If we set µ equal to the source’s peak bit rate, then we will
observe no accumulation of cells in the buffer. This is because the cells arrive as fast as they are transmitted out. If we slightly reduce the service rate µ, then we will see that
cells are beginning to accumulate in the buffer. If we reduce the service rate still a little bit more, then the buffer occupancy will increase. If we keep repeating this experiment each
time slightly lowering the service rate, then we will see that the cell loss rate begins to increase. The equivalent bandwidth of the source is defined as the service rate e at which
the queue is served that corresponds to a cell loss rate of ε. The equivalent bandwidth of a source falls somewhere between its average bit rate and its peak bit rate. If the source
is very bursty, it is closer to its peak bit rate; otherwise, it is closer to its average bit rate. Note that the equivalent bandwidth of a source is not related the source’s SCR.
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
