**4.1. Performance model: pace tourist enabling mechanism**

The formulated QoS metrics are the channel capacity and latency. The channel capacity for the space vehicle is formulated considering cases where the proposed handover mechanism is used and not used. The channel capacity achievable by the space vehicle in the terrestrial plane, aerial plane and space plane are denoted as *Cter*, *Cae* and *Csp* respectively and can be expressed as:

$$\mathbb{C}\_{tr} = \sum\_{z'=1}^{z'} \sum\_{b=1}^{d} \mathcal{B}(z', b) \log\_2 \left( 1 + \frac{\left. \Pr\_{tr} \left( \boldsymbol{\gamma}\_b, z' \right) \left| h\_{11} \left( \boldsymbol{\gamma}\_b, z' \right) \right|^2 \right.}{\left. \Pr\_{int} \left( \boldsymbol{\gamma}\_b, z' \right) \left| h\_{12} \left( \boldsymbol{\gamma}\_b, z' \right) \right|^2 + \sigma^2} \right) \tag{30}$$

$$\mathbf{C}\_{\rm av} = \sum\_{z'=1}^{z'} \sum\_{l=1}^{h} B(z', l) \log\_2 \left( 1 + \frac{P\_{tr}(\mathbf{b}\_l, z') |h\_{11}(\mathbf{b}\_l, z')|^2}{P\_{int}(\mathbf{b}\_l, z') |h\_{12}(\mathbf{b}\_l, z')|^2 + \sigma^2} \right) \tag{31}$$

$$\mathcal{L}\_{sp} = \sum\_{z'=1}^{z'} \sum\_{c=1}^{n} B(z', c) \log\_2 \left( 1 + \frac{P\_{tr}(\mathbf{p}\_c, z') |h\_{11}(\mathbf{p}\_c, z')|^2}{P\_{int}(\mathbf{p}\_c, z') \left|h\_{12}(\mathbf{p}\_c, z')\right|^2 + \sigma^2} \right); \mathbf{p}\_c \epsilon \text{ p} \tag{32}$$

Where:

*z*<sup>0</sup> is the channel *z*<sup>0</sup> which is distinct for each concerned communication entity.

*Ptr <sup>γ</sup>d; <sup>z</sup>*<sup>0</sup> � �*, Ptr* <sup>Ϸ</sup>*l; <sup>z</sup>*<sup>0</sup> ð Þ and *Ptr* <sup>ƿ</sup>*c; <sup>z</sup>*<sup>0</sup> ð Þ are the operational data transmit power between the space vehicle and (i) terrestrial wireless network on channel *z*<sup>0</sup> , (ii) high altitude platform on channel *z*<sup>0</sup> and (iii) communication satellite on channel *z*<sup>0</sup> respectively.

*Pint <sup>γ</sup>d; <sup>z</sup>*<sup>0</sup> � �*, Pint* <sup>Ϸ</sup>*l; <sup>z</sup>*<sup>0</sup> ð Þ and *Pint* <sup>ƿ</sup>*c; <sup>z</sup>*<sup>0</sup> ð Þ is the interference power between the space vehicle and (i) terrestrial wireless network on channel *z*<sup>0</sup> , (ii) high altitude platform on channel *z*<sup>0</sup> and (iii) communication satellite on channel *z*<sup>0</sup> respectively.

*<sup>h</sup>*<sup>11</sup> *<sup>γ</sup>d; <sup>z</sup>*<sup>0</sup> � �*, h*<sup>11</sup> <sup>Ϸ</sup>*l; <sup>z</sup>*<sup>0</sup> ð Þ and *<sup>h</sup>*<sup>11</sup> <sup>ƿ</sup>*c; <sup>z</sup>*<sup>0</sup> ð Þ are the transmit channel gain between the space vehicle and (i) terrestrial wireless network on channel *z*<sup>0</sup> , (ii) high altitude platform on channel *z*<sup>0</sup> and (iii) communication satellite on channel *z*<sup>0</sup> respectively.

*<sup>h</sup>*<sup>12</sup> *<sup>γ</sup>d; <sup>z</sup>*<sup>0</sup> � �*, h*<sup>12</sup> <sup>Ϸ</sup>*l; <sup>z</sup>*<sup>0</sup> ð Þ and *<sup>h</sup>*<sup>12</sup> <sup>ƿ</sup>*c; <sup>z</sup>*<sup>0</sup> ð Þ are the transmit channel gain between the space vehicle and (i) terrestrial wireless network on channel *z*<sup>0</sup> , (ii) high altitude platform on channel *z*<sup>0</sup> and (iii) communication satellite on channel *z*<sup>0</sup> respectively.

The average channel capacity of the space vehicle is denoted as *Cave* and given as:

Lunar Science: Internet for Space Tourism http://dx.doi.org/10.5772/intechopen.89124 191

$$\mathbb{C}\_{\text{ave}} = \frac{1}{3} \left( \mathbb{C}\_{\text{ter}} + \left. I \{ \boldsymbol{\gamma}\_d, \mathbf{b}\_l \} \right| \mathbb{C}\_{\text{ae}} + I(\mathbf{b}\_l, \mathbf{p}\_c) \mathbb{C}\_{\text{sp}} \right) \tag{33}$$

Where:

*I γd;* Ϸ*<sup>l</sup>* � �<sup>E</sup> f g <sup>0</sup>*;* <sup>1</sup> is the handover indicator between *<sup>γ</sup><sup>d</sup>* and <sup>Ϸ</sup>*l*. The cases *<sup>I</sup> <sup>γ</sup>d;* <sup>Ϸ</sup>*<sup>l</sup>* � � <sup>¼</sup> 0 and *I γd;* Ϸ*<sup>l</sup>* � � <sup>¼</sup> 1 signify that a handover is not executed and is executed between *<sup>γ</sup><sup>d</sup>* and <sup>Ϸ</sup>*<sup>l</sup>* respectively.

*I* Ϸ*l;* ƿ*<sup>c</sup>* ð ÞE f g 0*;* 1 is the handover indicator between Ϸ*<sup>l</sup>* and ƿ*c*. The cases *I* Ϸ*l;* ƿ*<sup>c</sup>* ð Þ¼ 0 and *I* Ϸ*l;* ƿ*<sup>c</sup>* ð Þ¼ 1 signify that a handover is not executed and is executed between Ϸ*<sup>l</sup>* and ƿ*c*respectively.

The latency associated with transmitting *D*<sup>0</sup> bytes of data without and with the incorporation of the proposed handover is denoted *β*<sup>1</sup> and *β*<sup>2</sup> respectively and given as:

$$\beta\_1 = 8 \times D' \times \left(\mathbb{C}\_{\text{ave}}\right)^{-1}\Big|\_{\substack{l\left(\mathbb{Y}\_d, \mathfrak{d}\_l\right) = 0, \ l\left(\mathfrak{d}\_l, \mathfrak{p}\_c\right) = 0}}\tag{34}$$

$$\beta\_2 = 8 \times D' \times \left(\mathbb{C}\_{\mathfrak{w}\mathfrak{e}}\right)^{-1} \Big|\_{\substack{\mathfrak{l}\left(\mathbb{V}\_d, \mathfrak{h}\right) = 1, \ \mathfrak{l}\left(\mathbb{V}\_l, \mathfrak{p}\_c\right) = 1}} \tag{35}$$

The cases 8 � *<sup>D</sup>*<sup>0</sup> � ð Þ *Cave* �<sup>1</sup> � � � *<sup>I</sup> <sup>γ</sup><sup>d</sup>* ð Þ *;*Ϸ*<sup>l</sup>* <sup>¼</sup>1*, <sup>I</sup>* <sup>Ϸ</sup>*l;*ƿ*<sup>c</sup>* ð Þ¼<sup>0</sup> and 8 � *<sup>D</sup>*<sup>0</sup> � ð Þ *Cave* �<sup>1</sup> � � � *<sup>I</sup> <sup>γ</sup><sup>d</sup>* ð Þ *;*Ϸ*<sup>l</sup>* <sup>¼</sup>0*, <sup>I</sup>* <sup>Ϸ</sup>*l;*ƿ*<sup>c</sup>* ð Þ¼<sup>1</sup> have not

been considered. This is because our discussion does not consider a partial handover as implied in the cases described by *I γd;* Ϸ*<sup>l</sup>* � � <sup>¼</sup> <sup>1</sup>*, I* <sup>Ϸ</sup>*l;* <sup>ƿ</sup>*<sup>c</sup>* ð Þ¼ 0 and *<sup>I</sup> <sup>γ</sup>d;* <sup>Ϸ</sup>*<sup>l</sup>* � � <sup>¼</sup> <sup>1</sup>*, I* <sup>Ϸ</sup>*l;* <sup>ƿ</sup>*<sup>c</sup>* ð Þ¼ 1. A partial handover results in a scenario where QoS of the space tourist subscribers suffer severe degradation due to frequent interruption.

#### **4.2. Performance model: cyber-physical aided cloud access system**

The deployment of either the UAV or MAV in the proposed cyber–physical cloud access system enables the delivery of cloud content when it could otherwise be challenging. This is due to the incidence of network congestion or any other event that could lead to high delay in the terrestrial wireless network segment. In the formulation, the cloud content traverses multiple cells in an infrastructure-based network. The occurrence of congestion on any of the forwarding network nodes increase the latency associated with accessing cloud content by remote subscribers. The probability of congestion on terrestrial wireless network *γ<sup>b</sup>* with own base station and associated gateway entity is denoted *Pco γ<sup>b</sup>* � �*; <sup>γ</sup><sup>b</sup>* <sup>E</sup> *<sup>γ</sup>*. The probability of deploying either MAVs or UAVs that spans the coverage of j j *γ* terrestrial wireless networks is denoted as *Pcy*ð Þ j j *γ* . Given that the channel capacity of *γ<sup>b</sup>* is denoted as *Th γ<sup>b</sup>* � �; the aggregate channel capacity associated with cloud content without and with the cyber–physical system is denoted as *Thcl* <sup>1</sup> *γ<sup>b</sup>* � � and *Thcl* <sup>2</sup> *γ<sup>b</sup>* � �, respectively.

$$\text{Th}\_1^{cl}(\boldsymbol{\gamma}\_b) = \left(\prod\_{b=1}^f P\_{co}(\boldsymbol{\gamma}\_b) \times \sum\_{b=f+1}^d P\_{co}(\boldsymbol{\gamma}\_b)\right) \times \text{Th}(\boldsymbol{\gamma}\_b) \forall \boldsymbol{\gamma}\_b \tag{36}$$

$$\text{Th}\_2^d(\boldsymbol{\gamma}\_b) = \left( \left( \prod\_{b=1}^f P\_{co}(\boldsymbol{\gamma}\_b) \times \sum\_{b=f+1}^d P\_{co}(\boldsymbol{\gamma}\_b) \right) + \left( \prod\_{b=1}^f P\_{cy}(\boldsymbol{\gamma}\_b) \times \sum\_{b=f+1}^d P\_{cy}(\boldsymbol{\gamma}\_b) \right) \right) \tag{37}$$
