1 Introduction

Computing infrastructures enable the processing of data from telescopes se seen in [1–2]. The computing infrastructure is connected to telescopes via fibre optic cable [3–4]. Developing nations with interests in conducting astronomy observations have limited access to supercomputing facilities but use converted telescopes [5,6,7]. The conversion increases the volume of raw data requiring processing. Therefore, it is important to find strategies to increase the amount of accessible computing platforms in developing nations.

Cloud computing platforms have been recognised to be suitable for processing astronomy data [8,9,10]. The use of cloud-based computing resources is challenging for most developing countries. This is because of the prohibitive costs associated with accessing the internet and uploading significantly huge volumes of data. Paradigms such as volunteer computing, grid computing and fog computing are candidate mechanisms for astronomy data processing but prohibitive because of the limited availability of costly high-performance end–user computing entities in developing nations.

Contribution The challenge being addressed in this paper is that of designing computing networks to execute astronomy data processing. The proposed computing network is used in a developing context. In a developing context, the execution of astronomy data processing is affected by capital constraints. The occurrence of capital constraints affects for science organizations in developing countries. In the proposed solution, the execution of astronomy data processing is done using two types of low operational cost data centre modules.

In the proposed research, the first type of data centre re–uses the existing infrastructure (real estate facility mainly) in non–utilized telephone exchange facilities. The second type of data centre is a plesiomarine data centre (PDC). The PDC leverages advances in aquarium technology [16,17,18]. The aquarium is considered because it hosts a significant amount of cooling water. The contributes are further enumerated as:

  1. 1)

    The paper proposes the astronomy computing diversity paradigm (ACDP). ACDP utilizes data centres that use previously un–utilized telephony infrastructure. The realized data centre is called the class A data centre (CACT). ACDP also uses plesiomarine data centres (PDC) i.e., the Class B data centre (CBCT). The joint use of the CACT and CBCT in ACDP aims to reduce the costs associated with establishing and operating computing facilities. The paper also proposes network architecture enabling communications between telescopes and the CACT or CBCT. The paper identifies components of the telephony infrastructure that can be re – used. This is done while describing their functionalities.

  2. 2)

    Secondly, the paper formulates the performance model to investigate the performance benefits of the proposed ACDP. The metrics are: (i) computing system costs, (ii) power usage effectiveness (PUE) and (iii) angular resolution. The performance metrics are investigated under different contexts via simulation. The paper also discusses trade–offs involving how the identified performance metrics are influenced by system determinant parameters.

The rest of the paper is organized as follows. Section II presents the relevant literature review. Section III describes the problem. Section IV focuses on the proposed ACDP. Section V formulates the performance model. Section VI presents simulation results. Section VII discusses aspects of future research. Section VIII concludes the paper.

2 Literature Review

The discussion in this section has three aspects. The first aspect focuses on discussing background work focusing on existing approaches and the computing need in astronomy. The second aspect describes the related work with focus on the realization future computing systems via the use of large aquaria systems. The third aspect reviews and summarizes the findings from the literature review with a view to establishing the basis for the challenge being addressed.

  1. A.

    Computing networks - existing approaches and the need in astronomy.

Developing countries have a significant amount of unutilized fixed-line telephony infrastructure. Fixed–line telephony uses the synchronous digital hierarchy (SDH) technology. The investment in SDH technology was significant in fixed-line telephony before the emergence of mobile wireless networks in developing countries. This has led to the availability of a significant number of SDH-related networking equipment in developing countries [11, 19–20]. There is also a global consensus on the need to modernize telecommunication networks using SDH technology [12–13]. Perrin in [13] recognises that SDH technology is being used by network operators.

The use of SDH technology poses problems for service providers who wants to retain their clients while reducing the management challenges. The use of internet protocol (IP) technology is recognised to be suitable. This is because the use of IP enables networks to benefit from the advantages of deploying packet switching. Packet switching is more advantageous than the circuit switching technology being used in SDH technology. The use of technologies that support packet switching instead of those incorporating circuit switching is recognized to be a suitable measure for implementing network transformation [12, 14].

The infrastructure developed and devoted to fixed-line telephony in developing nations has significant coverage and networking equipment. The equipment devoted to fixed-line telephony has been left significantly un–utilized due to the emergence of mobile wireless networks. In addition, fixed-line telephony infrastructure includes a significant amount of real estate. The concerned real estate are buildings capable of hosting computing platforms and systems suitable for processing astronomy data. The transition to the use of mobile wireless networks results in a case where these facilities are left un–used. However, these un–used facilities are suitable for hosting computing infrastructure suitable for astronomy related data processing. The use of real estate previously devoted to telephony as computing facilities for astronomy is motivated by [15]. The discussion in [15] describes how Google has utilized the facilities of a un–used paper mill to develop the Google Hamina data centre. The use of telephony infrastructure is only suitable where un–used exchanges exist. Therefore, a low-cost strategy is required to complement the computing platform hosted in a telephony exchange facility.

Amolo in [21] establishes the increasing need for high performance computing facilities in Africa. The discussion identifies that initiatives focused on increasing computing facilities in Africa are on the increase. Some of these initiatives are aided by donors. The discussion in [21] also notes that high-performance computing facilities (HPC) set up using local facilities have a small scale. The capabilities of the local and donor aided HPC facilities to process astronomy data due to the use of converted telescopes is not examined.

