Environment specific TCP upstream throughput models in IEEE802.11b WLAN

This paper presents our study on environment based dependence of TCP Upstream Throughput (TCP up T) on signal to noise ratio (SNR) for a single user in an IEEE 802.11b Wireless Local Area Network (WLAN). Small offices, open corridors and free space environments were studied using an infrastructure based network for different quality of service (QoS) traffic. Environment based Models that predict TCP up T directly from SNR for different signal categories were statistically generated, validated and compared with similar models that were earlier developed without considering specific environments. The first type of models developed in this work were developed from all data specifically collected from each environment while the second type of models were developed by first categorizing the data in each specific environment into different signal categories and then models were statistically generated for each signal category before combining them into one model equation. At the stated levels of significance and the different degrees of freedom, the developed models were accepted at 1% (for F test) and 0.5% (for T test). From the RMS errors computed, the specific environment based models developed in this work were more accurate (as they showed lower RMS errors compared with earlier similar models) in predicting TCP up T in IEEE 802.11b WLAN for a single user on the network. It was also observed that the second type of models were found to be more accurate having shown lower RMS errors. Keywords: TCP Upstream throughput, Signal to noise ratio, environment based empirical model,IEEE802.11b, WLANs

The internet has become an integral part of our everyday life (Mohammed, 2011). Smart phones, computers and other internet enabled devices can now use Wireless local area networks (WLANs) to access internet services in many homes and within organizations. This has made access to information easier and more efficient (Oghogho and Ezomo,2013). Throughput and the round trip time are the two most important metrics for determining the performance of WLANs (Geier, 2008a). Being able to predict and simulate the throughput in WLANs can help to determine the performance of such a network. A minimum throughput must be provided by a WLAN if it is to be considered to have provided sufficient coverage (Geier, 2008b).
Throughput measures the average data rate (in bits) that can be sent between one user and another in a network (Henty, 2001). Upstream and downstream throughputs are the speed of data sent from the Client to the WLAN radio and the speed of data sent from WLAN radio to the Client respectively. Oghogho,et al, (2018b) has shown that upstream and downstream throughput are appreciably different hence predicting them separately gives a more accurate result.
Throughput has been found to be significantly accurate when predicted from Signal to noise ratio (SNR) only (Henty, 2001;Oghogho, 2018a). However other metrics like the number of users, the protocol used for transmission, the traffic type and the environment used for measurement appreciably influences the result.
Existing studies as reported in Oghogho et al, (2018a) presented models which were developed from a combination of field data collected across different environments. However, environment specific based models have been found to be more accurate than others which were developed without considering specific environments (Zia et al, 2016;Damaris et al;2012). In this paper the author presents environment specific throughput models which were developed for better accuracy of throughput predictions in specific environments. Several researchers have provided models for predicting TCP throughput based on SNR only with reasonable accuracy. Oghogho, 2018a; provided a detailed review of throughput models based on SNR observed which applied cross layer modelling and considered single and multiple users, upstream and downstream throughput etc. Models considered by Oghogho 2018a; included those developed by Henty Environment Specific TCP Upstream Throughput…..740 OGHOGHO, IKPONMWOSA (2001), Metreaud, (2006, Oghogho et al, (2014), Oghogho et al (2015a), Oghogho et al (2015b), Oghogho et al, (2017) and Oghogho et al, (2018b). All of these models directly predict throughput from the SNR computed without specific consideration for particular types of environments. The need to more accurately predict throughput specifically for the different environments (offices, open corridor and free space like open parks and airports) where WLANs are frequently used led to this work presented in this paper. The objective of this paper is to provide environment specific TCP upstream throughput models that more accurately predicts the TCP throughput of a single user for different SNR observed.

