Survivability Assessment of Distributed Information and Telecommunication Networks Boris B. Iskolnyy, Roman V. Maximov, Sergey R. Sharifullin Shtemenko Krasnodar Higher Military School Krasnodar, Russia isk-boris@mail.ru; rvmaxim@yandex.ru; sharifullinsr@mail.ru Abstract—The methods are applicable upon comparative batches between the corresponding users, is formed assessment of distributed information-telecommunication dynamically [3]. networks as to their ability to provide information exchange A task of the integrated assessment of the quality of between correspondents in conditions of occasional and subsystems fully or partially not belonging to the assessor intentional (computer attacks, using of the software's arise. The given task is stipulated by using for information undeclared capabilities) software interferences (destructive software impacts). Impact of occasional and intentional exchange of large and dynamic integrated ITNs, virtually interferences causing occurrence of failure chains on the unpredictably including one highly-reliable elements (nodes network has been described in the network degradation model and connections between them functioning in the normal based on the percolation theory. The result of using of the mode) and excluding the other ones. I.e. the task of methods is increase of reliability of assessment of structures of assessment shall be resolved in the process of ITN distributed integrated information-telecommunication structuring – constant alternation of its topology and networks upon variation of the quantity of communication typology of its elements [4, 5, 6]. nodes and lines of the network. Provision of adaptation Real ITN structures are rather large, therefore the task of capabilities of networks in conditions of impact of destabilizing assessment of survivability of ITNs cannot be resolved by environmental factors is achieved by selection of the best (from the number of admissible alternatives) network structure, as analytical methods. In this connection it is customary [7, 8, well as by selection of the best solutions for restoration of the 9, 10, 11, 12] to settle such tasks with the help of the communication between the transit nodes. The methods imitation modeling. account security of communication lines, which, unlike the Shortages of well-known methods of PUCN assessment communication nodes, cannot be isolated from impacts of the put into practice are as follows: environment. narrowness of the area of application expressed in using of the local adaptation (coverage of specific fragments by Keywords—information security; networks; routing; adjustment) to variations of the structure and the quality of adaptation; network security tools; network intelligence gathering; intentional interferences; percolation network resources upon selection of the route of passing of information messages; I. INTRODUCTION insufficiently high reliability of results of assessment of Occasional and intentional software interferences are ITN structures upon increase of the number of disturbances reducing the quality of distributed integrated communication nodes and lines (at the same time the information and telecommunication networks (ITNs): real methods free from the given shortage are applicable only for data transfer rate (availability of redundancy of the service communication nodes and lines (structures) taken as the information contained in each of fragments of message endless ones as to the number of elements). batches reduces the real data transfer rate) and availability Low accuracy of the methods is stipulated by the of communication means (failure in maintenance of following: information systems) by creation of an abnormal additional decentralized adjustment of routes; load on processes and devices realizing them [1]. unacceptable time and resource expenditures for receipt Survivability of the system is its ability to perform main of the initial data on the large number of ITN elements; functions despite action of disturbances [2]. combinatorial complexity of the task of search of safe Correspondents exercise information exchange between routes on the large number of ITN elements; the protected ITN segments via a sequence of transit unacceptably low sensitivity of route safety indexes communication nodes and lines of the public-use connected with the fact that increase of the number of ITN communication networks (PUCN). At that the ITN elements will inevitably result in increase of the number of structure, including all alternatives of routes of message routes with the close value of the safety index; absence of accounting of safety of communication lines, which, unlike the communication nodes, cannot be isolated 59 from impacts of the environment, as they are not localized the capability to provide information interaction of within the limits of the controlled zones. Compromise of the correspondents in conditions of intentional and occasional communication line is possible by placement of passive software interferences resulting in reduction of the quality means of the malefactor on communication lines or by of ITNs and creating an abnormal load on the device's radio-electronic suppression of long-length communication processes realizing the information interaction. lines, which will require significant means for search and Such a task-setting enables to formulate the following elimination of reasons of reduction of values of complex contradictions. safety indexes of communication lines. Contradiction between the necessity to provide a high The goal of the methods is resolution of the task of reliability of results of assessment and increase of the comparative