Backes et al. in [22] examine the use of HPC for astronomy in Namibia. It is observed that the acquisition of HPC infrastructure is challenging due to prohibitive costs. The Namibian astronomy community addresses this challenge by forming collaborations with other organizations. An example of such an organization is the centre for high-performance computing in Cape Town. It also aims to re–use part of the compute cluster sponsored by the Texas Advanced Computing Centre. The discussion in [23] shows that Namibia aims to participate in the square kilometre array project with focus on conducting multi–wavelength astronomy observation. The processing of the emerging data when Namibia joins the square kilometre array requires access to additional HPC facilities. The challenge arises when Namibia uses more telescopes due to the conversion of un–used satellite earth stations.

Povic [24] and examine the development of astronomy in Africa. The discussion in [24] considers the influence of technological advances on telescope design. However, the role of computing i.e., data processing requires further consideration. This is because the discussion in [24] does not examine the role of the computing entities in astronomy data processing. Therefore, it is important to consider novel approaches for obtaining low-cost HPC entities that are linked to telescopes in a cost–effective manner.

The deployment of a high number of telescopes as seen in [23–24] results in an increase amount of data requiring processing. The realization of the processing can be done via the use computing platforms and benefits from cloud computing. Therefore, the astronomy organization has significant concern as regards ensuring that cloud computing is utilized at low operational cost.

Cloud computing has been observed to have a high operational cost due to the necessity of cooling. The energy spent cooling has been observed to degrade data centre power usage effectiveness (PUE). The ocean has been considered as a suitable location for future data centres [25,26,27,28]. The use of the ocean or maritime resources provides a natural coolant for data centre cooling and enhances the PUE. The siting of data centres in the ocean reduces cooling costs and enables low-latency access for subscribers living close to the ocean. These benefits have motivated the current use of the ocean for hosting future data centres [28]. However, the consideration of the ocean as the platform for next-generation data centres and cloud platforms is not feasible.

This is because of the sustainability challenges arising when a considerable number of data centres are deployed in the ocean. It is expected that several emerging players in the cloud computing industry will also leverage this opportunity. This makes it important to determine the number of cloud platforms that the ocean can accommodate without posing risks to oceanic bio–diversity. It is also important to determine the effect of deploying a large number of cloud platforms in the ocean on the oceanic temperature. The answers to these questions are important for the research community and the safe deployment of ocean-based data centres and next-generation cloud computing platforms.

An alternative approach that enables the use of maritime resources is required. Such an approach should avoid the difficulties that emerge because the aforementioned questions remain unanswered. The approach employed by Microsoft uses an artificial reef equipped with computing payload [25]. The siting of artificial reefs in the ocean on a large-scale makes it important to consider the sustainability challenges identified above.

However, the use of the ocean in the manner proposed in [25,26,27,28] requires having access to capabilities to deploy data centers in the ocean. The execution of deployment in this manner requires having access to facilities enabling the deployment of computing facilities in the underwater environment. The realization of this objective is challenging for a capital constrained organization, especially in a developing context. Nevertheless, it is important that capital constrained organizations benefit from the cooling capacity of water. In addressing the challenge of ensuring that capital constrained organization benefits from the cooling capacity of water, this paper considers the siting of computing systems in large–sized aquaria. The use of large–sized aquaria presents a low-cost alternative to accessing the ocean resources. Therefore, it is more suitable for capital constrained organizations than accessing the ocean. The environment of a large-sized aquarium is considered because it shares similarities with the sub–ocean environment. This perspective is considered feasible due to the increasing use of advanced technology in aquaria as seen in [16,17,18].

The focus of the discussion in [25,26,27,28] has not examined the server payload design. In this case, it is important that the payload being used as a low cost. An example of a low cost payload is the disaggregated server [29,30,31]. The disaggregated server can be used as the computing entity in computing systems designed to have a low cost. Furthermore, the donation of un-utilized infrastructures for use in astronomy in a manner similar to the conversion of un – utilized earth stations to telescopes as seen in [5,6,7] though beneficial has not been identified. In this regard, it is important that a transition from telephony technology such as synchronous digital hierarchy (SDH) to internet protocol (IP) makes telephony network infrastructure suitable. This is because of the availability of un-utilized telephony infrastructure that previously used SDH [11,12,13, 32,33,34,35].

B. Suitability of large aquaria and future computing systems.

The siting of data centres in existing aquaria extends the usefulness of water in cooling data centres. In the case where there is no existing large aquarium, a large aquarium can be established for the purposes of providing support for data centres. This is feasible considering advances in aquaria systems [36,37,38,39,40].

Ma et al. [36] identify that aquaria can be used in home and commercial applications. It is recognized that the incorporation of industrial structure can enable aquaria scaling for commercial purposes. In this case, the scaling is intended to ensure that the industrial scale aquarium has increasing practical usage. It is recognized that the aquarium can be designed for use in a large breeding sink for increased system application.

Patin et al. in [37] in a contextual study set within the United States recognize the importance of public aquaria and experimental aquaria systems. The experimental aquaria systems are designed to emulate the ocean environment. The discussion in [37] identifies the ocean voyager as the largest indoor aquatic habitat in the United States with the capacity to hosting different marine mammals in an environment of artificial seawater. The study in [38] describes a 10-litre aquarium also being used for experimental purposes. In this case, the aquarium is small in comparison to that used in [37].

