Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04Q—SELECTING
  • H04Q3/00—Selecting arrangements
  • H04Q3/0016—Arrangements providing connection between exchanges
  • H04Q3/0062—Provisions for network management
  • H04Q3/0083—Network planning or design; Modelling of planned or existing networks
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
  • H04L41/12—Discovery or management of network topologies
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
  • H04L41/14—Network analysis or design
  • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L43/00—Arrangements for monitoring or testing data switching networks
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L47/00—Traffic control in data switching networks
  • H04L47/10—Flow control; Congestion control
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L47/00—Traffic control in data switching networks
  • H04L47/10—Flow control; Congestion control
  • H04L47/11—Identifying congestion
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L47/00—Traffic control in data switching networks
  • H04L47/10—Flow control; Congestion control
  • H04L47/19—Flow control; Congestion control at layers above the network layer
  • H04L47/193—Flow control; Congestion control at layers above the network layer at the transport layer, e.g. TCP related
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L47/00—Traffic control in data switching networks
  • H04L47/10—Flow control; Congestion control
  • H04L47/26—Flow control; Congestion control using explicit feedback to the source, e.g. choke packets
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L47/00—Traffic control in data switching networks
  • H04L47/10—Flow control; Congestion control
  • H04L47/28—Flow control; Congestion control in relation to timing considerations
  • H04L47/283—Flow control; Congestion control in relation to timing considerations in response to processing delays, e.g. caused by jitter or round trip time [RTT]
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L43/00—Arrangements for monitoring or testing data switching networks
  • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
  • H04L43/0823—Errors, e.g. transmission errors
  • H04L43/0829—Packet loss
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L43/00—Arrangements for monitoring or testing data switching networks
  • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
  • H04L43/0852—Delays
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L43/00—Arrangements for monitoring or testing data switching networks
  • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
  • H04L43/0852—Delays
  • H04L43/0864—Round trip delays
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L43/00—Arrangements for monitoring or testing data switching networks
  • H04L43/16—Threshold monitoring

Definitions

• the invention relates to the monitoring and simulation of complex systems.
• the present invention improves the situation.
• the invention proposes to use a representation in so-called "max-plus” algebra of complex systems, such as communication networks and in particular flow and congestion control.
• the scalar max-plus algebra is a semi-ring on the real line where the addition becomes the "max" function (largest value among a set of values) and the multiplication, the "plus” function (sum ).
• max-plus algebra allows the calculations of a complicated system to be reduced to a simple matrix representation.
• the Applicant has shown and verified in practice that the use of max-plus algebra adapts very satisfactorily. monitoring and simulating systems such as a communications network, whether controlled or not. It makes it possible in particular to overcome the random nature of the parameters of the network, while considering a plurality of nodes.
• the Applicant has shown that the representation of a network using a TCP protocol is linear in max-plus algebra, which makes it possible, in practice, to apply simple data processing.
• the present invention therefore relates to a device for assisting in monitoring and / or simulating a complex system, in particular a communication network.
• a memory for storing first data representative of network parameters, as well as for receiving at least second data representative of events in the network, a portion of said memory being reserved for storing data in matrix form,
• a modeling module for constructing at least a first matrix and a current matrix respectively as a function of the first data and of the second data, according to a chosen model
• a pilot module for repeatedly applying the first matrix and the current matrix to the calculation module, the product matrix obtained becoming a new first matrix.
• - a static modeling sub-module to build the first matrix as a function of the first data
• - a dynamic modeling sub-module to build at least one current matrix as a function of the second data
• the device of the invention is capable of processing matrices comprising dynamically variable coefficients, including at least the above-mentioned current matrix.
• the matrices constructed are advantageously of the same dimension.
• These second data preferably include information relating to losses in the network, to transverse flows in the network, with respect to a controlled connection to be monitored or simulated, to congestion in the network, or even to timeouts in the so-called "time-out" network.
• the product matrix obtained is a vector represented by a matrix with a single column, which makes it possible to limit the treatments and their duration.
• the first matrix, representative of the parameters of the network, is advantageously structured at the outset as a vector.
• the product matrix obtained is representative of a throughput in the network associated with the connection to be monitored or simulated, of an average throughput in the network, or even of fluctuations in a throughput snapshot in the network.
• the modeling module is arranged to successively build a plurality of matrices, in number corresponding substantially to the number of packets in the network.
• the model chosen preferably includes consideration of the variable size of a window used to control the number of packets in the network.
• TCP type protocol typically comprising discipline routers of the "first come first served” type, or alternatively routers with discipline of the FQ type (from the English "weighted fair queu - ing ").