assessment of ITN survivability providing resource required for the resolution thereof caused by increase of reliability of results of assessment upon variation variation of the number of communication lines and nodes of the number of communication nodes and lines of ITNs of ITNs exposed to the impact of interferences. from the structures, the size of which can be taken as the Contradiction between the need to give assessment to final one as to the number of elements, to the larger adaptation capabilities of ITNs and the necessity to obtain structures, the size of which can be taken as relatively the given assessment of prospective values of safety indexes endless, in conditions of impact of intentional and of communication nodes and lines accounting the occasional software interferences on the assessed ITNs, as destructive environmental impact. well as provision of adaptation capabilities of ITNs in The methods are aimed to elimination of the given conditions of impact of the destabilizing environmental contradictions. factors. Probability Pvc of violation of communication between It is possible to increase reliability of the result of correspondents (users) is taken as the integral index of ITN comparative assessment of ITN structures by accounting of survivability, and the availability factor FAi, where i = 1, 2, the prospective reduction of values of safety (protection) 3, …, n, characterizing the node's capabilities to provide indexes of communication nodes and lines, as well as at the users with communication services with the required quality expense of the critical area occupied by the interval of - as the survivability index of the ITN node. The order of values of the critical ratio of «dangerous» and «safe» receipt of index values, particular criteria and their communication nodes and lines obtained in experiments contribution to the final assessment are forth below in the with various random sequences. text below. Provision of adaptation capabilities of ITNs in conditions The theoretical basis of the methods are the percolation of impact of destabilizing environmental factors is achieved theory, mathematical statistics theory and probability by selection of the best (from the number of admissible theory. Impact of intentional and occasional software alternatives) ITN structure, as well as by selection of the interferences on ITNs causing sequences of failures is best solutions for restoration of the communication between similar to the process of percolation specified in works [13, the transit nodes. The assortment of alternative structures for 14] and gives an opportunity to describe processes of the the given purpose shall be preliminary found by monitoring epidemic on the degrading ITN structure globally, but in a of PUCN with the help of the specialized software like simple form. Within the framework of the percolation Visual Route or tracert (traceroute in Unix), ping and theory the given task is resolved on nodes and on pathping tools built in Windows operating systems. connections [2]. II. MEANINGFUL (PHYSICAL) PROBLEM DEFINITION III. ITN DEGRADATION MODEL, RESOLUTION OF THE Routing of message batches in ITNs and transfer thereof PERCOLATION TASK ON NODES via communication lines for provision of information In order to achieve the goal of the methods upon exchange between correspondents is made in PUCN transit resolution of the percolation task on nodes the following nodes. sequence of actions shall be performed. It is necessary to set Determination of the route of movement of message initial data: communication scheme of management bodies; batches in PUCN is a complex task as between each pair of requirements to the ITN quality indexes and the minimally correspondents there is a large assortment of alternative admissible value of the complex safety index ICmin; routes. Selection of the route is made in PUCN nodes identifiers of nodes and availability of communication lines (routers of communication operators). Criteria of selection between them. The structure and parameters of the of the route from the number of admissible alternatives are distributed ITN (typology of its elements) are determined by prospective throughput capacity and workload of the above-listed initial data. At that the communication communication lines (channels); delays made by channels scheme and requirements to the ITN quality indexes are set and their reliability; number of transit PUCN nodes and by the system of the higher level of the hierarchy – by the their reliability. management system of the office, in which interests the For provision of safety of information interaction of communication is arranged. If it is impossible to receive the correspondents it is necessary to make comparative information on the PUCNs structure as the initial data from assessment of alternative ITN structures with due account of the communication operator, then it shall be preliminary 60 found by monitoring of the PUCN with the help of the the ITN's structure there are, as a rule, alternatives of specialized software. Fullness and reliability of results of variants of routing of message batches. The required monitoring is determined by the quantity and mutual survivability and reliability of communication systems is location (spatial span) of monitoring means. In the given achieved by backup of communication channels and by the case reliability is determined by the isomorphism of results known adaptive routing methods (realized locally by the of monitoring and of the structure of the real PUCN. It is equipment of communication operators). expedient to have monitoring points in each PUCN- Let's, for example, the j-sequence variant of the connected protected ITN segment. As a result such a multi- idealized regular ITN structure be a structure, in nodes of agent software will enable to settle tasks of the subsystem of which there are communication nodes (Figures 1-2), the pj- monitoring of the topology and typology of ITNs for sequence share of which (black-color nodes) is the determination of the whole assortment of alternative ITN «dangerous» one, and the possibility of passage of message structures for information exchange between management batches between users 1 and 2 is excluded. Chains (black- bodies. color nodes and connections between them) are formed Availability (good action) factor of i-sequence ITN node from such adjacent nodes and are memorized. In the given is the availability factor calculated by the following example it is obvious that with the pj-sequence part shown formula: FAi = ((Тi – ТDi) / Тi) ∙ 100%, where ТDi – duration on (Figure 1, a) and (Figure 1, b) of «dangerous» nodes of the time interval, within which services from the from their total number (pj = 0.3) there is a large number of communication node with the required quality are alternatives of routing of messages between ITN users unavailable to users («downtime»); Тi – aggregate time of (white-color nodes and connections between them on work of the ITN node. Impact of occasional and intentional (Figure 1, b), some of them are shown on the figure by interferences on the ITN node creates an abnormal arrows). (additional) load on the communication and devices For prospective reduction of I Ci values caused by impact realizing it. As a consequence, ТDi – duration of the time of occasional and intentional interferences on interval, within which services from the communication communication channels and ITN nodes it is necessary to node with the required quality are unavailable to users increase the share of «dangerous» nodes by the value of Δp. («downtime») – increases, and the availability factor of the The given value (Δp) shall be set within the interval ITN note – decreases. Experience of ITN exploitation and of Δp = 0.01..0.2 of the required accuracy of calculation experiments on its fragments show that the value of the results. It follows from the figure (Figure 2, a) that with the minimally admissible value of the availability factor shall be pj-sequence part of «dangerous» nodes shown on (Figure 2), set within the following interval: 0.6 < FAmin < 1. where pj = 0.5, there are only 4 alterative variants of routes Further it is necessary to calculate values of the of message batches between the users shown on the figure complex safety index for each ITN node. The I Ci, complex by arrows. In order to calculate pkj, the critical ratio of index of the i-sequence ITN node shall be understood as «safe» and «dangerous» nodes, for each j-sequence variant makeup (its rationed numeric value) of safety parameters of connection of users it is necessary to increase the share of characterizing the ITN node's capability to withstand «dangerous» nodes consistently by the value of Δp realization of security threats. Calculation of I Ci can be made by different methods: summation, multiplication or as the arithmetic mean of safety parameters of the unit. Besides, preliminary set initial data as ITN parameters shall include additionally set the minimally admissible value of the complex safety index ICmin for ITN nodes and alternative variants of connection of users to ITNs. The value of ICmin shall be set as a requirement (directive) with due account of realization of safety functions providing the level of the minimal confidence to the manufacturer and the operator of the equipment (regulated normatively). Experience of exploitation of ITNs and experiments on its fragments show that the value ICmin shall be set within the following interval: 0.5 < ICmin < 1. Then it is necessary to compare the value of the calculated complex safety index ICi of the i-sequence ITN node with the preliminary set minimally admissible value ICmin. When ICi < ICmin the i-sequence node shall be memorized as the «dangerous» one, and when ICi ≥ ICmin the node shall be memorized as the «safe» one. Upon increase of Fig. 1. Variant of the regular ITN structure with the different number of communication nodes (till the relatively large quantity) in «dangerous» nodes. 61 (where, for example, Δp = 0.01) up to fulfillment of the Further, it is necessary to rank alternative variants of condition pj = pkj, at which the adjacent «dangerous» nodes connection of users by the meaning of the pkj (critical ratio of create chains excluding an opportunity of information «dangerous» and «safe» nodes) value. For the given purpose exchange for users. it is necessary to measure out tkj values of the alternative After calculation of pkj, the critical ratio of «dangerous» (competing) ITN structures on the time scale. Thus, for and «safe» nodes, for each alternative ITN structure and example, from graphs on (Figure 3, b) and (Figure 3, d): ranking of alternative variants of connection of users to ITNs tk1 ≈ 260 sec, tk2 = 225 sec. in accordance with pkj values it is necessary to select From two competing (alternative) structures it is additional variants among them with the admissible pkj value necessary to select the variants with the value tkj ≥ tk minj and to (admissible variants) (pkj ≥ pADD) and memorize them. memorize them. Let's tk minj = 250 sec. Then it is necessary to calculate the availability factor of Then it is necessary to select from graphs on (Figure 3, b) each «dangerous» FAi of the i-sequence ITN node and to and (Figure 3, d) the structure no.1 as tk1 ≈ 260 sec that compare its value with the preliminary set minimally corresponds to the condition tkj ≥ tk minj (260 sec > 250 sec). If admissible FAmin. Where FAi ≥ FAmin it is necessary to tk minj < 225 sec, then the reasons for selection are insufficient memorize the i-sequence node as the «available» one, and an additional criterion is required. otherwise, i.e. where FAi < FAmin it is necessary to memorize A set of «unavailable» nodes connected with each other the node as the «unavailable» one. creates a cluster inside the ITN. For example, the task of Then it is necessary to reduce the value of the search of the cluster's structurally separated branches availability factor of the ITN node FAi consistently by the connected with its frame via the sole node is formed. value of Δd until fulfillment of the condition FAi < FAmin. The value of Δd shall be set within the interval Δd = 0,01 ÷ 0,1 of the required accuracy of calculation results. Further it is necessary to calculate duration of the time interval TAi, within which the condition FAi ≥ FAmin has been fulfilled. Interferences injected to one or more ITN points reduce availability of ITN nodes. Graphs on (Figure 3, b) and (Figure 3, c) illustrate the dynamics of alteration of the number of ITN nodes in the action front of the interference. For example, (see graph on Figure 3, b), in the «D» point the number of ITN nodes in the action front of the interference is equal to 35 nodes as of the moment of time t1 ≈ 90 sec: i.e. on the 90th second (from commencement of observation) interferences reducing the value of FAi by the value of Δd concurrently exist concurrently on 35 ITN nodes. And for the time tkj the number of pj «unavailable» ITN nodes will achieve the value of pkj (point «Е1» on (Figure 3, a) and point «Е2» on (Figure 3, c). Fig. 2. Variant of the regular ITN, alternative routes. Fig. 3. Graphs illustrating the dynamics of growth of the number of «unavailable» ITN node in the two competing variants of the ITN structure. 62 It is expedient to construe the given task in the subject where pj < pjk, i.e. is relatively small one, provides area of networks and communication systems as follows: it is admissibly small (and even negligibly small) probability of necessary to find all «unavailable» ITN nodes, «replacement» violation of communication between users. of any of which by the «available» nodes will result in Probability of violation of communication sharply destruction of the cluster of «unavailable» nodes and increases upon increase of pj up to the area of the critical restoration of the communication between users. Such nodes values about pjk ≈ 0.6, and when pj → 1 (pj > pjk) increases are called as the «dissecting» ones. The more «dissecting» up to the one [15]. nodes – the more prospective opportunities for restoration of communication between the ITN users. IV. COMPARATIVE ASSESSMENT OF THE FINAL On (Figure 4) in the ITNs general structure one of the STRUCTURES OF INTEGRATED ITNS, RESOLUTION OF THE «dissecting» nodes is highlighted. PERCOLATION TASK ON CONNECTIONS For search of the «dissecting» nodes it is necessary [14] to For the final structures the value of pkj – is a random calculate the connectivity index N of each i-sequence value, the RMS deviation of values of which increases «unavailable» ITN node for each j-sequence connection of under the power-law with reduction of the number of users, to set the minimal value of connectivity Nmin of the communication nodes and/or lines. For the final structures «unavailable» transit ITN nodes, to select those there is no clearly defined threshold of pkj, but there is a «unavailable» ITN nodes, the connectivity index of which is critical area occupied by the interval of values p j D , k N = Nmin, and to memorize them. After that it is necessary to increase the FAi value of each i-sequence «unavailable» obtained in D-number experiments with various random transit ITN node until fulfillment of the condition sequences. Besides, the critical value pkj for communication FAi ≥ FAmin and to check availability of communication nodes in all practical ITN topologies is always less than the between users. one for the communication lines as in case of failure of any If communication between users is not restored, then it one communication node not the one communication line, is necessary to increase the value of the minimal but all communication lines of the given node are disrupted. connectivity index Nmin of «unavailable» transit ITN nodes It means that assessment obtained without account of by one. If communication between users is restored, then it communication lines will be unreliable. is necessary to memorize the i-sequence «unavailable» The percolation task on connections is resolved in the transit ITN node as the «dissecting» one. way similar to the task on nodes. It is necessary to set Further, for substantiation of selection of a structure preliminary ITN parameters and alternative variants of from the number of alternatives it is necessary to rank connection of users. As parameters it is necessary to set alternative variants of ITN by the quantity of «dissecting» identifiers of the network's nodes, communication lines nodes and to select the variant with the maximum quantity between them; minimally admissible value of the complex of «dissecting» ITN nodes providing the largest prospective safety index ILmin for communication lines; total number opportunities for restoration of the communication between Dmax of random tests providing reliability of results of users. Probability PVC j of violation of communication experiments, the test's number shall be designated as between correspondents for the j-sequence structure is D = 1, 2, … Dmax. formalized as a functional dependence on the ratio pj of Imitation modeling of the ITN's degradation upon «dangerous» and «safe» nodes. The share of «dangerous» resolution of the percolation task on connections is performed in the way similar to the one specified in the above-mentioned task on nodes. It is necessary to allocate memory arrays for storage of identifiers of users and alternative routes of message batches, two-dimensional memory array (Table I) for storage of values of the critical ratio of «dangerous» and «safe» communication lines p kj D of each of D-number random tests by each j-sequence variant of connection of users, where j = 1, 2, … . It is necessary to form the topologic ITN scheme, from which it is necessary to allocate alternative routes of message batches for each pair of alternative variants of connection of users to the ITN. It is necessary to memorize alternative routes of message batches for each j-sequence variant of connection of users. The value of the current number of random tests Dcurr shall be set as equal to zero. In order to account prospective reduction of values of Fig. 4. Graphic interpretation of the «dissecting» node in the ITN, dimension 1000 x 1000 communication nodes. complex safety indexes of communication lines caused by impact of occasional and intentional interferences on the 63 ITN's communication lines it is necessary to increase the standard normal statistics for the sought probability, d – share of «dangerous» lines by the value of Δp and to find acceptable error. p kj D – the critical ratio of «dangerous» and «safe» Alternative order of calculation of the quantity Dmax of random tests upon practical realization of the imitation communication lines for each j-sequence variant of model Dmax is as follows. For each variant of connection of connection of users, at which the information exchange users to the ITN j first it is necessary to calculate the regular between users is excluded. For the given purpose it is necessary to select at random value of the sequence p kj D , where D = Dcurr, and then to the p Dj -sequence part of communication lines from the k calculate the arithmetic mean p j D under the whole set of total number thereof from each previously memorized variant of connection of users and to memorize them as the calculated values p kj D , i.e. iteratively. The obtained «dangerous» ones, to form connected chains from the k adjacent «dangerous» communication lines and to memorize sequence p j D tends to the exact resolution upon increase of them, then it is necessary to increase gradually the share of the number of tests Dcurr. Then the criterion of stoppage of «dangerous» communication lines by the value of Δp and to the iteration process will be p j DТЕК  p j DТЕК 1   , where k k repeat formation of the connected chain until fulfillment of D k the condition p j = p j D and to memorize the critical ratio ε is acceptable error. The value of the acceptable error shall kD be set declaratively, basing on the required accuracy of of «dangerous» and «safe» communication lines p in the j calculations. The range of values ε depends on the level of two-dimensional memory array (Table I). The value of Δp difference of the compared ITN structures and basing on the shall be set on the basis of the required accuracy of experience of calculations lies within the interval of calculation of results within the interval of Δd = 0.01 ÷ 0.1. 0,01    0,1 . After completion of the iteration process k The calculation result p j D shall be registered in the table of Dmax will be equal to Dcurr. the two-dimensional memory array for storage of values of Upon fulfillment of the condition Dcurr ≥ Dmax the value the critical ratio of «dangerous» and «safe» communication of the index of the center of the sampling distribution p j D k lines (Table I). under the whole set Dmax of random tests for each j- TABLE I. TWO-DIMENSIONAL MEMORY ARRAY OF VALUES OF THE sequence variant of connection of users shall be calculated CRITICAL RATIO as the mathematical expectation or the arithmetical mean or the geometrical mean or the harmonic mean or the average D k D max 1 2 3 4 5 Dmax =6 pj power value or the weighted average or the median or the j 1 0,726 0,548 0,262 0,738 0,250 0,417 0,490 mode values p kj D under the whole set of D random tests 2 0,565 0,318 0,271 0,129 0,341 0,071 0,282 under each j-sequence variant of connection of users. Results of calculation of indexes of the center of the …. sampling distribution p kj D under the whole set Dmax of After that it is necessary to increase the value of the counter of the number of random tests Dcurr by one and then random tests for two alternative ITN structures and Dmax = 6 to fix the number of the random test. are set forth in (Table I). At that in line 1 (Table I) there are Each random test Dcurr performed in the process of results of calculations for the ITN regular structure with the experiments with the help of the numeric modeling by the connectivity of each communication node equal to four. In Monte-Carlo statistic test method results in formation of line 2 (Table I) there are memorized results of calculations various structures from «dangerous» communication lines for the ITN regular structure with the connectivity of each connected with each other and in receipt of random values communication node equal to three. The arithmetic mean value shall be calculated by the p kj D , which shall be memorized in (Table I), while the following formula: condition Dcurr < Dmax limiting the total number of random 1 D max  max  p kj D . k max tests is fulfilled. 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