Celik et al. [39] recognize the importance of the role of the large aquaria systems in Turkey. In addition, the discussion recognizes the presence of large public aquaria systems in Europe with locations in France and Germany. The total water capacity of the aquarium is recognized to be 5000m3 and it is realized as a composite system comprising 45 tanks with large and small sizes. The discussion in [39] presents a list of large public aquaria systems with water volume capacity in the range (300–7500) m3 and comprising 17 to more than 70 tanks. The discussion recognizes that the large aquaria system can be realized as a multi–tank system. In this multi–tank system, the tanks in the aquaria can host different ocean mammals and have different applications.

Hasim et al. [40; 38] focus on describing how to ensure that the Jakarta public aquarium meets the interactive preferences of various categories of visitors to the public aquarium facility. It describes how to enhance the interface design to meet the viewing and entertainment preferences of categories of users that visit the public aquarium facility. This is being done with the aim of enhancing aquarium tourism by the use of enhanced interfaces via interior and exterior design.

In addition, the discussion in [41] recognizes the Two Oceans aquarium as a public aquarium system. The Two Oceans Aquarium provides entertainment through education. However, the discussion in [38] is focused on reviewing, examining, and executing a critical analysis of aquatic culture.

The discussion in [36,37,38,39,40,41] recognizes that large aquaria systems have applications as public entertainment (alongside education) facilities and use in scientific systems. In addition, it is recognized that technological advances can enable the scaling of small aquaria systems to large aquaria systems as seen in [36]. This scaling also implies that pseudo-marine systems designed for other applications such as that in [39]. In addition, pseudo-marine systems can be scaled to be useful as large aquaria systems. The application in [42] targets the design of a pseudo marine system for use in future computing applications. The environment in [40] has the potential to be capable of hosting marine life though this aspect has not been explored. The consideration of [36,37,38,39,40] and [41] enables a commercial case for public aquaria. In this case, the aquaria host services with revenue-earning potential for public aquarium systems. However, this is yet to receive research consideration.

  1. C.

    Findings from the literature review and background work.

The findings in the conducted literature review show that there is a recognized need for the design, development and use of computing systems in astronomy as seen in [22,23,24]. The review also shows that existing research has identified the need to utilize high performance computing facilities for scientific investigations in Africa [21]. Therefore, it can be seen that there is a need to deploy computing facilities for data processing in astronomy as seen in [22–23]. The case of Namibia identified in [22] by Backes et al. describes the case of capital constrained context being focused on a developing nation. In [22], the importance of having access to high performance computing facilities is recognized. The discussion by Amolo et al. [21] recognizes that donor participation enables the realization of high performance computing in capital constrained scenarios. However, the case where there are no donors has not been considered. It is also important to consider the case where donors are able to contribute other facilities besides computing entities. Therefore, it is important to address the case where astronomy organizations require access to computing facilities. In the concerned case, the available donors are not able to directly contribute high performance computing systems but other suitable facilities.

In addition, the reviewed research recognizes advances enabling the realization of underwater data centres as seen in [25,26,27,28]. The core benefit of underwater data centre is leveraging on water for low cost cooling. However, the use of underwater data centres is cost prohibitive for capital constrained astronomy organizations (CCAOs). Nevertheless, the design of systems that benefit from water’s high capacity without incurring the high costs associated with underwater data centres development and deployment beneficial. This is yet to receive research attention and is considered in the proposed mechanism being presented.

3 Problem Description

This section considers the problem of a CCAO conducting astronomy observations and processing the resulting data. The CCAO’s telescopes have been realized from uses un-utilized earth stations. Each telescope returns data requiring processing. Let \( \alpha \) and \( \beta \) denote the set of telescopes and available computing entities, respectively. In the consideration, the total number of telescopes and available computing entities are A and B, respectively.

$$ \alpha =\left\{{\alpha }_{1}, {\alpha }_{2},\dots,{\alpha }_{i},\dots, {\alpha }_{A}\right\} $$
(1)
$$ \beta =\left\{{\beta }_{1},{\beta }_{2},\dots,{\beta }_{j}\dots, {\beta }_{B}\right\} $$
(2)

The relations in (1) and (2) describe the telescopes and associated computing entities. The CCAO does not require the construction of extensive telescope data transport networks. Instead, the CCAO relies on existing networks or ensures close proximity between the computing entities and the telescopes. The computational capacity of \( {\beta _{j\,}}\,;\,\,{\beta _{j\,}}\, \in \,\,\beta \) is described by the parameter \( {C}_{p}\left({\beta }_{j}\right)\). The data requiring processing and arising from \( {\alpha }_{i}; {\alpha }_{i} \in \alpha \) is denoted by the parameter \( {C}_{p}\left({\alpha }_{i}\right)\). In addition, let \( {C}_{o} \left({\beta }_{j},{t}_{m}\right); {t}_{m} \in t;t=\{{t}_{1},{t}_{2},\dots,{t}_{m},\dots, {t}_{x}\} \) denote the operational cost of \( {\beta }_{j}\) at epoch \( {t}_{m}\). The CCAO requires additional computing resources if:

$$ \sum _{i=1}^{A}{C}_{p}\left({\alpha }_{i}\right) \ge \sum _{j=1}^{B}{C}_{p}\left({\beta }_{j}\right) $$
(3)

The relations in (3) shows the total computational capacity for all available computing entities (left hand side) and total size of data from all deployed and observing telescopes (right hand side). The context for which (3) is valid is one where the data requiring processing requires more computing resources than available on the computing entities. Given the threshold operating cost, \( {C}_{ope}^{th}\), the use of computing platforms is challenging if:

$$ \sum _{j=1}^{B}\sum _{m=1}^{x}{C}_{o} \left({\beta }_{j},{t}_{m}\right) \ge {C}_{ope}^{th} $$
(4)

\( x\) is the maximum number of epochs.

