Chapter 3. System Modelling and Performance Evaluation Techniques
3.4 Performance Metrics
The performance of the system is evaluated in terms of both QoS and energy efficiency. There is a trade-off between QoS and energy efficiency, such that although high energy efficiency is achieved, it may be achieved at the expense of satisfactory QoS. Emphasis is placed on energy efficiency being achieved with QoS targets being satisfied. The QoS metrics considered are the SINR, blocking probability, delay, and throughput. The energy reduction gain (ERG) described earlier in Chapter 2 (section 2.4) and the effective energy saving are the energy efficiency metrics considered.
3.4.1 Signal to Interference Plus Noise Ratio
The signal to interference plus ratio (SINR) is a fundamental performance metrics in wireless communication systems and it is described as the ratio of the desired received signal power to the sum of the powers of interfering signals and noise power at the receiver [130]. The SINR accounts for the propagation effects (path loss, shadowing and multipath fading) and the gains of the transmitting and receiving antenna. Given that signal power at the transmitter is , the SINR at the receiver is given by [131]:
(3.10)
where G is the effective gain accounting for the propagation effects and antenna gains, while is interference from other users and is the receiver noise power. The SINR determines the data rate at which a user (or MS) can transmit to or receiver from the BS. MS requests are served only if their SINR satisfies the SINR threshold condition. The SINR threshold is set to a value higher than the minimum SINR acceptable over the BuNGee network in order to guarantee the quality of on- going traffic when new users are admitted.
The data rates of MS are dependent on the SINR achieved at the ABS. In this work, the data rate, is estimated using the Truncated Shannon bound [132] as follows:
(3.11)
α is the attenuation factor, SINRminis the minimum SINR required for reception, and SINRmax is the SINR at which the maximum data rate, Rmax, can be achieved.
3.4.2 Blocking Probability
In conventional telephone system, the blocking probability (or grade of service) is the probability that a call arriving at a switch will be blocked [133]. In a system where calls that cannot be served immediately are put in a queue, this is interpreted as the probability of a call being delayed [134]. In this work, admission control is
used to determine whether a user data request would be served or not. If the SINR achieved by the user exceeds the admission threshold, the user is admitted into the network but it the SINR achieved is lower than the threshold, the user is denied access or blocked. The blocking probability is measured in terms of the file requests that are blocked by the network. Hence, the blocking probability, , is given by:
(3.12) where is the total number of blocked file transmission requests and is the total number of file requests. Blocking can occur as a result of unavailability of free channels for file transmissions or due to poor channel quality as a result of low SINR on free channels.
3.4.3 Average File Transfer Delay
The delay is another important measure of the QoS of a telecommunication system. Delay generally measures the waiting time before a service is provided. File transfer delay is considered in this work. This is measured as the time between the instance an initial file transfer request is made and the instance the file is received in entirety at the receiver. Queuing delay is not considered, once free resource is available to serve a file request it is processed; otherwise it is blocked and retransmitted at a later time. The retransmission time is assumed to be exponentially distributed with a mean equivalent to the current mean inter-arrival rate. The file transfer delay of all successfully transmitted files is averaged to obtain the average file transfer delay. Thus the average file transfer delay, , is given as:
(3.13)
where is the sum of the file transfer delay of all successfully transmitted files and is total number of successfully transmitted files.
3.4.4 Throughput
The throughput is another measure of QoS in telecommunication systems. It is particularly relevant to data transmission as it measures the rate at which the system delivers data offered to it. The throughput, , is measured herein in terms of the
ratio of the total files successfully delivered, , (measured in bits) to the duration of observation, , (measured in seconds). Thus the throughput, is given by:
(3.14)
3.4.5 Energy Reduction Gain
The energy reduction gain (ERG) described earlier in Chapter 2 is used to measure energy efficiency in this work and evaluated according to (2.9). The energy efficiency of the schemes proposed in this work are evaluated relative to a baseline scheme with the objective of serving user requests at the highest SINR available from the small cell BSs in the vicinity. In addition, all BSs are always on whether ZBSs or ABSs. The baseline scheme is, therefore, a high data rate centric scheme rather an energy efficiency centric type.
3.4.6 Effective Energy Saving
The effective energy saving is an energy efficiency metric proposed in this work to measure how well a scheme balances energy efficiency with QoS. It is estimated from the difference between the ERG and the percentage increase in delay of a test scheme relative to the baseline scheme.
If delay degradation (DD) is defined as follows:
(3.15)
where and are the average delays achieved by the baseline and test schemes respectively under the same system conditions.
Then the effective energy saving (EES) is given by:
(3.16) The metric effectively offset the energy savings calculated in terms of ERG by the loss of QoS in terms of delay degradation. Hence, with this metric the balance between energy efficiency and QoS can be easily observed with only the plot of the . This is unlike the previous energy efficiency metrics which require comparison
of delay or blocking probability graphs with the plot of these energy efficiency metrics to determine the balance between QoS and energy efficiency.