MATERIALS AND METHODS
The method used in Oghogho et al, (2014) and Oghogho et al, (2015a) was used in this work except that the models were developed for each specific environments (open corridor, small offices and free space) using only data collected in that environment. In this paper, open corridor, Small offices and free space are referred to as environment 1, environment 2 and environment 3 respectively. TCP upstream Throughput data were collected for a single user on an IEEE 802.11b WLAN. The data was sorted for different categories of signals (General, Strong, grey and weak) as described in Oghogho et al, (2014) and Oghoghoet al, (2015a). However the sorting was done separately for each environment unlike what was the case in Oghogho et al, (2014) and Oghogho et al, (2015a). Single User TCP upstream throughput models for IEEE 802.11b WLAN were statistically generated from the data using statistical package for social sciences (SPSS). All signals in environment 1 are in the strong signal range hence environment 1 does not have the second model which combines equations developed for strong, grey and weak signals respectively into one general equation. However for uniformity, model 1 is retained as an attachment to the name of the only model developed in environment 1.
Environment 2 consist of TCP upstream throughput data collected for all categories of signals (strong, grey and weak) hence two types of models were developed in environment 2. The first type of model was developed from the combined data in that environment while the second type of model was developed by first statistically generating model equations from data collected for each category of SNR and then combining the equations for the different signal categories to give one model equation for the entire SNR range. This was also done for environment 3. Validation data was collected from other environments different from where the Field data used for generating the model equations were collected. They were used to validate the models developed. Values of root mean square errors, F tests and T tests were used to further decide whether the models should be accepted or rejected.

RESULTS AND DISCUSSIONS
The field data description, the developed models and the accompanied discussions are presented in this section using graphs and tables. Table 1 shows the statistical parameters of TCPupT data collected for different SNR in all the environments. Fig. 1 shows averages of single user TCPupT field data plotted against SNR for all signal ranges in the three environments considered. All signals for which throughput was measured in environment 1 (open corridor) were in the strong signal range (≥25dBm) hence only strong signals data were collected for this environment. However Single user TCP upstream throughput data were collected for strong, grey and weak signals in environments 2 and 3. Environment is represented as " Env" in the Tables. From Table 1, it can be observed that the standard deviation (0.6387616 Mbps) and range (3.9Mbps) computed for the TCPupT obtained for all values of SNR considered were low in environment 1. This implies that TCPupT does not vary considerably in this environment for a single user on the network.  In environment 2, the standard deviation (1.9969Mbps) and range (6.8300Mbps) for TCPupT data collected for all SNR were relatively high compared to that of environment 1. This implies that TCPupT varies considerably in environment 2 than in environment 1 for a single user on the network over the entire range of signals. This difference in standard deviation observed between environment 1 and environment 2 is because in environment 1, TCPupT data could be collected for only strong signals while in environment 2, TCPupT data was collected for strong, grey and weak signals. For strong signals in environment 2, it was observed from Table 1 that the standard deviation (0.68137Mbps) and range (3.78Mbps) computed for the TCPupT data for single user were low. This is very comparable with what was observed in environment 1 where all signals are in the strong range. This implies that TCPupT does not vary considerably in environment 2 for a single user on the network when the signal is strong. Negatively skewed distribution (-1.976) was observed for TCPupT strong signal data in environment 2 as was also observed in environment 1. This means that TCPupT field data distribution has a longer tail towards the left of its observed mean of (5.8278Mbps) for strong signals. The observed range (3.78Mbps) for strong signal data only was appreciably lower than what was the case for all SNR data (6.8300Mbps) in environment 2. This is so because when the signal is strong, higher data rates are selected for data transmission but as signal degrades lower data rates are selected thereby increasing the TCPupT range observed for all SNR (strong through grey to weak signals) compared with strong signals only. For grey signals single user data in environment 2, it can be seen from OGHOGHO, IKPONMWOSA random even when signal has become grey or weak thus allowing the possibility of large variations for single user based on differences in the different environments. An obvious reason for the difference in standard deviation and range between TCPupT data for environment 3 and environment 1 occurs because data were collected for only strong signals in environment 1 while in environment 3, TCPupT data were collected for strong, grey and weak signals. Negatively skewed distribution (-0.983) was observed for All SNR TCPupT data in environment 3 for a single user on the network. From the observed Kurtosis (-0.862), the TCPupT distribution has a flat peak and light tails for all SNR in environment 3 for single user. For strong signals single user TCPupT data in environment 3, it can be seen from Table 1 that the standard deviation (0.60427Mbps) and range (3.68Mbps) obtained were low. This is very comparable with what was observed in environment 1 and environment 2 for strong signals. This implies that TCPupT does not also vary considerably in environment 3 for a single user on the network when the signal is strong. Negatively skewed distribution (-2.793) was observed for TCPupT strong signal data in environment 3. From the observed Kurtosis (9.700) for TCPupT single user data the distribution will have narrow peaks for strong signals in environment 3.
For grey signals single user data in environment 3, it can be seen from Table 1 that the standard deviation (0.87372Mbps) and range (4.40Mbps) for TCPupT were appreciably low for grey signals. This is a big deviation from what was observed in environment 2 where the standard deviation and range for TCPupT were high for grey signals. This is so because for single user, the WLAN client selects lower data rates more consistently when signal has become grey thus resulting in low TCPupT variation. There is a greater probability that the WLAN system continuously selects lower data rates for transmission in environment 3 (free space) compared with environment 2 (small offices) when signal is in the grey range. Note that in environment 3, grey signals occur when Client is very far from the WLAN radio unlike what is the case in environment 2 where the obstructions inside the building allows grey signals to be measured at distances not too far away from the WLAN radio. Positively skewed distribution (1.870) was observed for TCPupT data in environment 3 for grey signals. From the observed Kurtosis (3.428), TCPupT, has an arrow peak and heavy tails for grey signals in environment 3 for a single user on the network.
For weak signals single user data in environment 3, it can be seen from Table 1 that the standard deviation (0.32188Mbps) and range (1.18Mbps) for TCPupT (0.32188Mbps) were low for weak signals. This implies that when there is a single user on the network, TCPupT does not vary considerably, a trend that was also observed in environment 2. However for single user, the deviations observed for TCPupT in environment 3 is slightly lower than that of environment 2 for weak signals. TCPupT does not vary considerably for weak signals in this environment because when the signal has become weak for a single user, the WLAN Client which sends upstream data consistently uses low data rates for transmission hence the variation is low.