The relations in (4) consider the case where the computing facility used for astronomy data processing has a total operational cost exceeds the CCAO’s threshold operating cost. In addition, the case where the threshold acquisition cost is unable to support computing platform acquisition is considered. The use of the conventional cloud platforms is challenging for the CCAO if:

$$ \sum _{j=1}^{B}\sum _{m=1}^{x}{C}_{a} \left({\beta }_{j},{t}_{m}\right) \ge {C}_{acq}^{th} $$
(5)

Where \( {C}_{a} \left({\beta }_{j},{t}_{m}\right)\)the acquisition is cost of \( {\beta }_{j}\) at epoch \( {t}_{m}\) and \( {C}_{acq}^{th}\) is the threshold acquisition cost.

The CCAO requires mechanisms which ensure that the conditions in (3)–(5) do not hold. The realization of the non–validity of (3)–(5) requires that the CCAO uses computing entities that have low acquisition and operational costs.

4 Proposed Mechanism and Solution

This section discusses the proposed computing solutions. The computing entity that utilizes un–used telephony infrastructure is realized via a combination of disaggregated servers. The proposed combination enables the realization of the proposed CACT and CBCT. The proposed CACT, and CBCT are realized using disaggregated servers. Disaggregated servers are used as the core of the CACT, and CBCT because of their low acquisition and upgrading costs [29,30,31]. Disaggregated servers have low operational costs and are suited for the CCAO. The discussion here has two aspects. The first and second aspect focus on the CACT, and CBCT, respectively.

A. Class A Data Center (CACT).

The CACT is realized via the use of un-utilized telephony infrastructure in internet protocol based networks. This is feasible due to the transition to internet protocol (IP) technology [32,33,34,35]. The un-utilized telephony infrastructure includes fibre optic cables, multiplexers, demultiplexers and network switches. It also utilizes synchronous digital hierarchy (SDH). The use of SDH is beneficial due to the ease of executing multiplexing, and demultiplexing for accessing data streams. The unutilized telephony infrastructure has networking and associated power facilities. The power facilities has sections being used to operate the networking and cooling systems separately. The relation between the entities involved in a use of the CACT by the telescope for data processing is in Fig. 1. In Fig. 1, the computing entity that executes data storage and algorithm execution is realized using disaggregated server components. In Fig. 1, telescope data is transported to the computing infrastructure via the un-utilized telephony infrastructure.

The scenario in Fig. 1 shows how telescopes communicate with the CACT. The signals from all telescopes are combined to generate a high data rate signal stream by the multiplexer. The high data rate signal stream is transmitted via optical fibre cable. The multiplexed signal is separated by the demultiplexer. The separated signals are processed and stored on disaggregated servers from where the results of processing are accessed by users. Fig. 1 presents a network enabling data transfer from telescopes to the computing infrastructure. The data transfer is executed via the un–utilized telephone network infrastructure.

Fig. 1
figure 1

Relations between entities using un–utilized telephony infrastructure for astronomy data processing

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B. Class B Data Center (CBCT).

The proposed CBCT also uses disaggregated servers as the core computing system. However, the disaggregated servers are sited in an array of aquaria with varying sizes and dimensions to realize low cooling (operational) costs. The use of large-sized aquaria is cheaper than the current approach of utilizing the ocean’s resources for realizing low cost cooling. The use of the ocean in a sustainable manner requires the elaborate ocean bathymetry surveys on a large scale to limit the damage on aquatic bio–diversity. In addition, the use of ocean-based data centres require expensive networking systems to execute data upload. It is also costly to conduct maintenance procedures on ocean-based data centre in comparison to aquaria based data centres.

The siting of data centres in existing aquaria extends the usefulness of water in cooling data centres. In the case where there is no existing large aquarium, a large aquarium can be established for the purposes of providing support for data centres. In the presented research, the use of the aquarium system to provide cooling for aspects of computing and communication systems is considered. This is feasible since the temperature tolerance of ocean mammals are known in [43] and should be done in a manner that does not cause thermal stress on the marine mammals within a scientific aquarium facility. The avoidance of thermal stress is ensured by using fractionated server systems. The fractionated servers comprise inter–connected modules that are located in different aquarium environments. The proposed aquarium system has multiple chambers that host marine life and computing payload. The flow of water between these chambers is executed in a manner that temperature increase due to the hosted computing servers does not cause thermal stress.

The disaggregated server comprises several different subsystems with distinct functions. Given that \( {\beta }_{i}; {\beta }_{i}? \beta \) refers to a disaggregated server with multiple subsystems, \( {\beta }_{i}\) can be re–written as:

$$ { \beta }_{i}=\left\{{\beta }_{i}^{1},{\beta }_{i}^{2},\dots {,{\beta }_{i}^{f}\dots, \beta }_{i}^{g}\right\} $$
(6)

\( g\) is the maximum number of sub – systems.

The use of a disaggregated server as presented in (6) is considered by the CCAO due to the associated low costs.

