Leveraging on the Cognitive Radio Channel Aggregation Strategy for Next Generation Utility Networks

Abstract

Integrating cognitive radio into the current power grid is designed to enable smart communication and decisions within the grid. Communication within the grid is not feasible without channel(s) and most studies have emphasized the use of cellular spectrum. This study proposes a strategy that enables the use of television white space (TVWS) within the grid. To be specific, we propose using a next-generation utility network (Next-GUN), which leverages on the cognitive radio (CR) channel aggregation capability. This strategy enables the aggregation of idle TVWS into a usable channel, thus making the Next-GUN different from the traditional power network. Next-GUN differs in terms of security, reliability, self-awareness, and cross-layer compatibility to the interface, and conveys different traffic classes, thereby making it a hybrid system. It has no dedicated channel assigned to it, and hence, utilizes the idle TVWS opportunistically to transmit data. The proposed scheme was modelled as a Markovian process and analyzed using a continuous time Markov chain (CTMC). Extensive system simulations were performed to evaluate this proposed model and the corresponding comparison with the literature was done to see the improvement. The result of our comparisons shows that when channels are aggregated, more data/information are transmitted. In addition, the use of cognitive radios on a power network enables smart transaction because idle TVWS is utilized instead of congesting the GSM spectrum. Lastly, the power utility establishment can save the cost of paying for a licensed spectrum.

1. Introduction

One unique characteristic of cognitive radio technology (CRT) is its capability to integrate both wired and wireless technologies like the power grid, power-line communication (PLC), visible light communication (VLC), worldwide interoperability for microwave access (WiMAX) and long-term evolution advanced (LTE-A).

The advantage of integrating CRT has not been investigated in detail except in a couple of studies [1,2]. Therefore, the demand to fully integrate CRT into the current grid is predicated on developing a next-generation utility network with special features. The next-generation utility network (Next-GUN) has two main components, which include: (1) smart and non-smart metering infrastructure (SNSMI), and (2) the utility and control management center [3].

The Next-GUN model is a hybrid architecture created through the integration of wireless radio technologies that guarantee dependable, compatible and efficient access to the grid elements from generation to distribution [4]. To achieve this multifaceted hybrid network architecture, three basic network components are crucial. These include the customer area network (CAN) managed by the customer cognitive gateway (CCGW), the field area network (FAN) coordinated by the cognitive field gateway (CFGW), and the wide area network (WAN) controlled by the tier-three hybrid cognitive radio-based station (HCRBS). While the CCGW collates power consumption from homes, the CFGW plays the role of substation (data concentrator) that feeds the HCRBS for final decisions.

In other words, the HCRBS makes a final decision based on some conditions, such as the availability of idle channels (TVWS or spectrum-holes) and the traffic class that each sub-network (CAN and FAN) is carrying.

The fundamental difference between our proposed Next-GUN model and others in the literature is two-fold: (a) The application of a channel aggregation policy in all tiers of the network (from generation up to distribution). (b) The semi-independence given to the CCGW and CFGW (intelligent agent or subnetworks) to aggregate and utilize the spectrum-holes within its jurisdiction (coverage area) for daily and hourly data transmission, while still sending reports to the HCRBS for a superior decision. On these premises, we infer that our design is suitable for a next generation electricity/power grid.

The rest of the paper is structured as follows: Section 2 presents the preliminaries of the cognitive radio and the Next-GUN concept. Section 3 summarizes related work. Section 4 and Section 5 describe the network and the system model, respectively. Performance measures are found in Section 6, while numerical results and comparison are discussed in Section 7. The paper is concluded in Section 8.

2. Preliminaries of Cognitive Radio and Next-GUN

Cognitive radio is a paradigm shift from the conventional wireless communication system. This concept has been discussed extensively in the literature [5,6,7], and hence, this paper will not bore the reader with it. The core components that make up the Next-GUN architecture from generation to distribution, and the enabling functionalities of the system, are shown in Figure 1.

2.1. Customer Area Network (CAN)

A CAN is a region interconnected by a cognitive meter (smart meter), coordinated and controlled by the CCGW (a tier-one control node). The CCGW, being semi-independent, establishes connectivity between the smart meter in the CAN, while the CFGW detects and coordinates new devices joining the network via self-reconfiguration. The CAN also identifies available TVWS, ensures dynamic spectrum sharing and establishes a duplex connection through which smart-data is transmitted to the CFGW in one direction. In the other direction, it obtains feedback (e.g., price billing), which is relayed to the CAN and displayed by the smart meter installed in the customer premises [4,8].

2.2. Field Area Network (FAN)

The FAN is a region comprising several CANs within a given neighborhood radius. It is coordinated by the CFGW, a semi-independent second tier node. Its main responsibilities are to collate (data concentrator) smart-data from every CAN region within a neighborhood and deliver to the HCRBS, which then transmits to the utility establishment (management control center) via the WAN. The CFGW, being cognitive by design, identifies and manages new CCGWs joining the FAN, including non-smart meter users (NSMUs). It also ensures spectrum allocation among the CCGW, depending on demand and availability of TVWS. The CFGW creates a two-way communication link that sends and receives billings and pricings from the utility company [9,10]. Note, the CFGW has a higher processing speed than the CCGW because it handles more requests due to a larger coverage area.

2.3. Wide Area Network (WAN)

The WAN is a region consisting of several FANs with few NSMUs. In this paper, the WAN is described as the backbone of the Next-GUN architecture due to its wider coverage that spans the entire value chain from generation to distribution. It is comprised of two key components, which are the core and backhaul networks. These key components enable it to cover a wider region where the CFGW and CCGW are sited.

The core networks link the control center via the HCRBS (third-tier control terminal), while the backhaul is responsible for broadband connectivity to the FAN and CAN by leveraging on the available TVWS. The HCRBS, being the spectrum manager, recognizes the cognitive ability of the CCGW and CFGW. Hence, it gives some level of independence (semi-independence) to other cognitive gateways (CCGW and CFGW) to aggregate TVWS within a jurisdiction. This enables them to transmit smart data collated to the HCRBS. However, the HCRBS does the overall spectrum identification, collation, coordination, and allocation, and links the entire network setup to the management control center of the utility establishment in a duplex manner [4,8,9].

3. Related Works

Leveraging on the capability of cognitive radio technology (CRT) opens a new research space with lots of benefits to the power utility sector at large. This synergy has motivated several investigations in this regard. In [2] the author proposed the application of CRT on smart grid. In the study, a simple deign on how a smart grid should function was discussed. The author further proposed the functionalities of the future grid which includes self-reconfiguration, agility just to mention a few. However, did not go into details of the performance evaluation which our work will do. For example, the consideration of different traffic classes and new performance metric which we will be considering.

In [3], the authors proposed the application of cognitive radio (CR) based on the IEEE 802.22 standard in a smart grid WAN. This study investigated the benefits of the proposed scheme, including, but not limited to extended coverage, opportunistic access to the spectrum, scalability, self-reconfiguration and fault tolerance. However, this study did not consider the channel aggregation capability of CR, which we have done. In [4], the authors introduced the use of two bands. The first is the unlicensed industrial scientific and medical (ISM) band, which is used for normal transmission, while the second licensed band serves as a backup in case of interruption due the arrival of primary owners. This approach ensures the quality of service (QoS) of data communication is guaranteed in a CR-based network. In this study, both the ISM band and licensed band are sensed simultaneously and whenever the licensed band cannot guarantee the QoS, it stops sensing and accessing the ISM band. In [8], a cognitive radio-based smart grid communication network was proposed. In the study, the communication network requirements, architecture, and applications were recommended, however, without any performance investigation like our study. In [9], the authors studied the priority level of different classes of traffic carried by the CR-based smart grid communication network. This posed a scheduling challenge and so they proposed a QoS differential scheduling scheme. The scheduler is responsible for managing the spectrum resources and arranging traffic for the smart grid according to the priority. However, the scheme did not consider the worst-case scenario that could lead to force termination, blocking or dropping of services irrespective of the priority level, which our study has done, bearing in mind that the licensed users can arrive at any time.

