The maximum dimensions of the computer room for small corporate DC

. The maximum dimensional sizes of the computer room as a key architectural component of a data center have been justified, organized within various organizations of the construction industry. Mathematical models of the computer room have been introduced based on statistics of implemented projects, taking into account the presence of a central cross-connect and a ramp, as well as the routing of wired communication lines implemented within it. The criterion of the small size of the computer room as a structure allowing the organization of information exchange according to the spine-leaf scheme over twisted pair cables of the ISO/IEC 11801-1:2017 standard has been introduced. Assuming the use of a parallel transmission scheme involving Shannon's theorem and IEEE recommendations regarding operational margins, the maximum length of the line statistically associated with the dimensions of the computer room has been determined. An estimation of the maximum number of pizza-box type servers and standard 19-inch racks with heights of 42 units for their placement has been provided. The allocated power has been determined, taking into account the achieved level of technology, which is crucial from the perspective of designing the air conditioning and power supply systems.


Introduction
The activities of modern organizations in the construction industry are accompanied by the intensive use of information technologies, which are employed both for developing project solutions for specific projects and for managing the implementation process [1].Large volumes of information of various types, utilized in the course of production activities in today's reality, are stored and processed within a data center (DC), which assumes the role of a foundational element in the enterprise's information infrastructure.
Despite the rapid development of cloud computing and the consequent growth of publicly accessible data centers, the majority of industry organizations continue to utilize their own corporate data centers [2,3].This approach is linked to the greater efficiency of supporting current operations and commercial optimization through reduced costs associated with third-party resource engagement.The latter are concentrated in public facilities and are predominantly used for tasks demanding significant computational power, as well as a repository for completed projects.From the perspective of information security, the use of such public facilities as data exchange buffers with subcontracting organizations is not excluded.They can also function as hubs for facilitating collaborative work among remote collaborators and addressing other similar tasks.
A corporate data center, as a complex engineering structure, represents a costly facility that requires optimization from this perspective.One of the tasks addressed in the process of designing a corporate DC is determining its maximum dimensions.Knowledge of this parameter enables a rational allocation of computational resources between the corporate and publicly accessible facilities and greatly influences the organization's IT infrastructure development strategy.
Prominent scientific works dedicated to the issues of designing and constructing data centers predominantly focus on the implementation aspects of various engineering subsystems within them.In doing so, the area and dimensional specifications of the DC's equipment room, as a key architectural element, are often considered predetermined parameters.These parameters serve as a foundation when selecting specific design solutions.
Next, an approach to determining the dimensional specifications and area of the computer room for a small corporate data center is considered.Objects of the generalized small class, according to the well-known classification by Central Research Institute of Industrial Buildings and Structures, include facilities with a computer room area not exceeding 500 m 2 and a maximum of 200 server racks.By default, it is assumed that the computer room is fully equipped with engineering systems for guaranteed power supply, air conditioning, and management of the engineering infrastructure [4].
In this work, a small data center refers to a facility whose physical layer of the telecommunications infrastructure is implemented as a structured cabling system (SCS) [5,6].The SCS conforms to the requirements of standards ANSI/TIA-942B, ISO/IEC 11801-5:2017, and Russian national standard GOST R 59486-2021, and is exclusively based on twisted pair cables [7].The choice of this approach is motivated by the energy efficiency of this cable system variant, its ease of implementation, and subsequent operation.

2
The problem-solving approach and initial assumptions Compared to fiber-optic solutions, twisted pair cables provide slightly shorter communication distances.Considering this characteristic, the data center (CDC) that is defined as small within the scope of this work is categorized into a separate subclass.Consequently, the task at hand is addressed through the following scheme: 1.
The maximum communication distance between spine and leaf level switches is determined at a speed of 100 Gbps.

2.
The topological model of the data center's computer room is established.

3.
Using the data from implemented projects, the linear dimensions of the computer room are determined.

4.
Assuming the implementation of a cold and hot aisle containment system and utilizing data on typical dimensions of server racks and their heights, the arrangement of rows is established, and the maximum number of servers that determine the data center's computational capacity is calculated.It is assumed that the computer room has a simple rectangular shape, which corresponds to the majority of real-world facilities.The information infrastructure is implemented using a spine-leaf architecture, with leaf-level switches positioned at the top of server racks in a Top of Rack configuration.Servers in a 1U pizza-box form factor are utilized in this setup.
In the equipment room, a raised floor is incorporated, serving the purpose of housing the static air pressure chamber for the precision air conditioner within the cooling system.

