Aleación de magnesio

Numerical results are presented in this section to illustrate the effects on the performance metrics, when each of the queuing schemes are employed in the BS buffer of the system that was shown in Figure 4.21, modelled with the Continuous-Time Markov Chain models formulated above. The default system parameter values assumed in the Markov models used in the experiments are summarized in Table 4.3.

Table 4.3 Values of default parameters used in analytical models for comparative performance evaluation of the priority queuing schemes

Parameter Value

Mean total arrival rate (to RNC queues), λ 10 Mean service rate (at radio interface), µ 12 Probability of good channel state, Pg 0.8

RNC RT queue capacity, R 5

RNC NRT queue capacity, N 5

BS total queue capacity, T 10

TSP scheme threshold in BS queue, Rb 4

CPB scheme threshold in BS queue, Rc 4

PBS scheme threshold in the BS queue, th 4

traffic ratio 0.2, 0.4, 0.6, 0.8

Mean NRT arrival rate, λnrt λ * traffic ratio

A range of input traffic configurations with different NRT to RT flow traffic load ratios are considered. The total multiplexed traffic load is kept constant, while the RT packet loss probability, NRT packet loss probability, mean RT delay, and total (RT and NRT) packet loss, are taken as performance indicators for comparative analysis.

Figure 4.22 shows the mean RT delay for the compared schemes under NRT to total input traffic ratios of 0.2, 0.4, 0.6, and 0.8 respectively. A parameter value of 0.2, for example, means that on average 20% of packet arrivals are from the NRT flow while the remaining 80% are from the RT flow. Conversely, a parameter value of 0.8, indicates that 80% of packet arrivals are from the NRT flow while the remaining 20% are from the RT flow. This metric allows us to capture a wide range of (multi-class traffic) multiplexing configurations for the RT and NRT flows of the same multimedia session, and is used throughout the experiments.

From Figure 4.22, it can be seen that TSP and the CBP with precedence queuing schemes generally achieve the lowest mean RT flow delay due to RT service prioritiza- tion. With CBS applied in the BS, RT packets can traverse the system more easily than with PBS, because of better fairness in access to BS buffer space that CBS provides for RT flow compared to PBS which uses a threshold to limit access to BS buffer space. For this reason, CBS achieves lower mean RT delay compared to PBS. Note that even though TSP also uses a limiting threshold, Rb, the precedence queuing and service (time)

priority for RT flow, which are features absent in PBS, not only minimizes RT queuing delay but also allows transfer of RT packets from RNC to BS if there is available space while rb < Rb in the BS. Whereas, with PBS, even when BS buffer space is available as

long as t ≥ th ( th = Rb in the experiments), RT packets cannot go through the system.

An increase in the traffic ratio on the x-axis represents increase in NRT traffic com- ponent and a corresponding decrease in RT component; the effect of this is apparent in the PBS curve behaviour. i.e. the increase in the NRT flow component causes further stalling of RT flow in the RNC RT queue, leading to corresponding increase in delay. The opposite effect can be observed (to a lesser extent) in the TSP or CBP curves; i.e. RT delay lowers with decreasing RT flow component.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.2 0.4 0.6 0.8

Fraction of NRT arrivals in ov erall traffic

M e a n R T d e la y ( s ) PBS CBS CBP TSP

Figure 4.22 Mean RT delay vs. fraction of NRT arrivals in concurrent RT and NRT traffic for TSP, CBP, PBS, CBS queuing 0 0.01 0.02 0.03 0.04 0.05 0.06 0.2 0.4 0.6 0.8

Fraction of NRT arrivals in overall traffic

R T l o s s p ro b a b il it y PBS CBS CBP TSP

Figure 4.23 RT packet loss probability vs. fraction of NRT arrivals in concurrent RT and NRT traffic for TSP, CBP, PBS, CBS queuing schemes

From Figure 4.23, it can be observed that the lowest RT packet loss probabilities are generally obtained with TSP and CBP. PBS gives the highest RT packet loss probabili- ties. Similar to the case of delay performance in Figure 4.21, the observed better TSP RT loss performance is due to service (time) prioritization present in the scheme.

Figure 4.24 plots the NRT packet loss probabilities for all the schemes. Due to space priority mechanism in PBS for NRT flow, PBS showed the lowest NRT loss probability, followed by CBS, TSP and CBP respectively. Because of higher buffer utilization inherent in TSP queuing compared to CBP, it achieves better NRT loss performance than the latter.

Figure 4.25 shows that overall packet loss is highest with PBS, while overall packet loss is lowest with CBS. TSP gives lower overall packet loss than CBP, indicative of better BS buffer space utilization in TSP compare to CBP. As stated before, the CBS scheme always achieves a high degree of buffer utilization, which is the reason for the lowest overall packet loss when used in the BS compared to the others. Note also that TSP performance comes closest to CBS in Figure 4.25, illustrating the high buffer utilization capability of TSP as well.

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.2 0.4 0.6 0.8

Fraction of NRT arrivals in overall traffic

N R T l o s s p ro p a b il it y PBS CBS CBP TSP

Figure 4.24 NRT packet loss probability vs. fraction of NRT arrivals in concurrent RT and NRT traffic for TSP, CBP, PBS, CBS queuing schemes

0 0.01 0.02 0.03 0.04 0.05 0.06 0.2 0.4 0.6 0.8

Fraction of NRT arrivals in overall traffic

T o ta l lo s s PBS CBS CBP TSP

Figure 4.25 Overall packet loss probability vs. fraction of NRT arrivals in concurrent RT and NRT traffic for TSP, CBP, PBS, CBS queuing schemes

The results of the investigation provide insight into the comparative behaviours of the schemes over a range of traffic configurations for the multiplexed RT and NRT flows. Note that since two nodes are used, the experiments provide a glimpse into expected comparative end-to-end performance of the schemes in a more detailed system model.

The drawback of PBP and CBS compared to TSP is the tendency to compromise RT class QoS. On the other hand, the drawback of CBP is the lower buffer utilization and tendency to achieve lower NRT QoS compared to an equivalent TSP queue. This leads to the conclusion that compared to the conventional schemes, TSP is the most effective queuing scheme that can be used achieve a compromise between QoS requirements of RT and NRT classes of flows that are concurrent in a multi-class session, whilst also enabling a high degree of buffer utilization and low overall packet loss.

4.6 Chapter summary

This chapter presented the novel Time Space Priority (TSP) queuing system for buffer allocation and QoS management of multimedia traffic consisting of multiplexed real- time (RT) and non-real-time (NRT) classes of flows. The TSP queue is modeled using M2/M2/1/R, N queue, and a Continuous Time Markov Chain (CTMC) is used to

represent the system behavior from which the impact of traffic and configuration para- meters on the QoS performance of both flows is studied. The CTMC is generated and solved using the analytical modelling tool MOSEL-2, and the results are cross-validated with a discrete event simulation of the M2/M2/1/R, N queuing system using the C

language. The results’ validation are given in Appendix A. The results of the experi- ments highlight the importance of optimum TSP threshold selection, suggesting that a small TSP threshold, R, compared to the total buffer capacity, N is preferable from the viewpoint of joint RT and NRT QoS control. A function known as the WGoS criterion γ, is derived for calculating an optimum buffer threshold for joint RT and NRT QoS performance trade-off for a given total buffer capacity and traffic configuration using the TSP queuing model. Furthermore, in this chapter, an approach for dynamic buffer threshold optimization using an analytic engine comprising the TSP analytic model and WGoS function, is suggested.

The chapter also presented a comparative performance evaluation of TSP with exist- ing conventional queuing disciplines designed to give further insight into the merits and constraints of TSP and to assess its capability to enable joint RT and NRT QoS control compared to the conventional queuing disciplines. From the investigation, TSP achieves high buffer utilization, while proving to be the most effective queuing scheme that can allow customized preferential treatment to both RT and NRT components of the same multimedia session, allowing a reasonable compromise between their conflicting QoS requirements. In the subsequent chapters, TSP-based buffer management algorithms for user-specific multimedia traffic control in HSDPA system are proposed and evaluated.

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