Khan et al. [10] and Zaballos et al. [11] gave a comprehensive survey on cognitive radio smart grid architecture with an emphasis on the heterogenous architecture of the system. However, the author’s design did not consider the semi-independence/autonomous nature of the CCGW and CFGW, which our work proposed and considered in our analysis, making it unique. In [12], the authors studied the opportunities for integrating present-day electricity networks and information and communication technology (ICT). This study further highlighted challenges, such as cybersecurity of the grid as it is exposed to the internet, standard interoperability and cognitive access to radio spectra. However, the study in [12] did not emphasize the analytical aspect of the study using a detailed Markovian process that depicts the transaction between primary and secondary users, which our research did. Furthermore, as cognitive radio channel access and allocation policy is the foundation for the success of smart grid communication, several allocation strategies have been studied in [13,14,15,16,17].

In this paper, we propose and develop a Next-GUN that applies cognitive radio channel aggregation policies. The policy allows the aggregation of several idle primary user (PU) channels (TVWS) into a logical chunk. This in turn improves secondary user (SU) throughput (volume of smart meter readings sent/received per time) over wireless links. Our paper further establishes a detailed Markov chain-based analytical model for the proposed system and considers the performance measures (e.g., access, blocking and forced termination probabilities) that have not been considered before in smart communication design. The core contributions of this paper are summarized as follows:

• We propose the application of a cognitive radio channel aggregation strategy into an existing power grid, which to the best of our knowledge has not been proposed and applied.
• In our study, we propose using a semi-independent customer cognitive gateway (CCGW) and customer field gateway (CFGW), which aggregate and use the spectrum-holes within their jurisdictions for daily and hourly data transmission/reception.
• We analyzed the effect of access, blocking and forced termination probabilities, which has never been reported, particularly on the smart grid communication domain using a detailed Markov chain-based analytical model.
• We compared our model to closely related literature to determine the improvement made, depending on selected parameters.

4. Network Model

This section presents our proposed architecture shown in Figure 1. As mentioned earlier, the network model consists of three main symbiotic elements, which are the CAN, the FAN, and the WAN. These three units cover generation, transmission, and distribution, respectively. The essence of this model is to integrate all layers of the grid with cognitive radio technology (CRT). The cognitive radio probes TVWS and establishes a two-way communication between the smart meter users (SMU) and the billing/utility company.

As the present 900/1800/1900 MHz bands (GSM-bands) are faced with the challenge of congestion due to the proliferation of diverse applications and services, which has resulted in a spectrum crunch, integrating the power grid would worsen the spectrum condition. Hence, to avoid paying for spectrums that are already scarce, we suggest that power utility companies use this model to save costs by leveraging on the capability CRT for monitoring power infrastructure on a real/non-real time basis. In as much as the spectrum holes are utilized, not all the users within Next-GUN are treated equally due to traffic type orientation. In this regard, the SUs are categorized into two, which are the smart meter users (SMUs), denoted as SU₁, and non-smart meter users (NSMUs) denoted as SU₂.

Next-GUN Architecture and Principle of Operation

The Next-GUN architecture is presented in Figure 1. In this setup, the mode of operation occurs in such a way that the power consumed by smart devices and appliances in homes is displayed in the smart meter (SM) installed on the consumer’s premises. Then, the SM information is relayed to the nearest substation or data concentrator. Nonetheless, the data concentrator center falls under the FAN, which collates all data from the neighboring SM via the CFGW and transmits it to the billing/utility control center via the HCRBS.

The HCRBS, being the intermediary node with more robust cognitive capabilities, constantly scans the PU channel (TVWS), identifies spectrum holes (TVWS) and opportunistically utilizes these available resources to transfer the data/information to the utility center. On the other hand, if the utility management center wants to query or send pricing and billing information, the cognitive access point (CAP) interfaces with HCRBS using the same TV-band, and hence the information gets to the FAN and CAN. Some of the opportunistic SUs carry non-real-time traffic and equally want to access the TVWS, and so they probe both the CFGW/FAN and the HCRBS/WAN to check if there are remnants of resources of SMU/SU₁.

To avoid unfairness, the HCRBS gives SU₂ an opportunity; however, they are classified as low priority users because SU₁ are high priority users. This is because SU₁ carry real-time data, such as energy readings, faults and disturbance (intrusion), about the grid. The essence of the queue/buffer attached to the HCRBS in Figure 1 is to ensure that the SMU/SU₁ service is queued in the event of sudden interruption due to the batch arrival of PUs, and when the spectrum is fully occupied or is insufficient for SMU/SU₁. Nevertheless, SMU/SU₁ will not be queued continually, and hence can be dropped if prolonged in the queue/buffer due to their delay intolerance, unlike NSMU/SU₂, which can withstand delays.

5. Conceptual Assumptions and System Modeling

The concept of our system model is leveraged on the capability of CR. Precisely, the model focuses on the PU and SU channel configuration as shown in Figure 2. From the model, the TVWS (idle channel) is the currency that drives the communication transactions in the Next-GUN; hence, it was structured to ensure fairness and avoid collision among SUs. In this paper, few assumptions were made. We assumed an underlay perfect sensing [15] and that the system is comprised of U licensed channels owned by the PUs, while SUs opportunistically utilizes it.

The licensed channel is partitioned into V sub-channels for the two classes of SUs, thereby resulting in a maximum cardinality of UV sub-channels that are utilized by SUs (SMU and NSMU). SMU represents SU₁ with high priority access, while NSMU denotes SU₂ as a low priority user. The arrival of PUs and SUs follows a Poisson procedure with arrival rates of ${\mathsf{\lambda }}_{\mathsf{\rho }},{\mathsf{\lambda }}_{\mathrm{s}}$, respectively. Whereas the service times are exponentially distributed with the service rates ${\mathsf{\mu }}_{\mathrm{p}},{\mathsf{\mu }}_{\mathrm{s}}$ for the PUs and SUs, respectively [13,16,17]. For simplicity, we assumed ${\mathsf{\lambda }}_{\mathrm{s}}$ and ${\mathsf{\mu }}_{\mathrm{s}}$ to be the arrival and service rates of the SUs, respectively.

5.1. Next-GUN Resources Allocation Strategy

In the Next-GUN channel allocation policy, the sub-channels are divided into two parts. This is due to the two classes of SUs as illustrated in Figure 2 below.