3
The communication distance determination scheme The maximum communication range is determined with reference to the Shannon bandwidth W of the twisted pair cable channel.Taking into account the strong frequency dependence of the signal and noise components of the ACR(f) signal-to-noise ratio, we find the value of W as follows (1) where is f w -upper limit frequency of the cable channel.
The coefficients 4 and 0.6 before the integral take into account the adopted parallel transmission scheme over four twisted pairs of cable and the required operating reserves, respectively.
The value of f w is found as the solution of equation where is GNX(f,L) -the noise level at the input of the decision-making device of the network interface receiver; L -the so-called electrical length of the cable channel, taking into account the increased signal attenuation in flexible cord cables.;IL(f,L) -insertion loss of the cable channel including connectors.The established practice of implementing Structured Cabling Systems (SCS) in DC involves constructing the cable channel using a 2-connector scheme [8].The calculated model is presented in Figure 1.In determining the individual parameters included in equation ( 2) according to the models given in ISO/IEC 11801-1:2017, consider the following noise components listed in Table 1.
Table 1.Sources of interference at the input of the network interface decision-making device.

Source of interference
Self-transmitter Near-end cross talk transmitters Far-end cross talk transmitters

Numerical measure of interference intensity
Return Loss Near-end cross talk Far-end cross talk The signal level determining the value of the Attenuation-to-Crosstalk Ratio ACR(f,L) signal-to-noise ratio is calculated following the guidelines outlined in the ISO/IEC 11801-1:2017 standard.

4
Interference components and their summation At the input of the network interface decision-making device, three interference components listed in Table 1 are present.The sources creating them are independent, and the length of the cable channel up to the point of entry into the decision-making device is different.As a result, individual noise components are summed with arbitrary phase, as illustrated in Figure 2 using two of them as an example.
The average value of equation ( 3), assuming a uniform distribution of ξ, is found by taking the mathematical expectation of the corresponding function . (4) Therefore, the sought interference level will be (5)

SCS standards only standardize the value of PSACRF(f).
To transition to PSFEXT(f,L), used in equation ( 5), the following well-known relationship [9] will be used.

Characteristic of information transmission
In further analysis, we will consider the following two circumstances.Firstly, before being fed into the decision-making device of the network interface, the mixture of signal and noise undergoes complex processing, enhancing the transmission quality by suppressing specific interference components [10,11].We will represent this process by additional improvement of the parameters listed in Table 1.The achieved gain values are presented in Table 2.

ΔRL ΔPSNEXT ΔPSFEXT
The structural diagram of the input circuits of a network interface receiver performing "cleaning" of the input signal from noise is shown in Figure 3.The pre-processing of the input signal is accompanied by improving the parameters up to the level of RL + ΔRL, PSNEXT + ΔPSNEXT and PSFEXT + ΔPSFEXT, as well as leading to an increase in f w defined by (2).Violations of the model ( 4) do not occur up to frequencies of at least 4 GHz [12, 13] 3.This circumstance is taken into account in further calculations.

Maximum communication distance
The results of calculations for the frequency dependence of individual interference components and the attenuation introduced by the 2-connector cable channel with the structure shown in Figure 1, conducted in the MathCad environment, are presented in Figure 4.In this case, the electrical length of the cable channel is considered as a parameter.

Figure. 4. Frequency dependencies of individual interference components and insertion loss
The obtained dependencies, using equations ( 1) and ( 5), allow determining the Shannon capacity of the cable channel shown in Figure 1.The calculation results are presented in Table 3.Using linear interpolation, it is determined that a speed of 100 Gbps is achieved with a maximum electrical length of the cable channel L = 38 m.

