**2.2 Problem definition: the 'space tourist' subscriber**

The considered scenario comprises multiple networks enabling subscribers to access cloudbased content. Let *N, S* and *C* be the set of wireless networks, subscribers and cloud platforms, respectively. Such as:

**Figure 1.** Network scenario showing the system model.

$$N = \{n\_S, n\_T\} \tag{1}$$

$$S = \{\mathbf{s}\_1, \mathbf{s}\_2, \dots, \mathbf{s}\_x\} \tag{2}$$

$$\mathcal{C} = \left\{ \mathbb{C}\_1, \mathbb{C}\_2, \dots, \mathbb{C}\_y \right\} \tag{3}$$

$$m\_{\mathcal{S}} = \left\{ n\_{\mathcal{S}}^1, n\_{\mathcal{S}}^2, \dots, n\_{\mathcal{S}}^p \right\} \tag{4}$$

$$n\_T = \left\{ n\_T^1, n\_T^2, \dots, n\_T^q \right\} \tag{5}$$

Where:

*nS* and *nT* are the set of satellite and terrestrial wireless networks respectively.

*sz, sz*<sup>E</sup> *<sup>S</sup>* is the ð Þ*<sup>z</sup> th* subscriber desiring access to cloud-based content.

*nr S, nr <sup>S</sup>*<sup>E</sup> *nS* is the ð Þ*<sup>r</sup> th* satellite network.

*nu T, nu <sup>T</sup>*<sup>E</sup> *nT* is the ð Þ *<sup>u</sup> th* terrestrial wireless network.

*Ci, Ci* <sup>E</sup> *<sup>C</sup>* is the ð Þ*<sup>i</sup> th* cloud platform hosting content that subscriber *sz* seeks to access.

The coverage region of *n<sup>u</sup> <sup>T</sup>* and *n<sup>r</sup> <sup>S</sup>* are denoted as *α nu T* and *α n<sup>r</sup> S* , respectively. Let *I β;Ci; tj* <sup>E</sup> f g <sup>0</sup>*;* <sup>1</sup> *, <sup>β</sup>*<sup>E</sup> *nu <sup>T</sup>; nr S , tj* <sup>E</sup> *t, t* <sup>¼</sup> f g *<sup>t</sup>*1*; <sup>t</sup>*2*;*…*; tw* be the cloud access indicator at epoch *tj*. The states *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nu <sup>T</sup>;Ci; tj* <sup>¼</sup> 0 and *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *<sup>n</sup><sup>u</sup> <sup>T</sup>;Ci; tj* <sup>¼</sup> 1 signify that the ð Þ*<sup>i</sup> th* cloud platform *Ci* is inaccessible and accessible to base station entities of the ð Þ *<sup>u</sup> th* terrestrial wireless network at epoch *tj* respectively. The indicator *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nr <sup>S</sup>;Ci; tj* <sup>¼</sup> 0 and *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nr <sup>S</sup>; Ci; tj* <sup>¼</sup> 1 signify that the ð Þ*<sup>i</sup> th* cloud platform *Ci* is inaccessible and accessible to base station entities of the ð Þ*<sup>r</sup> th* satellite network, respectively. The ground-based entity of the ð Þ*<sup>r</sup> th* satellite network is the terrestrial component of a satellite network.

A scenario described by the transition *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nu <sup>T</sup>;Ci; tj* <sup>¼</sup> <sup>0</sup>*, I <sup>β</sup>* <sup>¼</sup> *<sup>n</sup><sup>u</sup> <sup>T</sup>;Ci; tj*þ<sup>1</sup> <sup>¼</sup> <sup>1</sup>*, tj*þ<sup>1</sup><sup>E</sup> *<sup>t</sup>* is one in which the cloud platform *Ci* is connected to network *nu <sup>T</sup>* at epoch *tj*þ<sup>1</sup> and not connected at epoch *tj* respectively. Another plausible scenario is *<sup>β</sup>* <sup>¼</sup> *<sup>n</sup><sup>u</sup> <sup>T</sup>;Ci; tj* � � <sup>¼</sup> <sup>0</sup>*, I <sup>β</sup>* <sup>¼</sup> *nr <sup>S</sup>;Ci; tj*þ<sup>1</sup> � � <sup>¼</sup> <sup>0</sup>*, <sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nr <sup>S</sup>;Ci; tj*þ*<sup>j</sup>* 0 � � <sup>¼</sup> <sup>0</sup>*, tj*þ*<sup>j</sup>* <sup>0</sup>E *t*, which describes a case where subscriber *sz* moves through the regions where access to cloud content via terrestrial network is infeasible at epochs *tj* and *tj*þ<sup>1</sup> but feasible at epoch *tj*þ*<sup>j</sup>* 0 .