The SMU/SU₁ is allocated $\mathsf{\beta }$ subchannels out of the cardinality (total capacity of subchannels) of $\mathrm{UV}$ and are bounded as $0\le \mathsf{\beta }\le \mathrm{UV}$. The NSMU/SU₂ is allocated $\mathrm{UV}-\mathsf{\beta }$ subchannels, which is the remainder of the resources. To minimize blocking and forced termination of SMU/SU₁ services, the PU utilizes its resources in an incremental and sequential manner $\left(1,2,\dots ,\mathrm{U}\right)$, while the HCRBS and its associated cognitive nodes probe the channel and assigned subchannels for SMU/SU₁ in a decremental successive pattern from $\mathrm{UV}$ to $\mathrm{UV}-\mathsf{\beta }+1$, i.e., ($\mathrm{UV},\mathrm{UV}-1,\dots ,\dots ,\left(\mathrm{U}-1\right)\mathrm{V},\dots ,\mathrm{UV}-\mathsf{\beta }+1$) in the opposite direction as shown in Figure 2. The leftover of $\mathrm{UV}-\mathsf{\beta }$ resources are allocated to NNSMU/SU₂ in a decremental order from $\mathrm{UV}-\mathsf{\beta }$ to 1 (i.e., $\mathrm{UV}-\mathsf{\beta },\mathrm{UV}-\mathsf{\beta }-1,\dots 1$).

Our approach ensures that SMUs/SU₁ are protected as real-time digital data are carried. This means that the NSMUs/SU₂ act as the sacrificial users, which shield the SU₁ from blocking or forced termination. We also assumed that the PU service requires one channel, while the SU service can aggregate $\mathsf{\beta }\ge 1$ resources, depending on the traffic demand. Further assumptions are perfect sensing of the cognitive nodes (HCRBS, CCGW and CFGW) on the PU activities (collision/interference avoidance) as in [11,12,13] and no common control channel for coordinating SUs, as assumed in [17,18,19], to avoid overhead. In addition, no geo-location for SUs, but identical bandwidth requirement with priority for SMU/SU₁ was assumed. To avoid total or partial starvation of NSMU/SU₂ due to SMU/SU₁ greedy tendencies [15,20], a conflict resolution strategy is invoked by the HCRBS to ensure fairness among SUs while upholding priority.

Therefore, to achieve maximum efficiency in service completion rate and fairness of priority SU traffic, the Next-GUN allocation policy aims at allocating $\mathsf{\beta }$ resources to SMU/SU₁ with a fairness indicator ${\mathrm{F}}_{\mathrm{Cg}}$ as in [13,21].

In this paper, throughput efficiency (call/service completion rate) of the SU is the average number of services that were successfully completed without interruption. It is a function of the blocking and forced termination (FT) probabilities of SUs. Consequently, the general fairness indicator ${\mathrm{F}}_{\mathrm{Cg}}$ is expressed as

$${\mathrm{F}}_{\mathrm{Cg}}=\frac{{\left({{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\partial }_{{\mathrm{su}}_{\mathrm{s}}}\right)}^2}{\mathrm{n}\ast \left({{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\partial }_{{\mathrm{su}}_{\mathrm{s}}}{}^2\right)}$$

(1)

For $n=2$ (n indicates the two classes of SUs (SMU/SU₁ and NSMU/SU₂).

$${\mathrm{F}}_{\mathrm{Cg}}=\frac{{\left({\partial }_{{\mathrm{su}}_1}+{\partial }_{{\mathrm{su}}_2}\right)}^2}{2\left({\partial }_{{\mathrm{su}}_2}^2+{\partial }_{{\mathrm{su}}_2}^2\right)}$$

(2)

where ${\partial }_{{\mathrm{su}}_1}$ and ${\partial }_{{\mathrm{su}}_2}$ are the throughput efficiency of SMU/SU₁ and NSMU/SU₂, and ${\partial }_{{\mathrm{su}}_{\mathrm{s}}}$ for both respectively. ${\mathrm{F}}_{\mathrm{Cg}}$ measures the extent of equity to which channel(s) are allocated among SUs [13,21]. The fairness model has a positive minimum bound of ${\varnothing }_{\min }$, which denotes the lower guaranteed value of ${\mathrm{F}}_{\mathrm{Cg}}$ and the maximum bound ${\varnothing }_{\max }=1.$ Note that a higher value of ${\mathrm{F}}_{\mathrm{Cg}}$ signifies a fairer resource distribution among SUs. The algorithm for the Next-GUN policy is found below.

5.2. Governing Protocol/Algorithm for Next-GUN

For every network architecture, there are rules and procedures that guide the functionality of that system. This section presents the governing protocol/algorithm (Algorithm 1) of our Next-GUN shown below.

Algorithm 1. Governing Protocol/Algorithm for Next-GUN.

//SMU/SU1 Arrival 1:  HCRBS checks the wireless link state and scans the TV-band for TVWS (spectrum holes);// HCRBS checks for free PU/TV-user channel i.e., PU/TV-user absent. 2:      HCRBS checks the cardinality of TVWS;// HCRBS test for number of channel-slot (resources) available. 3:   If enough resources (TVWS) exist 4:     Grant access/admission to SMU/SU1 =True;//admit and allocate channel-slot (TVWS) 5:    Else:// if insufficient 6:  Check if queue=True;// test if queue is not full/free/empty 7:    If queue=True:// queue is not full 8: Admit into queue=True with set-time://waiting in the buffer with predetermined time, while HRBS scans for TVWS. 9:   Else://scanning failed 10: Grant access/admission to SMU/SU1 =False;//block due to insufficient channel-slot (TVWS) 11:      If time out in queue=True //within allowed time to wait 12:   Drop queues= False// exceed time to wait hence dropped from 13:  Go to step 8//waiting to be served by the HCRBS 14:    Else 15:  Drop queues=True// forced termination due to time out/overstaying to avoid starvation of other SUs. 16: Go to start //NSMU/SU2 Arrival 17:    HCRBS checks for the remnant TVWS (spectrum holes) of SMU/SU1 18:   Call step 2 to 15:// calling subroutine 2 to 15 19:     Interchange SMU/SU1 for NSMU/SU2://run the same structure of command but for NSMU/SU2 //SUs Departure 20:   SUs vacates the TVWS:// SUs service completion. 21: Free spectrum are created for other SUs //PU (TV-user) Arrival 22:         TV-user arrives and picks some SU2 resources (from left to right) 23:    Go to step 1 to 2 24:     Go to step 18 // call subroutine for SUs 25:     Else:// all condition to keep SU2 can’t be met// worst case scenario 26:    SU2 drop =True;// forced-terminate of ongoing SUs service 27:  End if;// terminate if no event //PU (TV-user) Departure 28:   Go to step 1 to 2:// call and run subroutine 29:     If channel-slots=True;// free TVWS exists 30:      Go to 3 to 16:// call and run subroutine 31:  Ends 32:   Go to start// run the process until runtime elapse

5.3. System Model Analysis

In this analytical model, let ${\mathsf{\sigma }}_{\mathrm{p}},{\mathsf{\sigma }}_{{\mathrm{su}}_1},$ and ${\mathsf{\sigma }}_{{\mathrm{su}}_2}$ represent the channel efficiency ratio for the PUs, SMU/SU₁ and NSMU/SU₂, respectively. It can be expressed as [22,23]

$${\mathsf{\sigma }}_{\mathrm{p}}=\raisebox{1ex}{${\mathsf{\lambda }}_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{\mathrm{p}}$}\right.,{\mathsf{\sigma }}_{{\mathrm{su}}_1}=\raisebox{1ex}{${\mathsf{\lambda }}_{{\mathrm{su}}_1}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{{\mathrm{su}}_1}$}\right.,{\mathsf{\sigma }}_{{\mathrm{su}}_2}=\raisebox{1ex}{${\mathsf{\lambda }}_{{\mathrm{su}}_2}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{{\mathrm{su}}_2}$}\right.$$

(3)