Each subsystem \( {\beta }_{i}^{f}; {\beta }_{i}^{f} \in { \beta }_{i}\) is hosted in a different aquarium as shown in Fig. 2. In Fig. 2, the aquaria are realized via the combination of multiple sub-systems that jointly comprise the disaggregated data center. In this case, the cloud computing system is realized via disaggregated server components. The disaggregated servers constitute the cloud computing system. In Fig. 2, the sub–systems of the disaggregated servers are placed in water-resistant enclosures such as those in [34]. This ensures that the lifetime of the computing components in the disaggregated servers is not impaired due to being located in an aquatic environment.

The intra–CBCT communications switch enables communications between components in each aquarium to communicate with each other as shown in Fig. 2. A network switch enables communications between intra–CBCT communication switches. The aquarium is not linked to any external to avoid the additional cost that arises due to networking. Instead, astronomy data is obtained by the CCAO via the Internet and uploaded to the CBCT for processing and accessing results. In Fig. 2, the components \( {\beta }_{i}^{1}\) and \( {\beta }_{i}^{2}\) execute data storage. The components \( {\beta }_{i}^{3}\) and \( {\beta }_{i}^{4}\) are the micro–processor while the components \( {\beta }_{i}^{6}\) and \( {\beta }_{i}^{8} \)signify the computing memory modules and execute the functionality of the random-access memory (RAM).

The relation in Fig. 2 shows each aquarium hosting a CBCT. Fig. 2 present relations between each communication switch, and components of disaggregated servers. Furthermore, each aquarium is in a tank. The temperature of the outgoing water (after heat transfer) is such that it does not induce thermal stress in the marine life being hosted in each adjacent tank. The water is released for cooling and re-circulation after a temperature threshold which exceeds the thermal limits of marine mammals in the public aquarium is reached. The support of the infrastructure requires the execution of temperature detection, monitoring, water circulation, removal and re–introduction of cooling water.

The discussion in Table 1 presents the differences between the proposed ACDP and the existing computing platforms. In the comparison, the considered application requiring data processing is that of astronomy. The reference case being considered is that of the square kilometre array (SKA). The SKA has been considered because of its significance to astronomy and space science organizations in developing countries. Such organizations significantly fit in with the context of the CCAO.

Fig. 2
figure 2

Relations between entities enabling data processing using disaggregated servers in the CBCT

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Table 1 Comparison between the existing case [44] and proposed case
Full size table

An equally important concern that should be addressed for the proposed CACT, and CBCT is that of secured access i.e., security in accessing the computing system. The provisioning of a robust and resilient security mechanism and system is required to prevent unauthorized use of computing resources in the CACT, and CBCT. The challenge of ensuring high level of security should be addressed because of the prevalence of cybercrimes. The need to mitigate cyber-crime has motivated the training of professionals in developing and using robust post–quantum cryptographic approaches at the device level as seen in [45,46,47]. Research has also led to the development of novel robust security measures that utilize post–quantum cryptographic approaches for: (i) improving resilience against channel targeting attacks [48], (ii) protecting embedded systems from cyber-attacks [49], (iii) in the context of network of multiple sensors in future internet of things applications [50], and (iv) realizing robust public key crypts secured systems as seen in [51].

5 Performance Formulation

The performance of the proposed mechanism is evaluated using three metrics. These are the computing costs, power usage effectiveness (PUE) and angular resolution. The operational cost \( {C}_{o}\left({\beta }_{j},{t}_{m}\right)\) of the disaggregated server \( {\beta }_{j}\) at the epoch \( {t}_{m}\) is a function of the powering cost of sub–component \( {\beta }_{j}^{f}\) at epoch \( {t}_{m}\) denoted as \( {C}_{o,p}\left({\beta }_{j}^{f},{t}_{m}\right)\) and the cooling cost \( {C}_{o,cl}\left({\beta }_{j}^{f},{t}_{m}\right)\). The operational cost \( {C}_{o}\) can be evaluated as:

$$ {C}_{o}= \sum _{j=1}^{B}\sum _{f=1}^{g}\sum _{m=1}^{l}\left({C}_{o,p}\left({\beta }_{j}^{f},{t}_{m}\right)+{C}_{o,cl}\left({\beta }_{j}^{f},{t}_{m}\right)\right) $$
(7)

\( g\), and \( l \)are the maximum number of sub-components in the disaggregated server, and epochs, respectively.

In (7) the total operational cost is obtained as a sum of the dynamic powering cost and cooling cost described by the parameter \( {C}_{o,p}\left({\beta }_{j}^{f},{t}_{m}\right)\) and \( {C}_{o,cl}\left({\beta }_{j}^{f},{t}_{m}\right)\), respectively.

The relation in (7) focuses on how the use of disaggregated servers influences the operational cost of data centres and cloud computing platforms. This does not consider how the use of an aquarium reduces the cooling cost. The cooling effect in this case is modelled by the cooling factor. The cooling effect of the natural coolant in the aquarium is not derived from the electricity provided to operate the data centre comprising multiple disaggregated servers in the aquarium. Hence, the operational costs should be removed from the electricity consumed in cooling the existing servers that utilize cooling systems driven by electricity. Let \( \theta \left({\beta }_{j}^{f},{t}_{m}\right)\) denote the cooling factor of the natural coolant on the subsystem \( {\beta }_{j}^{f}\) at epoch \( {t}_{m}\). The cooling effect is modelled as an instantaneous variable considering the varying chemical composition of water within the aquarium. The specific heat capacity of water is denoted as \( {C}_{w}\). The specific heat capacity of the natural coolant in the aquarium at epoch \( {t}_{m}\) is denoted \( {C}_{aq}\left({t}_{m}\right)\). The cooling factor for the aquarium, \( \theta \left({\beta }_{j}^{f},{t}_{m}\right)\) is:

$$ \theta \left({\beta }_{j}^{f},{t}_{m}\right)= \frac{{C}_{aq}\left({t}_{m}\right)}{{C}_{w}} $$
(8)