Dimensions of the equipment room
The dimensions of the computer room will be determined through the maximum permissible length of a permanent link.To establish a connection between the cable channel lengths and permanent link, let's harmonize with lines operating at a speed of 40 Gbps, where the maximum length of a permanent link cannot exceed 32 meters [15].With a typical patch cord extension factor of 1.5, this results in a maximum length of one patch cord: (38 -32) / (1.5 x 2) = 2 meters, which is sufficient for the normal operation of the cable system.
In the vast majority of cases, the computer room in a data center has a rectangular shape with dimensions g and h.Let's introduce the concept of the shape coefficient k = h/g.The statistics of this coefficient are presented in Figure 5.As a reasonably accurate estimate of the maximum length of a permanent link, the semi-perimeter of the computer room can be used.From this, we obtain the following simple equation: The cabling system in the DC computer room is built exclusively with factory-made pre-terminated cables, produced by the manufacturing company with a specific interval.For the range of 30 -40 meters, this interval is 5 meters.Taking this characteristic into account, we will modify equation ( 7) by introducing a corresponding margin tied to the allowable cable length.As a result, we arrive at the following relationship:

Layout of equipment in the computer room
The obtained results also allow addressing the practical question of determining the layout of equipment in the equipment room.The traditional layout is based on forming a system of cold and hot aisles, with a central zone allocated for the installation of the main distribution frame and spine-level switches.Uninterruptible power sources and precision air conditioners are positioned along the long wall of the room, separated from the server racks of the cold and hot aisles by a 1.8-meter space to prevent the recirculation of cooled air.
Usually, 20% of the equipment room's area is allocated for the main distribution frame.In the same allocated area, a ramp is provided, which is used for transporting heavy equipment.
Server racks typically have standard dimensions of 600 x 1200 mm [16].The total maximum length of a row in this case will not exceed 7.6 -1.8 = 5.6 meters, potentially allowing for the placement of no more than 9 racks in a single row.This means it's possible to utilize one-sided delivery of cooled air from the precision air conditioner into the space beneath the raised floor.
To enhance operational conditions in the equipment room, two technical aisles are organized: one from the side of the air conditioner and UPS, and another from the opposite side.
The equipment layout scheme is shown in Figure 6.It is worth noting that the computer room generally accommodates 56 racks, providing 3 square meters per rack.This corresponds to the typical equipment density as per standard regulations.

Estimation of equipment power consumption
In the computer room of the considered DC, there are a total of 56 racks, each with a standard height of 42U or 47U.Assuming full utilization of each rack and equipment power consumption at 200 W, we obtain a power consumption of 4.1/4.4kW per rack, resulting in 250 kW for the equipment room.The Power Usage Effectiveness (PUE) coefficient for estimation can be taken as 2, meaning the overall power consumption will not exceed 500 kW.
In the case of employing a 1 + 1 power redundancy scheme for the power supply system, it is acceptable to have only two UPS.

Figure 1 .
Figure 1.Two-Connector Model of the Cable Channel

Figure 2 .
Figure 2. Summation of interferences from independent sources If we adopt the notation system of the model in Figure 2, where |[A,B]| = a and |[B,C]| = b, then

Figure 3 .
Figure 3. Simplified structural diagram of the input circuits of a network interface receiver.The second feature is that category 8 cables that are actually available for SCS construction often demonstrate obviously better parameters compared to those values contained in the ISO/IEC 11801-1:2017 standard [14].The excess level is shown in Table.3.This circumstance is taken into account in further calculations.

Figure. 5 .
Figure. 5. Histogram of the distribution of the equipment room's shape coefficient: mean value 0.34, standard deviation 0.12 (compiled by the author).

( 8 )
Its solution gives x = 22.4 m, which means the computer room can have dimensions of up to 22.4 x 7.6 meters and a maximum area of 232 square meters.

Figure. 6 .
Figure.6.The dimensions of the equipment room, the layout scheme for forming the cold and hot aisle system, and the placement of other equipment.

Table 2 .
Degree of suppression of individual interference components through pre-processing of the signal-noise mixture.

Table 3 .
Normalized and actual values of certain parameters for Category 8.2 serial cables from various manufacturers.

Table 3 .
The dependence of Shannon capacity on the electrical length of the 2-connector cable channel.