Therefore, the mean number of PUs (${\mathsf{\delta }}_{\mathrm{p}})$, SMU/SU₁ $\left({\mathsf{\delta }}_{{\mathrm{su}}_1}\right)$ and NSMU/SU₂ $\left({\mathsf{\delta }}_{{\mathrm{su}}_2}\right)$ in the network steady-state can be estimated by substituting (3) as in [22,23]:

$${\mathsf{\delta }}_{\mathrm{p}}=\raisebox{1ex}{${\mathsf{\sigma }}_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\mathsf{\sigma }}_{\mathrm{p}}\right)$}\right.=\raisebox{1ex}{${\mathsf{\lambda }}_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{\mathrm{p}}\left(1-{\mathsf{\sigma }}_{\mathrm{p}}\right)$}\right.$$

(4a)

$${\mathsf{\delta }}_{{\mathrm{su}}_1}=\raisebox{1ex}{${\mathsf{\sigma }}_{{\mathrm{su}}_1}$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\mathsf{\sigma }}_{{\mathrm{su}}_1}\right)$}\right.=\raisebox{1ex}{${\mathsf{\lambda }}_{{\mathrm{su}}_1}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{{\mathrm{su}}_1}\left(1-{\mathsf{\sigma }}_{{\mathrm{su}}_1}\right)$}\right.$$

(4b)

$${\mathsf{\delta }}_{{\mathrm{su}}_2}=\raisebox{1ex}{${\mathsf{\sigma }}_{{\mathrm{su}}_2}$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\mathsf{\sigma }}_{{\mathrm{su}}_2}\right)$}\right.=\raisebox{1ex}{${\mathsf{\lambda }}_{{\mathrm{su}}_2}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\mu }}_{{\mathrm{su}}_2}\left(1-{\mathsf{\sigma }}_{{\mathrm{su}}_2}\right)$}\right.$$

(4c)

Based on our estimation in (4a) to (4c), the number of channels utilized by the SUs (SMU/SU₁ and NSMU/SU₂) ${\complement }_{{\mathrm{su}}_{\mathrm{s}}}$ would be

$${\complement }_{{\mathrm{su}}_{\mathrm{s}}}=\left[\mathrm{U}-\left({\mathsf{\delta }}_{\mathrm{p}}\right)\right]\mathrm{V}$$

(5)

While the number of channels assigned to SU₁ (i.e., ${\complement }_{{\mathrm{su}}_1{}_{\mathsf{\beta }}}$) can be computed on the premise of our estimations in (4) using this expression:

$${\complement }_{{\mathrm{su}}_1{}_{\mathsf{\beta }}}={\complement }_{{\mathrm{su}}_{\mathrm{s}}}\left[\raisebox{1ex}{${\mathsf{\delta }}_{{\mathrm{su}}_1}$}\!\left/ \!\raisebox{-1ex}{$\left({\mathsf{\delta }}_{{\mathrm{su}}_1}+{\mathsf{\delta }}_{{\mathrm{su}}_2}\right)$}\right.\right]=\left\{\left[\mathrm{U}-\left({\mathsf{\delta }}_{\mathrm{p}}\right)\right]\mathrm{V}\left[\raisebox{1ex}{${\mathsf{\delta }}_{{\mathrm{su}}_1}$}\!\left/ \!\raisebox{-1ex}{$\left({\mathsf{\delta }}_{{\mathrm{su}}_1}+{\mathsf{\delta }}_{{\mathrm{su}}_2}\right)$}\right.\right]\right\}$$

(6a)

For the convenience of the reader, the number of channels assigned to SU₂ (${\complement }_{{\mathrm{su}}_2{}_{\mathrm{UV}-\mathsf{\beta }}}$) can be expressed as

$${\complement }_{{\mathrm{su}}_2{}_{\mathrm{UV}-\mathsf{\beta }}}={\complement }_{{\mathrm{su}}_{\mathrm{s}}}\left[\raisebox{1ex}{${\mathsf{\delta }}_{{\mathrm{su}}_2}$}\!\left/ \!\raisebox{-1ex}{$\left({\mathsf{\delta }}_{{\mathrm{su}}_1}+{\mathsf{\delta }}_{{\mathrm{su}}_2}\right)$}\right.\right]=\left\{\left[\mathrm{U}-\left({\mathsf{\delta }}_{\mathrm{p}}\right)\right]\mathrm{V}\left[\raisebox{1ex}{${\mathsf{\delta }}_{{\mathrm{su}}_2}$}\!\left/ \!\raisebox{-1ex}{$\left({\mathsf{\delta }}_{{\mathrm{su}}_1}+{\mathsf{\delta }}_{{\mathrm{su}}_2}\right)$}\right.\right]\right\}$$

(6b)

5.4. Continous Time Markov Chain (CTMC) Model Analysis

To capture PU/SU activities (PU, SU arrival and departure), the Next-GUN scheme is modelled as a three state CTMC with a general state represented by $\mathsf{\varphi }=\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$, where $\mathrm{x},\mathrm{y},\mathrm{z}$, are the number of PU, SU₁ and SU₂ occupying the channels, respectively. The feasible state space $\mathsf{\Omega }$ is expressed as $\mathsf{\Omega }=\left\{\mathsf{\varphi }|0\le \mathrm{x}\le \mathrm{U};0\le \mathrm{y}\le \mathsf{\beta };0\le \mathrm{z}\le \mathrm{UV}-\mathsf{\beta };\mathrm{xV}+\mathrm{y}+\mathrm{z}\le \mathrm{UV}\right\}$. The state probability $\mathrm{P}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$ can be obtained with the normalized equation as shown in (7). The probability of state $\varphi$ can be obtained, given the state probability $\mathrm{P}\left(\mathsf{\varphi }\right)$.

$$\mathrm{P}\mathsf{\eta }=0,{\displaystyle \sum }_{\mathsf{\varphi }\in \mathsf{\Omega }}\mathrm{P}\left(\mathsf{\varphi }\right)=1,$$

(7)

where η is the transition rate matrix. Note $\mathsf{\pi }\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$ is the index function presented as:

$$\mathsf{\pi }\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\{\begin{array}{c}1 \mathrm{if} \mathrm{state} \left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \mathrm{is} \mathrm{possible}\\ 0 \mathrm{otherwise}\end{array}$$

For ease of understanding of the state transition analysis, we adopt a probability notation on k as the quotient when β is divided by V with l as the reminder. This implies that $\mathsf{\beta }=\mathrm{kV}+\mathrm{l};0\le \mathrm{k}<\mathrm{U};0\le \mathrm{l}<\mathrm{V}$. In the same vein, $\mathrm{y}={\mathrm{k}}^{*}\mathrm{V}+{\mathrm{l}}^{*};0\le {\mathrm{k}}^{*}<\mathrm{U};0\le {\mathrm{l}}^{*}<\mathrm{V}$ if k^* is the quotient when y is divided by V and the remainder is l^*. The possible state transitions are developed and summarized in

Table 1. Transition table.

