Determination of the patch cords lengths distribution physical layer of the modern automation systems of smart city and smart home by the Monte Carlo method

. A method for determining the distribution of patch cord lengths for the formation of the physical layer of modern IP-control systems is proposed. Assuming the formation of the switching field on a regular basis and the equiprobable connection of individual ports, a procedure was developed for determining the probability density function of the cord lengths, taking into account the necessary margin in case of unevenness of the laying. The calculation of the distribution has been performed and it is shown that it is advisable to use patch cords with a length of 1–2 m in control systems.


Introduction
One of the main requirements of permanent residents and guests of modern urbanized areas is to ensure a certain level of comfort, which is achieved by the introduction of a large number of engineering systems both at the city level and in individual residential and public buildings [1 -4]. The greatest effect of the operation of such systems is achieved if they are operated as a single complex, which, in turn, requires the creation of an automated control system for both the entire city and individual buildings. At a certain level of integration of the control system with the serviced object, a qualitative transition occurs and the latter turns into an intelligent one [5 -7].
The Smart Home automation system as an integral part of Smart City [8,9], regardless of scale, is built in accordance with the time-tested model of open systems. The physical layer as a basic component can be implemented in different ways, but in most cases this involves wired communication channels, which, in accordance with the requirements of the standards, are implemented in the form of SCS (Structured Cable System).

Research objective
SCS as a system can contain two main parts: line cables and switching equipment, with the help of which various active network devices are connected to the cables [10]. Individual line cables are led to technical rooms, where they are connected to group patch panels. When forming transmission channel, the ports of the panels and LAN switches are connected to each other. The combination of panels, switches and auxiliary elements forms a switching field.
Port connection can be done by switches or patch cords, Fig. 1. Switch panels are approved for use by ISO/IEC 11801-1:2019 [11]. The switch state can be changed manually or automatically. Such panels are very rare. They are only seriesproduced by the Israeli company RiT Technologies. The reason for this: • low functional flexibility, because the switch works only for two ports located one above the other; • panels allow to create a switching field only according to the cross-connect scheme, which reduces its resultant density. Therefore, in the future, we will focus only on the second option: connecting ports with patch cords. The shortest cords should be used, when forming the transmission channel. This improves two key parameters for the cable system operation.
• the quality of information transmission over the cable channel (attenuation of the patch cord cable with stranded wires is 1.2-1.5 times higher than that of the rigid installation cable with solid wires) [12,13]; • the cable system administration conditions due to the absence of loops [14,15]. An effective solution to these problems is extremely complicated by a high level of resource utilization, which is typical for modern structured cable systems Fig. 2. This requires the use of patch cords of various lengths, the number of which is subject to a certain distribution. The purpose of this work is to determine such distribution.

Rules for defining the switching field and mathematical model
Further analysis assumes • the information system is implemented entirely on the basis of IP technology [16]; • the switching field is built on separate functional sections, each containing only the same-type equipment [17]; • the functional section equipment is housed in an 800 mm wide 19-inch cabinet; [18 -19]; • patch panels and switches have a 1U of height case and a 24 port construction density per 1U height; • existing differences in the form factor of panels and switches are considered negligible; • for switching, patch cords of the minimum possible length are used, switching between different ports is equally probable [20]; • switching is carried out only between panels and switches, i.e. between different functional sections of the switching field; • functional sections on both sides are supplemented with vertical cable organizers; • every two panels/switches of the functional section are complemented by a horizontal organizer [21]. The latter increases the efficiency of administration due to the fact that after connecting the patch cord cable to the panel/switch port, it immediately goes into the organizer and does not cross the adjacent row of outlets.
The switching field implementing these principles is shown in Fig. 3. From the right side of Fig. 3 it follows that regardless of the connected ports for any patch cord, can be written as Hor Ver (1) where Hor a horizontal part of the cable; Ver a vertical part of the cord; 1.1 an empirical margin for unevenness of laying, connecting a patch cord to patch panels and likewise. Taking into account the random nature of the switching field individual ports connection for the Fig. 3 structure using the notation system introduced there for (1)    is presented in Fig. 5 and considering the specified 19-inch cabinet format does not depend on the number of serviced terminal devices.  The calculation results using (4) are shown in Fig. 7. In the process of numerical modeling using a random number generator, a set of 20 values of random vectors ( ; ; ; ) [ P ] K was formed followed by averaging. The maximum number of N terminal devices serviced by SCS also varied. The diagram on Fig. 6 is of a general nature and allows solving the problem of choosing the distribution of cords for a typical case of constructing an automatic control system. This is due to the fact that, according to available statistics, the average number of serviced terminal devices in a modern control system amounts approximately to 140.

Conclusion
The most popular cords in the technical rooms of control systems are not 1-2 m long.
Short 60 cm cords are in demand only in small control systems with the number of serviced terminal devices not exceeding 100-120.
The problem was solved using general-purpose software, and performing calculations does not require large computational tasks.
Taking into account the small number of input parameters, the proposed method can easily be extended to free-hand switching field configurations on the 19-inch equipment, provided that its structure is formed regularly.