The variable *I β; Ci; tj* � � can have a varying number of contexts described by transitions between different scenarios for different *β, Ci* and *tj*. A common factor across these scenarios is the implied assumption that *N* ∩ f g *nS*∪*nT* 6¼ ∅. However, this does not consider the requirement to provide internet access in outer–space. Hence, another scenario that is yet to be considered is one described as *N* ∩ f g *nS*∪*nT* ¼ ∅ that considers the space tourist subscriber which has not been considered.

In the terrestrial plane, the subscriber *sz* accesses the cloud content from a terrestrial location. However, cloud content can be accessed from other locations such as the ocean, and near space regions. Let *θ* denote the set of possible subscriber locations, such as:

$$\boldsymbol{\Theta} = \left\{ \theta\_{\mathcal{S}}, \theta\_{\mathrm{ac}}, \theta\_{\mathrm{su}} \; \right\} \tag{6}$$

$$\theta\_{\mathcal{S}} = \left\{ \theta\_{\mathcal{S}}^1, \theta\_{\mathcal{S}}^2, \dots, \theta\_{\mathcal{S}}^p \right\} \tag{7}$$

$$\boldsymbol{\Theta}\_{\text{ae}} = \left\{ \boldsymbol{\Theta}\_{\text{ae}}^1, \boldsymbol{\Theta}\_{\text{ae}}^2, \dots, \boldsymbol{\Theta}\_{\text{ae}}^m \right\} \tag{8}$$

$$\boldsymbol{\Theta}\_{su} = \left\{ \theta\_{su}^{1}, \theta\_{su}^{2}, \dots, \theta\_{su}^{\ell} \right\} \tag{9}$$

Where

*θ<sup>g</sup>* and *θae* are the set of ground and aerial locations respectively.

*θc <sup>g</sup>, θ<sup>c</sup> <sup>g</sup>* E *θ<sup>g</sup>* is the *cth* ground location.

*θn ae, θ<sup>n</sup> ae* E *θae* is the *nth* aerial location.

*θsu* is the set of locations in space.

*θv*0 *su; θ<sup>v</sup>*<sup>0</sup> *su*E *θsu* is the *v*<sup>0</sup> sub – orbital location.

The definition of *θ* excludes the underwater and underground locations.

There is coverage for locations *<sup>θ</sup><sup>g</sup>* and *<sup>θ</sup>ae* given that *<sup>I</sup> <sup>β</sup>* <sup>¼</sup> *nu <sup>T</sup>;Ci; tj* � � <sup>¼</sup> <sup>1</sup>∀*θg, <sup>θ</sup>ae* hold true. The condition *I β;Ci; tj* � � <sup>¼</sup> <sup>1</sup>∀*θg, <sup>θ</sup>ae* indicates that there is no network coverage for locations *<sup>θ</sup><sup>g</sup>* and *θae*. Satellite and terrestrial wireless networks cannot deliver cloud access to space tourist subscribers when:

$$\left\{ I\{\beta = n\_T^u, \mathbb{C}\_i, t\_j\}, I\{\beta = n\_T^u, \mathbb{C}\_i, t\_{j+1}\}, I\{\beta = n\_T^u, \mathbb{C}\_i, t\_{j+\not\cdot j}\}, \dots, I\{\beta = n\_T^u, \mathbb{C}\_i, t\_w\} \right\} = 0, \forall \theta\_{su} \tag{10}$$

$$\left\{ I\{\beta = n\_S^r, \mathbb{C}\_i, t\_{\rceil}\}, I\{\beta = n\_S^r, \mathbb{C}\_i, t\_{\neq \cdot}\}, I\{\beta = n\_S^r, \mathbb{C}\_i, t\_{\neq \cdot \'}\}, \dots, I\{\beta = n\_T^u, \mathbb{C}\_i, t\_w\} \right\} = 0, \forall \theta\_{\mathrm{su}} \tag{11}$$

This is because terrestrial and satellite networks do not provide internet access for space tourist subscribers.

Let *N*<sup>0</sup> denote the set of updated set of wireless networks such that:

$$N' = \left\{ N, \phi\_{\rm SL} \right\} \tag{12}$$

Where *ϕSU* is the network designed to provide access to cloud content for *θsu*, then it is desired that:

$$\left\{ I\left(\left(\mathbf{N'}\cap\mathbf{N}\right)',\mathbb{C}\_{i},t\_{\parallel}\right), I\left(\left(\mathbf{N'}\cap\mathbf{N}\right)',\mathbb{C}\_{i},t\_{\neq 1}\right), I\left(\left(\mathbf{N'}\cap\mathbf{N}\right)',\mathbb{C}\_{i},t\_{\neq \neq'}\right),..., I\left(\left(\mathbf{N'}\cap\mathbf{N}\right)',\mathbb{C}\_{i},t\_{w}\right) \right\} = 0,\forall\theta\_{\mathbf{s}}\tag{13}$$

This paper designs a network architecture which ensures that (13) holds true at all epochs.