Possible State Events
Activity	Present State	Other States	Transition Rate	Conditions: If	Outcomes
(a) Transition from generic state$\mathbf{\left(}\mathit{x}\mathbf{,}\mathbf{ }\mathit{y}\mathbf{,}\mathit{z}\mathbf{\right)}$to other states when$\mathit{z}\mathbf{=}\mathbf{0}$
PU AR and request for channel	$\left(\mathrm{x},\mathrm{y},0\right)$	$\left(\mathrm{x}+1,\mathrm{y}-\mathrm{V},0\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y}-\mathrm{V},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}=\mathrm{UV}$	$\mathrm{V}$ Services of SU1 will be FT if no resources exist elsewhere or failed exit.
		$\left(\mathrm{x}+1,{\mathrm{k}}^{*}\mathrm{V},0\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,{\mathrm{k}}^{*}\mathrm{V},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\left(\mathrm{U}-1\right)\mathrm{V}<\mathrm{xV}+\mathrm{y},$ and $\mathrm{y}={\mathrm{k}}^{*}\mathrm{V}+{\mathrm{l}}^{*}$ $(0\le {\mathrm{k}}^{*}\le \mathrm{U},0\le {\mathrm{l}}^{*}<\mathrm{V})$	The ${\mathrm{l}}^{*}$ service of SU1 will be blocked.
		$\left(\mathrm{x}+1,\mathrm{y},0\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}\le \left(\mathrm{U}-1\right)\mathrm{V}$	PU will be allocated a channel and SU1 will not be blocked or FT
PU DP after service completion		$\left(\mathrm{x}-1,\mathrm{y},0\right)$	$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y},0\right){\mathrm{x}\mathsf{\mu }}_{\mathrm{p}}$	No condition	Frees up the channel(s)
SU1-AR and request for service	$\left(\mathrm{x},\mathrm{y},0\right)$	$\left(\mathrm{x},\mathrm{y}+1,0\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}+1,0\right){\mathsf{\lambda }}_{{\mathrm{su}}_1}$	$\mathrm{xV}+\mathrm{y}<\mathrm{UV}$	SU1 is admitted and access/aggregate vacant subchannels
SU1-DP after service completion		$\left(\mathrm{x},\mathrm{y}-1,0\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}-1,0\right){\mathrm{x}\mathsf{\mu }}_{{\mathrm{su}}_1}$	No condition	Frees up the channel(s) for other SUs
SU2-AR request for the remnant of the sub-channel(s)		$\left(\mathrm{x},\mathrm{y},1\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y},1\right){\mathsf{\lambda }}_{{\mathrm{su}}_2}$	When both $\mathrm{xV}+\mathrm{y}<\mathrm{UV}$ and $\mathrm{x}<\mathrm{U}-\mathrm{k}$	SU2 can be given access to the remnant or unoccupied subchannel(s)
SU2-DP	SU2-departure will not be captured because of the criteria/some condition. For convenience and space, we will used DP for depart, AR for arrive, and FT for forced termination.
(b) Transition from other state to state$\left(x, y,z\right)$when$z=0$
PU-AR and request for service	$\left(\mathrm{x}-1,{\mathrm{y}}^{*},{\mathrm{z}}^{*}\right)$	$\left(\mathrm{x},\mathrm{y},0\right)$	$\mathsf{\pi }\left(\mathrm{x}-1,{\mathrm{y}}^{*},{\mathrm{z}}^{*}\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}=\mathrm{UV}$ and ${\mathrm{k}}^{*}=\mathrm{k}$ Where ${\mathrm{y}}^{*}+{\mathrm{z}}^{*}=\mathrm{V}0\le {\mathrm{y}}^{*}\le \mathrm{l}$ and $0\le {\mathrm{z}}^{*}\le \mathrm{V}-\mathrm{l}$	In this scenario, ${\mathrm{k}}^{*}$ SU1 and ${\mathrm{z}}^{*}$SU2 will be FT their services as PU gain access and utilize the channels(s)
	$\left(\mathrm{x}-1,\mathrm{y}+\mathrm{v},0\right)$	$\left(\mathrm{x},\mathrm{y},0\right)$	$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y}+\mathrm{v},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$0\le \mathrm{v}\le \mathrm{V}$	In this event, only $\mathrm{v}$ SU1(s) suffer from FT when PU access and utilized the channel(s).
	$\left(\mathrm{x}-1,\mathrm{y},0\right)$		$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}<\mathrm{UV}$	None of the SU(s) will be FT even as PU access one channel.
PU DP after service completion	$\left(\mathrm{x}+1,\mathrm{y},0\right)$		$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y},0\right)\left(\mathrm{x}+1\right){\mathsf{\mu }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}\le \left(\mathrm{U}-1\right)\mathrm{V}$	Releases subchannels
SU1-AR and request for service	$\left(\mathrm{x},\mathrm{y}-1,0\right)$	$\left(\mathrm{x},\mathrm{y},0\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}-1,0\right){\mathsf{\lambda }}_{{\mathrm{su}}_1}$	No condition	occupies subchannels
SU1-DP after service completion	$\left(\mathrm{x},\mathrm{y}+1,0\right)$		$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}+1,\mathrm{z}\right)\left(\mathrm{y}+1\right){\mathsf{\mu }}_{{\mathrm{su}}_2}$	$\mathrm{xV}+\mathrm{y}<\mathrm{UV}$	Releases subchannels
SU1-DP after using the remnant of subchannel	$\left(\mathrm{x},\mathrm{y},1\right)$		$\mathsf{\pi }\left(\mathrm{x},\mathrm{y},1\right){\mathsf{\mu }}_{{\mathrm{su}}_2}$	$\mathrm{xV}+\mathrm{y}<\mathrm{UV}$ and $\mathrm{x}<\mathrm{U}-\mathrm{k}$	Releases subchannels
(c) Transition from generic states$\left(x, y,z\right)$to other states when$z>0$
PU-AR and request for channel	$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$	$\left(\mathrm{x}+1,\mathrm{y},\mathrm{z}-\mathrm{V}\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y},\mathrm{z}-\mathrm{V}\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}=\mathrm{UV}$ and $\mathrm{x}<\mathrm{U}-\mathrm{k}-1$	AR of a PU will cause SU2 $\mathrm{V}$ services to be blocked being the sacrificial users while SU1 will not since is a high priority user.
		$\left(\mathrm{x}+1,{\varnothing }_{\min }\left[\mathrm{kV},\mathrm{y}\right],0\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,{\varnothing }_{\min }\left[\mathrm{kV},\mathrm{y}\right],0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}=\mathrm{UV}$ and $\mathrm{x}=\mathrm{U}-\mathrm{k}-1$ If $\mathrm{y}>\mathrm{kV}$	AR of a PU will cause all SU2 services to be blocked $\left(\mathrm{y}-\mathrm{kv}\right)$ services of SU1 will FT else no SU1 services to be blocked/dropped
		$(\mathrm{x}+1,\mathrm{y},\left(\mathrm{U}-\mathrm{k}-\mathrm{x}-1\right)\left(\mathrm{V}-\mathrm{l}\right)$	$\mathsf{\pi }(\mathrm{x}+1,\mathrm{y},\left(\mathrm{U}-\mathrm{k}-\mathrm{x}-1\right)\left(\mathrm{V}-\mathrm{l}\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\left(\mathrm{U}-1\right)\mathrm{V}<\mathrm{xV}+\mathrm{y}<\mathrm{UV}$ and $\mathrm{x}<\mathrm{U}-\mathrm{k}-1$	AR of a PU will block ongoing services of SU2 without any SU1 FT
		$\left(\mathrm{x}+1,{\varnothing }_{\min }\left[\mathrm{kV},\mathrm{y}\right],0\right)$	$\left(\mathrm{x}+1,{\varnothing }_{\min }\left[\mathrm{kV},\mathrm{y}\right],0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\left(\mathrm{U}-1\right)\mathrm{V}<\mathrm{xV}+\mathrm{y}<\mathrm{UV},$ and $\mathrm{x}=\mathrm{U}-\mathrm{k}-1$ If $\mathrm{y}>\mathrm{kv}$ else if ($\mathrm{y}\le \mathrm{zn}$)	AR of a PU will block all ongoing services of SU2 services. Then $\left(\mathrm{y}-\mathrm{kn}\right)$ services of SU1 will be FT with, no need blocking SU1
		$\left(\mathrm{x}+1,\mathrm{y},\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y},0\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathrm{y}\le \left(\mathrm{U}-1\right)\mathrm{V}$	None of the SU1(s) will be FT even as PU access one channel.
PU-DP after service completion		$\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}\right){\mathrm{x}\mathsf{\mu }}_{\mathrm{p}}$	No condition	Releases subchannels
SU1-AR, request and occupy subchannel	$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}+1,\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}+1,\mathrm{z}\right){\mathsf{\lambda }}_{{\mathrm{su}}_1}$	$\mathrm{xV}+\mathrm{y}+\mathrm{z}<\mathrm{UV}$ and $\mathrm{y}<\mathsf{\beta }$	Occupies subchannels
SU1-DP after service completion		$\left(\mathrm{x},\mathrm{y}-1,\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}-1,\mathrm{z}\right){\mathrm{y}\mathsf{\mu }}_{{\mathrm{su}}_1}$	No condition	Releases subchannels
SU2-AR request for the remnant of the sub-channel(s)		$\left(\mathrm{x},\mathrm{y},\mathrm{z}+1\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y},\mathrm{z}+1\right){\mathsf{\lambda }}_{{\mathrm{su}}_2}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}<\mathrm{UV}$	Occupies subchannels
SU2-DP after service completion		$\left(\mathrm{x},\mathrm{y},\mathrm{z}-1\right)$	$\left(\mathrm{x},\mathrm{y},\mathrm{z}-1\right){\mathrm{y}\mathsf{\mu }}_{{\mathrm{su}}_2}$	No condition	Releases subchannels
(d) Transition from other states to generic state$\left(x, y,z\right)$when$z>0$
PU-AR and request for channel	$\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}+\mathrm{v}\right)$	$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}+\mathrm{v}\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}=\mathrm{UV}$ and $0\le \mathrm{v}\le \mathrm{V}$	$\mathrm{v}$ SU2 are the only ones affected when PU access the channel(s)
	$\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}\right)$		$\mathsf{\pi }\left(\mathrm{x}-1,\mathrm{y},\mathrm{z}\right){\mathsf{\lambda }}_{\mathrm{p}}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}<\mathrm{UV}$	None of the SUs will be FT even as PUs access one channel.
PU-DP after service completion	$\left(\mathrm{x}+1,\mathrm{y},\mathrm{z}\right)$		$\mathsf{\pi }\left(\mathrm{x}+1,\mathrm{y},0\right)\left(\mathrm{x}+1\right){\mathsf{\mu }}_{\mathrm{p}}$	$\mathrm{xV}+\mathsf{\beta }+\mathrm{z}\le \left(\mathrm{U}-1\right)\mathrm{V}$	Releases subchannels
SU1-AR, request and occupy sub channel	$\left(\mathrm{x},\mathrm{y}-1,\mathrm{z}\right)$	$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$	$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}-1,\mathrm{z}\right){\mathsf{\lambda }}_{{\mathrm{su}}_1}$	No condition	Occupies subchannels
SU1-DP after service completion	$\left(\mathrm{x},\mathrm{y}+1,\mathrm{z}\right)$		$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}+1,\mathrm{z}\right)\left(\mathrm{y}+1\right){\mathsf{\mu }}_{{\mathrm{su}}_1}$	No condition	Releases subchannels
SU2-AR request for the remnant of the sub-channel(s)	$\left(\mathrm{x},\mathrm{y},\mathrm{z}-1\right)$		$\mathsf{\pi }\left(\mathrm{x},\mathrm{y}-1,\mathrm{z}\right){\mathsf{\lambda }}_{{\mathrm{su}}_2}$	No condition	Occupies subchannels
SU2-DP after service completion	$\left(\mathrm{x},\mathrm{y},\mathrm{z}+1\right)$		$\mathsf{\pi }\left(\mathrm{x},\mathrm{y},\mathrm{z}+1\right)\left(\mathrm{z}+1\right){\mathsf{\mu }}_{{\mathrm{su}}_2}$	$\mathrm{xV}+\mathrm{y}<\mathrm{UV}$	Occupies subchannels