In (8), the cooling factor has been derived as a ratio of the specific heat capacity of the aquarium at the time epoch \( {t}_{m}\) to the specific heat capacity of water. Furthermore, the relations in (8) show that a lower cooling factor is obtained for liquids having a specific heat capacity lower than water. Such liquids are better coolants than water. In this case the specific heat capacity of water is considered to be ideal. Water is taken as a reference because of its high specific heat capacity.

The determination of \( \theta \left({\beta }_{j}^{f},{t}_{m}\right)\) is challenging where the use of the ocean is intended to obtain the best cooling for future data centres and cloud computing platforms. This arises due to the challenges of determining the specific heat capacity of water at various locations in the ocean across multiple epochs. However, the determination of \( \theta \left({\beta }_{j}^{f},{t}_{m}\right)\) is less challenging for an aquarium environment. The operational costs after incorporating the cooling effect is denoted \( {C}_{o}^{{\prime }}\) and given as:

$$ {C}_{o}^{{\prime }} =\sum _{j=1}^{B}\sum _{f=1}^{g}\sum _{m=1}^{l}\left({C}_{o,p}\left({\beta }_{j}^{f},{t}_{m}\right)+{C}_{o,cl}\left({\beta }_{j}^{f},{t}_{m}\right) \left(1- \theta \left({\beta }_{j}^{f},{t}_{m}\right)\right)\right) $$
(9)

The operational cost formulated in (9) is realized as a sum of the powering cost (first term on the right-hand side) and the cooling cost considering the effect of the cooling factor (second term on the right-hand side). The effect of the cooling factor has not been considered in the second term on the right-hand side of the cost presented in (7).

The PUE is another important metric that is formulated in this section. The power consumed in operating and cooling the disaggregated server component \( {\beta }_{j}^{f}\) at epoch \( {t}_{m}\) is denoted \( {P}_{op}\left({\beta }_{j}^{f},{t}_{m}\right)\) and \( {P}_{cl}\left({\beta }_{j}^{f},{t}_{m}\right)\) respectively. The PUE for the CACT and CBCT is denoted \( {\vartheta }_{CACT}\) and \( {\vartheta }_{CBCT}\) respectively and given as:

$$ {\vartheta }_{CACT}= \sum _{j=1}^{B}\sum _{f=1}^{g}\sum _{m=1}^{l}\left(\frac{{P}_{op}\left({\beta }_{j}^{f},{t}_{m}\right)}{{P}_{op}\left({\beta }_{j}^{f},{t}_{m}\right)+{P}_{cl}\left({\beta }_{j}^{f},{t}_{m}\right) }\right) $$
(10)
$$ \begin{array}{l}{\vartheta _{CBCT}}\, = \\\sum\limits_{j = 1}^B {\sum\limits_{f = 1}^g {\sum\limits_{m = 1}^l {} \left( {\frac{{{P_{op}}\left( {\beta _j^f,\,{t_m}} \right)}}{{{P_{op}}\left( {\beta _j^f,\,{t_m}} \right)\, + \,\left( {{P_{cl}}\left( {\beta _j^f,\,{t_m}} \right)\,\left( {1 - \theta \left( {\beta _j^f,\,{t_m}} \right)} \right)} \right)}}} \right)} } \end{array} $$
(11)

The relations in (10), and (11) describe the PUE for the CACT, and CBCT, respectively. The PUE is obtained as a ratio of the power used to operate the computing aspect (server component) to the total power supplied. In the relations in (10), and (11), the numerator describes the power used to operate the computing aspect (server component). The total power supplied is the sum of the operational power and cooling power (as presented in the denominator for (10), and (11)).

We also investigate how ACDP influences the angular resolution. ACDP enables CCAOs that were previously unable to conduct radio astronomy observations to engage in astronomy observations. The availability of converted telescopes and associated computing infrastructure makes it possible for more CCAOs to conduct astronomy observations. This increases the baseline of deployed telescopes. Let \( {\alpha }_{M} \) and \( {\alpha }_{N}\)denote the set of telescopes deployed by non–CCAOs and CCAOs, respectively.

$$ { \alpha }_{M}=\left\{{\alpha }_{M}^{1},{\alpha }_{M}^{2},\dots, {\alpha }_{M}^{Q}\right\} $$
(12)
$$ { \alpha }_{N}=\left\{{\alpha }_{N}^{1},{\alpha }_{N}^{2},\dots, {\alpha }_{N}^{Q}\right\} $$
(13)

In (12), and (13), the non–CCAOs and CCAO have \( Q\) telescopes as the overall total. Furthermore, the non – CCAOs and CCAOs have been considered to utilize a similar number of telescopes.