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Environment 3 is a free space environment.   To test the developed models the author defines the following hypothesis: Null hypothesis 1; H0= Proposed TCPupT model does not fit the data well and the slope of the regression line does not differ significantly from zero for a single user on the network. (This means that TCPupT is not significantly dependent on SNR for a Single User on the network). Alternative hypothesis 1; HI= Proposed TCPupT model fits the data well and the slope of the regression line differs significantly from zero for a single user on the network. (This means that TCPupT is significantly dependent on SNR for a Single User on the network).
The model parameters and the F-distribution and T test results are shown in Table 2. From the decision and remark column in Table 2, it can be seen that H0 was rejected (implying that H1 should be accepted) and all the models were accepted at 1% level of significance at the respective degrees of freedom. The RMS errors computed by comparing the developed models in this paper with similar models are presented in Table 3. TCP upstream validation data for single user collected specifically for each environment were used to estimate the RMS errors.  It can be seen from Table 3 that the TCPupT models developed in this work performed better than other similar TCPupT models developed in previous work. This has justified the need for carrying out this work. However the second model developed in this work (by first statistically generating model equations from data collected for each category of SNR and then combining the equations for the different signal categories to give one model equation for the entire SNR range) performed better in most cases considered as seen in Table 3. Fig. 2, Fig. 3, and Fig.4 show the graphs of TCPupT developed in this work plotted against SNR along with TCPupT Validation data average, and the other similar models with which they were compared in environment one, two and three respectively. It can also be seen that the models Environment Specific TCP Upstream Throughput…..746 OGHOGHO, IKPONMWOSA developed in this work follows the validation data more closely than the other models earlier developed in all the environments considered.
Conclusion: In this paper, environment specific TCP Upstream Throughput (TCPupT) models based on SNR for a single user in an IEEE 802.11b WLAN have been presented. TCPupT data for strong, grey and weak signals and different QoS traffic were collected for each environment and used to develop the respective models which passed the F and T tests and performed better than other similar existing models considered when the RMS errors were compared. These models serve as a useful predictive tool for WLAN installers and network designers needed to make better informed decision.