Remark: AR and DP denote arrival and departure respectively of PU or SU while FT represent forced termination.

below for convenience of illustration.

6. Performance Measure

The performance analysis of this work is aided by the premise of [13,21,24]; however, a unique allocation policy with a performance metric was used in our detailed evaluations. The reason for the choice of theses performance indices was to see how the system responded to arrival, departure and interruption by the PUs. In addition, no study on smart grid communication has considered these indices to the best of our knowledge, making our work unique.

6.1. Blocking Probability

The blocking probability ${\mathrm{P}}_{{\mathrm{b}}_{\mathrm{su}}}$ is the sum of all probabilities of states that cannot admit or give access to SUs into the network. However, arriving SUs will be blocked if:

• There are insufficient idle channels to commence service, irrespective of the class of SUs.
• The sum of the available idle channel(s) is less than the lower bound.

Hence the blocking probability for SU₁ ${\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}$ can be expressed, as in [13,21], as

$${\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}={\displaystyle \sum }_{\mathrm{x}=0}^{\mathrm{U}-\mathrm{K}-1}{\displaystyle \sum }_{\mathrm{z}=0}^{\mathrm{UV}-\mathsf{\beta }}\mathrm{P}\left(\mathrm{x},\mathsf{\beta },\mathrm{z}\right)+{\displaystyle \sum }_{\mathrm{x}=\mathrm{U}-\mathrm{k}}^{\mathrm{U}}\mathrm{P}\left(\mathrm{x},\left(\mathrm{U}-\mathrm{x}\right)\mathrm{V},0\right)$$

(8)

Similarly, the blocking probability for SU₂ ${\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}$ is expressed as

$${\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}{\displaystyle \sum }_{\mathrm{x}=0}^{\mathrm{U}-\mathrm{K}-1}{\displaystyle \sum }_{\mathrm{y}=0}^{\mathrm{UV}-\mathsf{\beta }}\mathrm{P}\left(\mathrm{x},\mathsf{\beta },\left(\mathrm{U}-\mathrm{x}\right)\mathrm{V}-\mathsf{\beta }\right)+{\displaystyle \sum }_{\mathrm{x}=\mathrm{U}-\mathrm{k}}^{\mathrm{U}}{\displaystyle \sum }_{\mathrm{y}=0}^{\mathsf{\beta }}\mathrm{P}\left(\mathrm{x},\mathrm{y},0\right)$$

(9)

6.2. Throughput Efficiency

As stated earlier, the throughput efficiency is the service completion rate, which is a measure of how SUs successfully complete their service for every arrival, as in [24]. For SU₁ and SU₂ respectively, it can be expressed as

$${\partial }_{{\mathrm{su}}_1}={\mathsf{\lambda }}_{{\mathrm{su}}_1}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}\right)\left(1-{\mathrm{P}}_{{\mathrm{f}}_{{\mathrm{su}}_1}}\right)$$

(10)

$${\partial }_{{\mathrm{su}}_2}={\mathsf{\lambda }}_{{\mathrm{su}}_2}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}\right)\left(1-{\mathrm{P}}_{{\mathrm{f}}_{{\mathrm{su}}_2}}\right)$$

(11)

6.3. Access Probability

The acceptance probability implies that enough channels exist for the SUs when they arrive with a high possibility of being granted admission into the network. It also infers that the residual channels after PU occupancy are greater than or equal to the resources required by the SUs. It can be expressed in terms of probability as the rate of not being blocked. For SU₁ and SU₂ respectively, it can be expressed as

$${\mathrm{P}}_{{\mathrm{a}}_{{\mathrm{su}}_1}}=\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}\right)$$

(12)

$${\mathrm{P}}_{{\mathrm{a}}_{{\mathrm{su}}_2}}=\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}\right)$$

(13)

Note that the probability of access and blocking is unity as shown in Equation (14)

$${\mathrm{P}}_{{\mathrm{a}}_{\mathrm{su}}}+{\mathrm{P}}_{{\mathrm{b}}_{\mathrm{su}}}=1$$

(14)

This should not be misunderstood for the throughput efficiency in (10); however, they are related.

6.4. Force Termination Probability

The force termination (FT) occurs whenever ongoing SU (SU₁ or SU₂) services are pre-empted by the PU arrival. This suggests that the SU could not successfully exit from an idle channel(s). The blocking probability for SU₁ can be expressed as

$$\begin{gathered} {\mathrm{P}}_{{\mathrm{f}}_{{\mathrm{su}}_1}}=\frac{{\mathsf{\lambda }}_{\mathrm{p}}}{{\mathsf{\lambda }}_{{\mathrm{su}}_1}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}\right)}·{\displaystyle \sum }_{\mathrm{x}=\mathrm{U}-\mathrm{k}}^{\mathrm{U}-1}{\displaystyle \sum }_{{\mathrm{l}}^{*}=0}^{\mathrm{V}}{\mathrm{l}}^{*}\left(\mathrm{x},\left(\mathrm{U}-1-\mathrm{x}\right)\mathrm{V}+{\mathrm{l}}^{*},0\right) \\ +\frac{{\mathsf{\lambda }}_{\mathrm{p}}}{{\mathsf{\lambda }}_{{\mathrm{su}}_1}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_1}}\right)}·{\displaystyle \sum }_{{\mathrm{l}}^{*}=1}^{\mathrm{l}}{\displaystyle \sum }_{\mathrm{z}=0}^{\mathrm{UV}-\mathsf{\beta }}{\mathrm{l}}^{*}\mathrm{P}\left(\mathrm{x},\mathrm{kV}+{\mathrm{l}}^{*},\mathrm{z},0\right) \end{gathered}$$

(15)

Similarly, the forced termination probability for SU₂ ${\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}$ is expressed as

$$\begin{gathered} \frac{{\mathsf{\lambda }}_{\mathrm{p}}}{{\mathsf{\lambda }}_{{\mathrm{su}}_2}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}\right)}·{\displaystyle \sum }_{\mathrm{x}=0}^{\mathrm{U}-\mathrm{k}-2}{\displaystyle \sum }_{\mathrm{y}=0}^{\mathsf{\beta }}{\displaystyle \sum }_{{\mathrm{z}}^{*}}^{\mathrm{V}}{\mathrm{z}}^{*}\mathrm{P}\left(\mathrm{x},\mathrm{y},\left(\mathrm{U}-\mathrm{k}-\mathrm{x}-1\right)\mathrm{V}-\mathrm{l}+{\mathrm{z}}^{*}\right) \\ +\frac{{\mathsf{\lambda }}_{\mathrm{p}}}{{\mathsf{\lambda }}_{{\mathrm{su}}_2}\left(1-{\mathrm{P}}_{{\mathrm{b}}_{{\mathrm{su}}_2}}\right)}·{\displaystyle \sum }_{\mathrm{y}=0}^{\mathsf{\beta }}{\displaystyle \sum }_{\mathrm{z}=1}^{\mathrm{UV}-\mathsf{\beta }}\mathrm{zP}\left(\mathrm{U}-\mathrm{k}-1,\mathrm{y},\mathrm{z}\right) \end{gathered}$$

(16)

7. Numerical Results and Discussion

Our numerical results and discussions will be categorized into two sub-sections. The first sub-section evaluates and compares the two classes of secondary users (SMU and NSMU) within the proposed Next-GUN model. While the second subsection will compare our proposed model to other similar investigations in the literature and the improvements made. The range of parameters used for the PUs is ${\mathsf{\lambda }}_{\mathrm{p}}={\mathsf{\mu }}_{\mathrm{p}}\le 5.0$, while for SUs it is ${\partial }_{\mathrm{su}}={\mathsf{\lambda }}_{\mathrm{s}}={\mathsf{\mu }}_{\mathrm{s}}\le 3.0$.

7.1. Evaluation and Comparison of SM and NSM Users Within the Proposed Next-GUN Model

This subsection evaluates the performance of the Next-GUN model with respect to PU/SU events (arrival and departure). Our numerical results are anchored on four cardinal indices, which are the throughput efficiency, blocking, access and forced termination probabilities. A software tool (Matlab) was used to execute the simulations for the strategies with regards to the SMU and NSMU (SU₁ and SU₂, respectively). In addition, we adopted some parameters [12,15,16] and averaged 100 obtained values to obtain the result from 10⁶ iterations. However, there are variations based on the indices like blocking, access and forced termination probabilities, which we introduced.

Figure 3 and Figure 4 show the effects of incremental arrivals of PUs (TV-users) on the network. Figure 3 shows that in the event of batch arrivals, the SUs (SU₁ and SU₂) would experience difficulties accessing the TVWS. This difficulty results in a decrease of access probability (admittance into the networks). In addition, fewer or no spectrum holes would be accessible to service the SUs request, hence a decrease in access into the system would result. Figure 3 illustrates that if the number of accessible subchannel(s) is not enough based on the conditions in the algorithm, access would be denied (blocked).

This consequently increased the blocking probability due to PU mass arrival as shown in Figure 4. On the contrary, once PUs depart, more spectrum-holes (TVWS) are made available for SUs. This, however, depicts a mirror behaviour, which validates the expressions in Equations (12)–(14). Nevertheless, SU₁ showed an improved performance compared to SU₂ due to the priority given to it by the HCRBS.

In Figure 5, the SU throughput is at its peak when the TV-users are absent from the spectrum. As such, the HCRBS utilizes the TVWS by aggregating and allocating more spectrum resources to the SUs, which results in a high completion rate irrespective of the traffic class, the policies and the wireless link state. Nonetheless, the throughput efficiency decreases as the PU arrives. By direct comparison, the throughput efficiency of SU₁ is superior to SU₂ due to the preferential treatment given to it and the nature of its traffic. This is unlike Figure 5, where throughput efficiency drops due to the arrival of the PU.

In Figure 6, the throughput efficiency improves owing to lighter traffic flow from the PU events. Therefore, arrived SUs can complete their transactions deprived of interruption from PU’s ON–OFF activities [25,26]. This implies that the PU has an erratic behaviour and as such, when the SU arrives and the PU is in an OFF/Idle state, the SUs can be serviced (given channel resources to transmit with) before the PU transit to the ON/Busy state.

In Figure 7, the forced termination probability increases considerably as PUs arrive. Specifically, from the point where the arrival rate ${\mathsf{\lambda }}_{\mathrm{p}}=$ 1.4 to ${\mathsf{\lambda }}_{\mathrm{p}}=$ 1.6, the forced termination increased sharply. This is due to increased arrivals (batch) from 0.1, which implies a single arrival to 1.8, which denotes 18 arrivals of PUs on the Next-GUN system. This otherwise affects the SU transactions because the PUs will grab its channels without prior notice. As such, the HCRBS will try to rescue the SU service, or else it will be forced to terminate its ongoing services. Due to its flexibility and superior capability, the smart meter response is faster and better at every point compared to the non-smart users.

In Figure 8, the forced termination probability decreases and decays to zero as the SUs experience abundant TVWS resources (left to right axis movement). This implies that SU arrivals are serviced immediately without delay, irrespective of the class of SU (SU₁ or SU₂). On the other hand (right to left movement), the force termination probability will increase when there are insufficient channel resources, thus reaffirming the importance of channel aggregation and its effect on SU performance.

The result in Figure 9 indicates that the likelihood of SU service being blocked on arrival will diminish once there are abundant idle TVWS to jump on after careful sensing of the TV-band. Normally, it is expected that the blocking probability decreases as the arrival/service rate of the SU is increased. Recall, we are aggregating channels, which implies that the SU throughput (volume of the packet sent) will be higher than usual. For instance, an SU using one channel to transmit packets cannot be compared to an SU that has aggregated or combined five channels. This means that the likelihood of that SU being blocked will be minimal because it will transmit its packets faster. On the other hand, if the graph is viewed from the left direction, the blocking probability will definitely increase due to loss or inadequate TVWS. This is the beauty of our proposal.

The results in Figure 10 are in consonance with Figure 9 and validates (12)–(14) from our analysis. It suggests that once there is abundant idle TVWS to jump on, the access probability will naturally increase because of adequate TVWS to aggregate. It also implies that once the SU gains access into the TVWS, it will be served immediately without delays. For example, if the blocking probability is ${\mathrm{P}}_{\mathrm{b}}=0.3$ irrespective of the users selected, the access probability is ${\mathrm{P}}_{\mathrm{a}}=1-{\mathrm{P}}_{\mathrm{b}}$, then ${\mathrm{P}}_{\mathrm{a}}=1-{\mathrm{P}}_{\mathrm{b}}$ $=0.7$ and vice-versa as illustrated in the results. Note, the worst-case scenario of this study would be that all channel(s)/TVWS are occupied and the HCRBS/CCGW/CFGW will have to probe continually, which will likely lead to force termination or blocking/dropping of services. This implies that the SUs will be stripped of their aggregated channel(s) with no other free ones to aggregate. This, of course, might not often happen considering the ON–OFF erratic behaviour of PUs.

7.2. Comparison of the Proposed Next-GUN Model and Some Studies in the Literature

As part of the contribution of this work, this subsection compares the proposed Next-GUN model to closely related works in the literature. We compared our work with two scenarios: (a) when there is No Aggregation (NA), and (b) when Channel Aggregation Strategy (CAS) is applied but in this case, the sub-intelligent agents (subnetworks agents) are not independent or semi-independent. In other words, in CAS, every subnetwork reports to the cognitive base station irrespective of how minute the decisions are. This increases complexity and burden on the central fusion center, and as such, degrades performance, and hence cannot be applied to smart grids or the internet of things.

As stated earlier, the essential difference between our proposed Next-GUN model and the others in the literature is twofold. (a) The application of channel aggregation policy in all tiers of the network (from generation up to distribution). (b) The semi-independence given to CCGW and CFGW (intelligent agent or subnetworks) to aggregate and use the spectrum-holes within its jurisdiction (coverage area) for daily and hourly data transmission, while still sending reports to the HCRBS for a superior decision. Hence, this design is suitable for deployment in this work. Part of our future work will be on the deployment of this Next-GUN concept in the internet of things (IoT), guided by [27] with the characterization of SU (IoT-agent) behaviour as in [28,29] using optimization strategies of [30].

In Figure 11, we notice that when there are fewer aggregated channels, the force termination is high (from right to left x-axis) and vice-versa from left to right x-axis. Furthermore, when there is no aggregation, the force termination probabilities are highest, meaning that the PU has arrived unannounced and taken back its channel. This consequently causes the SUs to terminate ongoing services. However, we also notice that because the Next-GUN is a more robust model with intelligent subnetworks, it slightly outperformed CAS and outrightly outperformed the NA, owing to its lower force termination probability.

Figure 12 illustrates what happens when the PUs arrive. First, they depart the spectrum unannounced and arrive without notice. This behaviour naturally affects SU’s ongoing service. Because they are the licensed owner, they occupy the spectrum-holes and any SU service trying to access the system is blocked. In most cases, the PUs do not occupy all the channel at once due to their ON–OFF activities. This enables the intelligent agents to optimistically probe and utilize the vacant channels. By comparison, the NA has the worst or highest blocking probability, due to no strategy being applied, followed by CAS.

The proposed Next-GUN and CAS have a better or lowered blocking probability. However, the proposed Next-GUN showed a slight superiority to CAS, particularly in batch arrival of PUs, which is the worst-case scenario.

Figure 13 illustrates SU throughput efficiency (rate of successful package delivery) as the SU arrives and aggregates channels. The logic is that, when enough channels are available, the SU aggregates more and consequently this translates to high package delivery to destination. In other words, as the SUs are serviced (allocated more channels), there is a clear tendency for higher package capacity transmission. In the same vein, if the service rate diminishes as a result of increased arrival of PU, there will be a drop-in throughput efficiency or rate of delivery. By comparison, there was no clear-cut superiority of Next-GUN over CAS initially from our results. However, as the SU service rate increased due to surplus channels and the increased arrivals of SUs, the Next-GUN began to show its superiority over CAS. Nevertheless, a point occurred when both strategies were of equal strength.

The numerical result in Figure 14 clearly affirms that the PUs are the licensed owners of the TVWS. This is clearly shown because as the PU’s arrival increases, the SU access or admission into the spectrum decreases, meaning that the SU must depart for the original owner to utilize its channels. Therefore, it is natural that when the owner of a resource arrives unannounced or by given prior notice, the tenant must vacate. On the contrary, when the PUs are absent or occupying a few channels, the SUs will gain more access into the channel to transmit its data. As Figure 13 shows, the more PUs arrive and occupy its spectrum, the admission or access given to the SU reduces. However, it is highly unlikely that PU will occupy all the slots or channels and so the SU constantly probes for spectrum holes.

Because the CAS and Next-GUN have aggregation strategies, they tend to perform far better than the NA, which is a conventional wireless technology. As presented in the results, Next-GUN outperformed the CAS due to its robust architecture and algorithms. This is not to say CAS is not good, but for us to exploit a licensed spectrum and decongest the current spectrum that is currently facing crunch and scarcity, we need a more intelligent software-driven model like Next-GUN.

8. Conclusions

Contemporary research is geared towards a multidisciplinary domain, targeted to developing robust and intelligent systems. This study has shown and reaffirms the importance of applying and integrating cognitive radio technology into our present-day power grid network and future research. It further shows that the TVWS is very useful in these days of spectrum crunch and scarcity based on the performance indices shown. In addition, most power utility establishments around the globe would not only want to make their network smart for easy and convenient data logging and monitoring, but more importantly, save the cost of paying for a licensed band. This work has shown and demonstrated to the best of our understanding the strength of the proposed software-driven Next-GUN model, which in turn is geared towards the heterogeneous wireless networks like 5G. Our future work would be in two parts. First, we will look at the smart grid internet of things (SG-IoT) using CRT and the effect of a queuing regime like the M/G/1 and M/G/K queuing model on the proposed scheme. Secondly, we will consider the effect of a queuing regime and malicious attack on the cyber–physical system.