The baseline for telescopes in \( {\alpha }_{M} \) and \( {\alpha }_{N}\)are denoted \( \varsigma\left(\left|{\alpha }_{M}\right|\right)\) and \( \varsigma\left(\left|{\alpha }_{N}\right|\right)\) respectively. Given a wavelength \( {\lambda }_{obs}\), the angular resolution before and after incorporating ACDP is denoted as \( {p}_{1}\) and \( {p}_{2}\) respectively.

$$ {p}_{1}= {\lambda }_{obs} {\left(\varsigma \right(\left|{\alpha }_{M}\right|\left)\right)}^{-1} $$
(14)
$$ { p}_{2}= {\lambda }_{obs} {(\varsigma \left(\left|{\alpha }_{M}\right|\right) + \varsigma (\left|{\alpha }_{N}\right|\left) \right)}^{-1} $$
(15)

6 Discussion of Simulation Results

The discussion in this section presents the results of performance evaluation. The simulation scenario being considered is one in which a capital constrained astronomy organization (CCAO) is executing the processing of astronomy data. The CCAO computing infrastructure comprises the proposed CACT, and the CBCT. Both the CACT, and the CBCT comprise disaggregated servers. In the case of the CACT, the cooling is realized from energy sources that are independent of the server operational power. This is because of the existing infrastructure base associated with telephony network centres. Therefore, the powering of the cooling system for the CACT does not use energy from the same source as the disaggregated servers.

The value used for the average operational cost per server and the average server operational power in the simulation are obtained from [45], and [45–46], respectively. In addition, the scenario considers that the telescopes obtained from the converted unutilized earth stations present a high volume of data requiring processing per second. The telescopes have an observational frequency of 100 MHz. The servers being used operate for variable duration in the on – peak, and off – peak states. The proportion of time spent in off–peak and on–peak periods are: (i) 50% off–peak and 50% on–peak, (ii) 25% off–peak and 75% on–peak, and (iii) 75% off–peak and 25% on–peak. The simulation is done using the parameters in Table 2.

Table 2 Simulation parameters
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The rest of the discussion in this section i.e., performance evaluation is divided into three aspects. The first aspect presents the results of performance evaluation with regards to the operational cost. The second aspect focus on the performance evaluation results for the power usage effectiveness (PUE). The third aspect discuss the evaluation results obtained via simulation for the angular resolution.

  1. A.

    Performance evaluation results – operational costs.

The use of disaggregated servers enables both CACT and CBCT to have a reduced operational cost than existing cases in developing nations where disaggregated servers are not used. The operational costs obtained via simulation for the CACT and CBCT are shown in Fig. 3a and b, respectively.

From the results in Fig. 3a and b, it can be seen that the use of the aquarium is beneficial as its application reduces operational costs. The use of the CACT and CBCT reduces the operational costs for CCAOs in developing nations. The use of the aquarium cooling reduces operational costs by an average of 78.6%, 79.9% and 78.4% for case 1, case 2 and case 3, respectively.

Therefore, the results show that a CCAO utilizing telescopes realized from earth station conversion and with increased astronomy data can realize data processing at low costs. The low-cost benefit in this case arises from the use of the proposed ACDP. ACDP supports the incorporation of the CACT and CBCT with reduced operational costs as seen in the results presented in Fig. 3a, and Fig. 3b, respectively.

Fig. 3
figure 3

a Operational costs of CACT b Operational costs of CBCT

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It can also be seen that the use of the data centre during off–peak duration does not necessarily result in reduced operating costs. This is due to the ratio of the off–peak charge to the on–peak charge. The ratio of the off–peak charge to the on–peak charge involved in the simulation is 0.3542.

  1. B.

    Operational costs – performance usage effectiveness (PUE).

The simulation procedure and performance evaluation also investigates the PUE of the CACT (no aquarium) and CBCT (with aquarium having varying cooling factors). The result of the PUE is shown in Fig. 4. From the results in Fig. 4, it can be seen that the use of the aquarium (CBCT) with a cooling factor of 0.36 and 0.45 enhances the PUE. In this case, the PUE is enhanced compared to the case where there is no aquarium (corresponding to the CACT). The two cases where there is an aquarium correspond to the CBCT. The obtained PUE is compared to the ideal PUE value of 1.0.

In the case of the CACT (‘without aquarium’), the obtained PUE falls short of the ideal by 30.9% on average. The PUE is observed to fall short of the ideal value of unity by 18.4% on average when the cooling factor has a value of 0.45. In the case where the cooling factor is 0.36, the PUE is observed to fall short of the ideal by 22.3% on average. It can be seen that the use of the aquarium and leveraging on the cooling factor enables the realization of a PUE that is closer to the ideal value of unity. The PUE is enhanced by 8.6% and 12.5% when the cooling factor is 0.36 and 0.45, respectively.

Fig. 4
figure 4

Results of PUE obtained by simulation

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Fig. 5
figure 5

Results of PUE for different cooling factors

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From the results of performance evaluation that has been discussed, it can be seen that the use of the proposed approach with aquarium-based computing system improves the PUE. For computing systems, a lower PUE is more beneficial than a higher PUE figure. An improvement of the PUE for the concerned CCAO signifies that a larger proportion of the input power is used to execute algorithm processing. A consideration of different cooling factors in this case enables the effect of varying water composition on the PUE to be evaluated. Hence, an improvement in the PUE is beneficial for operating computing platforms in astronomy.

  1. C.

    Performance evaluation – angular resolution.