The discussion so far assumes that data access from the cloud in the contexts considered above is accompanied with a high QoS. This assumes the availability of reliable network infrastructure. For instance, this assumption is not true where exists poor availability of highperformance terrestrial network infrastructure, or subscribers' inability to access expensive satellite networks. This assumption is true for cloud service providers in nations with a high population demanding access to cloud content; described by the conditions:

$$I\left\{I(\beta=n\_T^{\mu}, \mathbb{C}\_i, t\_{\bar{\gamma}}), I\left(\beta=n\_T^{\mu}, \mathbb{C}\_i, t\_{\bar{\gamma}+1}\right), I\left(\beta=n\_T^{\mu}, \mathbb{C}\_i, t\_{\bar{\gamma}\cdot\bar{\gamma}'}\right), \dots, I\left(\beta=n\_T^{\mu}, \mathbb{C}\_i, t\_w\right)\right\} = 0, \forall n\_T, \theta\_{\bar{\mathcal{S}}} \quad \text{(14)}$$

$$I\left\{I(\beta=n\_{\mathcal{S}}^{r},\mathbb{C}\_{i},t\_{\dagger}),I\middle|\beta=n\_{\mathcal{S}}^{r},\mathbb{C}\_{i},t\_{\dagger+1}\right\},I\left(\beta=n\_{\mathcal{S}}^{r},\mathbb{C}\_{i},t\_{\dagger+\dagger}\right),...,I\middle|\beta=n\_{\mathcal{T}}^{u},\mathbb{C}\_{i},t\_{w}\right\}=0,\forall n\_{\mathcal{S}}\tag{15}$$

If we let *D sx; tj* � � and *Th sx; β; tj* � �*, β* E *n<sup>u</sup> <sup>T</sup>; nr S* � � denote, respectively, the size of data accessed by *sx* from network entity *β* and throughput associated with data accessed by *sx; sx* E *S* via network entity *β* at epoch *tj*, then the mean latency Eð Þ *sx* can be expressed as:

$$\mathbb{E}(\mathbf{s}\_{\mathbf{x}}) = \frac{1}{2} \left( \frac{1}{w\eta} \sum\_{j=1}^{w} \sum\_{r=1}^{p} \frac{I(\boldsymbol{\beta} = n\_{\mathrm{S}}^{r}, \mathbf{C}\_{i}, t\_{\dagger}) D(\mathbf{s}\_{\mathbf{x}}, t\_{\dagger})}{\mathrm{Tr}(\mathbf{s}\_{\mathbf{x}}, \boldsymbol{\beta} = n\_{\mathrm{S}}^{r}, t\_{\dagger})} + \frac{1}{w\eta} \sum\_{j=1}^{w} \sum\_{u=1}^{q} \frac{I(\boldsymbol{\beta} = n\_{\mathrm{T}}^{q}, \mathbf{C}\_{i}, t\_{\dagger}) D(\mathbf{s}\_{\mathbf{x}}, t\_{\dagger})}{\mathrm{Tr}(\mathbf{s}\_{\mathbf{x}}, \boldsymbol{\beta} = n\_{\mathrm{T}}^{q}, t\_{\dagger})} \right) \tag{16}$$

Given the threshold latency *lth*, the subscriber *sx* has a significant delay if Eð Þ *sx* ≫ *lth*. The delay Eð Þ *sx* refers to that of a single subscriber. In the case of multiple subscribers, the latency E1ð Þ *sz* is given as:

$$\mathbb{E}\_{1}(\mathbf{s}\_{z}) = \frac{1}{2} \left( \frac{1}{w\eta z} \sum\_{j=1}^{w} \sum\_{r=1}^{p} \sum\_{z=1}^{x} \left( \frac{I\{\boldsymbol{\beta} = n\_{\mathcal{S}}^{r}, \mathbb{C}\_{i}, t\_{\boldsymbol{\beta}}\} D\{\mathbf{s}\_{z}, t\_{\boldsymbol{\beta}}\}}{\text{Tr}\{\mathbf{s}\_{x}, n\_{\mathcal{s}}^{r}, t\_{\boldsymbol{\beta}}\}} \right) + \bar{Y}\_{1} \right) \tag{17}$$

$$\dot{Y}\_1 = \underbrace{1}\_{\text{wprz}} \sum\_{j=1}^{w} \sum\_{u=1}^{q} \sum\_{z=1}^{x} \left( \frac{I\{\beta = n\_{\text{S}}^{r}, \mathbf{C}\_{i}, t\_{j}\} D(\mathbf{s}\_{z}, t\_{j})}{\text{Tr}\{\mathbf{s}\_{x}, n\_{\text{s}}^{r}, t\_{j}\}} \right) \tag{18}$$

There is a significant degradation associated with accessing cloud-based content when E1ð Þ *sz* ≫ *lth*,. Hence, a solution which ensures that the condition E1ð Þ *sz* ≤ *lth* holds true for a significantly long duration is required. Such a solution is proposed in this paper. This section presents the two challenges being addressed in this paper, namely:

