In the next step, the services of the VNOs have to be granted with a portion of the network capacity. The primary goal in the allocation procedure is to increase the total network data rate, while considering the priority of different services, subject to the constraints. On the ground of this fact, the objective function for VRRM is the total weighted network data rate, being expressed for cellular RATs as:. N srv : number of services for each VNO,. The weights in 14 are used to prioritise the allocation of data rates to services, being a common practice to have the summation of all them equal to unit.
It is desirable that the services with the higher serving weights receive data rates higher than the ones with the lower serving weights. The equivalent function for WLANs is. In 15 , W SRb is introduced to give priority to services with a higher data rate per session. Assigning these services to a Wi-Fi network reduces collision rates, leading to a higher network data rate. Obviously, assigning zero to this weight completely eliminates the average data rate effect i.
It can also be subject to modifications during runtime, based on measurements and reports. In addition to increasing network data rate, a fair resource allocation is another objective in VRRM. On the one hand, the model is expected to allocate more resources to services with a higher serving weight, while on the other hand, services with a lower weight not being served at all or being served in very poor conditions are not acceptable. A fair allocation of resources is achieved when the deviation from the weighted average for all services is minimised:.
In order to better discuss the balance between these two objectives, i. The highest resource efficiency i. This means that, as the network capacity increases, the summation of the weighted data rate in 14 increases as well. In the same situation, the fairness objective function also reaches its maximum:.
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Based on 19 and 20 , the complete objective function for the management of virtual radio resources is defined as:. N SmaxRb : number of subscribers using the service with maximum data rate,. In 18 and 21 , the allocated data rate for a specific service is defined as:. In addition, there are more constraints for VRRM to allocate data rates to various services, which should not be violated.
The very fundamental constraint is the total network capacity estimated in the last section. The summation of all assigned data rates to all services cannot be higher than the total estimated capacity of the network:. The data rate offered to GB and BG services imposes the next constraints. The data rate allocated to these services has to be higher than a minimum guaranteed level for both GB and BG and lower than the maximum guaranteed one for GB only :.
Based on this model, the objective function presented in 21 has to be optimised subject to constraints addressed in 18 , 24 , 25 and In the allocation process, there are situations where resources are not enough to meet all guaranteed capacity, and the allocation optimisation is no longer feasible.
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A simple approach in these cases is introduced in [ 9 ], which is to relax the constraints by the introduction of violation also known as slack variables. In case of VRRM, the relaxed constraint is given by:.
By introducing the violation parameter, the former infeasible optimisation problem turns into a feasible one. The optimal solution maximises the objective function and minimises the weighted average constraints violations. The weighted average constraints violation is defined as follows:. The objective function presented in 21 has also to be changed as follows:.
However, the definition of fairness in a congestion situation is not the same, i. Fairness constraints are changed as follows:.
The management of virtual radio resources is a complex optimisation problem, since network status and constraints vary in time. In [ 8 , 9 ], it is proposed to divide the time axis into decision windows and to maximise the objective function in each of these intervals, independently. However, the output of partial VRRM may only be a local optimum and not the global one, since the effect of each decision on the network state and other dependencies are neglected.
Nevertheless, partial VRRM is a simple solution, which can be used as the starting step and reference point. This table also presents the maximum data rate for each RAT in downlink. Besides the usual human interaction services, one is also considering several machine-to-machine M2M applications, as this is one of the areas foreseen for large development of VNOs. In order not to compromise the objective function for achieving fairness, the fairness weight, W f , in 22 is considered to be unit, leading to a maximum fairness, while W SRb in 15 is heuristically chosen to be 0.
Each VNO is assumed to have subscribers, where each one requires the average data rate of 6. In the second step, the number of subscribers for each VNO is swept from low load up to high load , in order to observe how VNOs capacity and their services are affected by this increase of load. For the network capacity estimation, in addition to the general approach, the other three, i. Equation 7 is used to obtain the PDF for the general approach and 12 for the other ones.
Using 5 and 12 , the PDF and the cumulative distribution functions CDFs of the considered network capacity are obtained. As expected, the lowest network capacity estimation is achieved by applying the pessimistic PE approach, since the assumption is the allocation of RRUs to mobile terminals with the lowest SINR.
In this PE approach, the median capacity of the network for regular urban environments is 1. Moreover, Fig. When adding the capacity offered by traffic offloading to Wi-Fi APs in regular urban environments i. The comparison of Figs. The total network capacity, according to Fig. The interdecile intervals range in between 2. However, VoIP is not following the same rule, since it has a relatively high serving weight, which overcomes the effect of the average data rate in 15 , hence, being allocated a comparatively high data rate from both type of networks; the same phenomenon can be observed among M2M services, i.
The upper boundary in the allocation of virtual resources to the services is the primary difference between the services of VNO GB and BG, in other words, while the data rates allocated to services of the guaranteed VNO are bounded by maximum guaranteed values, the services of VNO BG have no limitation. In this section, one analyses the performance of the proposed model under different network traffic loads.
The number of subscribers is swept between and 1 per VNO i. The contracted data rate for each VNO increases from 1. The total minimum guaranteed data rate, i. Since network capacity is considerably higher than the minimum guaranteed data rates, best effort services are also served well; the allocation of 2. The reason behind this observation is the maximum guaranteed data rate of the guaranteed services. The guarantee data rates grow up to 6. Obviously, the share of the best effort services in this situation considerably decreases.
As shown in Fig. In addition, the increase of the subscribers to makes the total minimum guaranteed data rate of the three VNOs equal to the total network capacity, which means that the data rates allocated to the services of VNO BE reach zero. Furthermore, Fig. By increasing the number of subscribers, demand increases 4. It can be seen that the streaming services are the ones with the highest volume, having the highest data rate; the minimum guaranteed data rate varies between 0. The other service classes i. It can be seen that, in the low load situation, the maximum guaranteed data rates are assigned, but as demand increases, data rates move towards the lower boundary.
The interactive service class is a very good example for this behaviour: while it receives the maximum guaranteed data rate of 0. Considering the slope of allocated data rates in various services, the effect of serving weights and the service volume can be seen.
Since the interactive class has a lower serving weight compared to the conversational one, it receives almost the minimum acceptable data rate with subscribers; in the same situation, conversational services are still provided by the highest acceptable data rate. The effect of channel quality on the management of virtual radio resources by considering the three approaches i. As long as the data rates are in the acceptable region shown by the solid colour , there is no violation of the SLAs and guaranteed data rates. However, VNO GB faces the violation on the minimum guaranteed data rate in the PE approach, as the number of subscribers passes while at least 3.
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The VNO requires at least 4. In these cases, the high SINR leads to the high network capacity, and the model is not only able to serve the minimum guaranteed data rates, but it can also serve acceptable data rates to the BE and BG VNOs. It can be seen that the conversational class i. In the PE case, although for high-density situations the data rate decreases to a minimum guaranteed data rate, the services of this class never experience violation of the guaranteed data rate. Likewise, the streaming class is always served with a data rate higher than the minimum guaranteed. The maximum guaranteed data rate in heavy load reaches 5.
For interactive and background classes, it is shown that they face violation of minimum guaranteed data rate in the PE approach. The violation situation in the background class is, to such an extent, that no capacity is allocated to its services when there are more than subscribers per VNO. The data rate allocated to the interactive class reaches VNO BG does not have a maximum guaranteed data rate or high boundary for allocation of data rates. In conclusion, the effect of channel quality on the total available resource, and consequently on the performance of VRRM, is studied in this section.
Through numeric results, one shows that the proposed model for managing virtual radio resources can serve different service classes of VNOs with different requirements, while offering an acceptable level of isolation. As evidence to this claim, one can consider services of the conversational class, i. Likewise, the minimum guaranteed data rates are offered to the relevant VNOs. Moreover, the prioritising of service classes offered by VRRM enables to serve the more important services, even when there are not enough resources. A model for the management of virtual radio resources in a full heterogeneous network i.
In the first step, the model maps the number of the available RRUs from different RATs onto the total network capacity by obtaining a probabilistic relationship.
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The model is able to consider multiple channel quality assumptions for the terminals through different estimation approaches. The allocation of resources to maximise the weighted data rate of the network based on the estimated network capacity is the next step. The serving weights in the objective function make possible to prioritise services.
The resource allocation in a shortage of resources i. In addition, the model also considers fairness among services.