The use of the proposed ACDP enables CCAOs to deploy more telescopes. These telescopes can form arrays with existing telescopes to improve the angular resolution associated with astronomy observations. The deployment of additional telescopes is feasible because of the increased computing facilities that are now accessible to the CCAO. The angular resolution is examined for cases where arrays of telescopes are not used and when arrays of telescopes are used. The angular resolution that is obtainable when additional telescopes are not deployed to form a larger array with the existing array of telescopes is shown in Fig. 6. The angular resolution that is obtained via simulation when additional telescopes are deployed to form a larger array with the array of telescopes is shown in Fig. 7.

Fig. 6
figure 6

Angular resolution before combining CCAO telescopes with existing deployed telescopes

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The results presented in Figs. 6 and 7 indicate that the use of additional telescopes (when ACDP is incorporated) improves the angular resolution. This is because of the increased baseline. In Fig. 6, the angular resolution is influenced by the non–uniform distance between telescopes in the existing array. This non – uniform distance between telescopes implies that the baseline is varying leading to the angular resolution significantly increasing in some epochs. In other epochs, a marginal improvement in the angular resolution is observed in the simulation.

The addition of varying numbers of telescopes from the CCAO improves the angular resolution as seen in the results presented in Fig. 7. The angular resolution is increased when the CCAO deploys 15 and 20 telescopes as depicted in Fig. 7. The angular resolution is observed to be fairly constant in Fig. 7 than that of Fig. 6. This is because of the significant increase in baseline when CCAO telescopes at distant locations are incorporated into the existing array. Investigation shows that the angular resolution is enhanced by 99% on average by deploying more telescopes when ACDP is incorporated. The use of angular resolution is improved by 40.4% on average when the CCAO deploys 20 telescopes. Therefore, the deployment of 20 telescopes results in an improved angular resolution than when 15 telescopes are deployed. Therefore, the use of the proposed ACDP also enhances the angular resolution.

Fig. 7
figure 7

Angular resolution obtained after combining CCAO telescopes with existing deployed telescopes

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7 Aspects for Future Work

The important aspects of the proposed solutions requiring future research is investigating the relations between the cooling factors for the CBCT, its coolants and operational duration. The development of a tier rating for different sizes of the proposed CACT, and CBCT also requires further investigation. In addition, further research is required to investigate adaptation of existing network protocols. The network protocols enable communications between the CACT, and CBCT and associated network entities. This is done for an end to end connectivity between the deployed telescopes and the CACT or CBCT.

In addition, the design of an environment friendly energy system for enabling the operation of the CACT, and the CBCT has not been considered. The non –consideration is because of the focus of the presented research on the design and presentation of the network architecture. In addition, an important aspect that needs to be considered in the future research is that of implementing secured access mechanisms. The secured access mechanisms prevent and limit unauthorised access to the computing systems described in the CACT, and CBCT. Furthermore, advances in the design of energy efficient post – quantum robust security algorithms designed for constrained operational scenarios such as those in [52,53,54,55] should also be considered with a view to achieve integration.

8 Conclusion

This paper addresses the challenges faced by capital-constrained astronomy organizations (CCAOs). The concerned CCAOs utilize telescopes realized from converted un-used earth stations. They also seek to access additional computing facilities to process their increasing data due to the use of converted telescopes. The CCAOs have weak internet infrastructure and unable to afford on–line access to cloud platforms. Therefore, the CCAOs are not able to upload substantial amounts of astronomy data to the cloud. Hence, the concerned organizations need their own computing facilities which must be low-cost and highly efficient. The research recognises the suitability of disaggregated servers in this regard. Disaggregated servers have been identified to have low-costs and better performance than the existing servers used in data centres. The paper proposes the astronomy computing diversity paradigm (ACDP). ACDP uses disaggregated servers which combine two types of computing entities. The computing entities are the Class A computing entity (CACT) and Class B computing entity (CBCT). The CACT re–uses the existing un–used infrastructure previously dedicated to fixed-line telephony networks in developing nations where most CCAOs are located. The CBCT leverages on advances in aquarium technology and focuses on the deployment of disaggregated servers in aquaria. The aquaria are considered suitable because of the abundance of water and the ability to site the components of disaggregated servers in separate locations. The use of disaggregated servers by CCAOs in developing nations enables the concerned countries to benefit from the low-cost and operational benefits of disaggregated servers. Therefore, the use of disaggregated servers with the combined benefits of CACT and CBCT enables ACDP to outperform the existing approach where non–disaggregated servers are used. Simulation has been conducted to investigate the performance of ACDP combining CACT and CBCT. Performance evaluation is done via numerical simulation. The evaluation is done to investigate the performance of the CACT and CBCT. Results show that the CBCT has a reduced operational cost and enhanced PUE in comparison to CACT. The operational cost is reduced by up to 79% on average. The PUE is enhanced by up to 12.5% on average. Therefore, it can be concluded that the use of CBCTs is advantageous for CCAOs in areas with aquaria. Therefore, the use of ACDP advocating for the adoption of the CACT and CBCT is beneficial to astronomy organizations. The research has focused on the CCAO case. Such astronomy organizations can be found in developing countries with interests in science advancements. The results shows that the use of ACDP enables the low–cost processing of astronomy data. Future research is required to address the case where CACT and CBCT are simultaneously available wherein a selection between the two is required. The selection in this case can be executed considering different objectives of the CCAO. In addition, a practical approach is required to determine the relations between telescope hardware, and computing platform data processing capability. Future work should also address how the disaggregated servers incorporates self-healing capability to ensure data processing while avoiding vendor lock in.