• the TCP protocol controlling the network can also be based on a Reno model or a Tahoe model, as we will see below.
• the network service can be deterministic, or even random, as we will see in detail below.
• the present invention also relates to a method for assisting in monitoring a complex system, in particular a communication network.
• a method generally comprises the following steps: a) obtaining first data representative of parameters of the network, b) constructing a first matrix, according to a chosen model, as a function of said first data, c) receiving, at a chosen time, at least second data representative of events in the network, d) construct at least one second matrix of dynamically variable structure, according to the chosen model, as a function of the second data, and e) perform on said matrices a product forming operation according to algebra called MAX-PLUS, the product matrix obtained being representative of the state of the network at said selected time.
• MAX-PLUS algebra
• the method advantageously includes the following additional step: f) repeating, at selected times, steps c), d) and e) , while the product matrix obtained becomes the first matrix after step e).
• the present invention also relates to a method for simulating a complex system, in particular mechanisms and controls of flow and congestion in a communication network.
• This process generally comprises the following steps: a) obtaining first data representative of parameters specific to the network, b) constructing a first matrix, according to a chosen model, as a function of said first data, c) simulating events in the network and predicting at less second data representative of said events, d) construct at least a second matrix according to the chosen model, as a function of said second data, and e) perform on said matrices a product forming operation according to the so-called MAX-PLUS algebra, the product matrix obtained being representative of a state of the network undergoing said events.
• this method advantageously comprises the following additional step: f) repeating, for successive events, steps c), d) and e) , while the product matrix obtained becomes the first matrix after step e).
• FIG. 1A schematically represents a device within the meaning of the present invention
• FIG. 1 schematically represents a number K of tandem queues in a network, with flow control
• FIG. 2A represents an example of a step-by-step evolution of daters and of the size of a window used to control the number of packets in the network
• FIG. 2 represents interactions between several packets in the network
• FIG. 4 illustrates a graphic interpretation of the asymptotic rates in a TCP protocol network based on the Reno model with deterministic delays
• FIG. 5 represents a variation in the throughput, obtained by simulation and showing a decrease in the throughput in the event of random losses in the network
• FIG. 6 represents a variation of the throughput (curve in solid lines), obtained by simulation, in a TCP protocol network based on a Reno Markovian model
• FIG. 7 represents comparative variations in throughput, obtained by simulation, in TCP protocol networks based respectively on a Reno deterministic RD (solid lines), Reno markovian RM (long dashed lines), Tahoe deterministic TD ( medium dotted lines) and Tahoe markovian TM (short dotted lines),
• FIG. 8 represents a variation of the throughput (curve in solid lines), obtained by simulation, in a TCP protocol network based on a Tahoe model with exponential phase,
• FIG. 9 represents comparative variations in bit rates, obtained by simulation, in a TCP protocol network based on a Tahoe model with services s 3 and s 8 respectively constant and equal to 1, and - Figure 10 schematically shows a network with its queues and routers.
• Annex I includes the formulas and equations E1 to E28 to which the detailed description below refers.
• Annex II includes the bibliographic references [1] to [13] indexed in square brackets in the description below.
• the device is in the form of a computer comprising a central unit UC provided with a microprocessor ⁇ P which cooperates with a motherboard CM.
• This motherboard is connected to various equipment, such as a COM communication interface (of Modem type or other), a ROM read only memory and a RAM working memory (random access memory).
• the motherboard CM is also connected to a graphical interface IG, which controls the display of data on an ECR screen that the device includes.
• input means such as a CLA keyboard and / or an input device called "mouse" SOU, connected to the central unit UC and allowing a user interactivity with the device.
• the ROM memory or even the RAM memory stores the first aforementioned data, representative of the parameters of the network (topology, properties of the routers, etc.).
• the RAM memory receives the aforementioned second data, representative of events in the network (transverse flows, congestion, losses, etc.).
• these second data can be received by the COM communication interface.
• the acquisition of these second data can be performed by a calculation based on a simulation model, as will be seen below.
• the RAM memory at least can be addressable as a function of rows and columns of matrices and thus allow storage of data in matrix form.
• the ROM memory includes a MOD modeling module which, in cooperation with the microprocessor ⁇ P, makes it possible to construct the aforementioned first matrix and a current matrix, respectively as a function of the first data and of the second data, according to a chosen model which will be seen further.
• the ROM memory comprises a module CAL which, in cooperation with the microprocessor ⁇ P, makes it possible to carry out, on at least two matrices of dynamically variable structure, a product forming operation according to the MAX-PLUS algebra.
• dynamically variable structure matrices means matrices whose coefficients at least are dynamically variable.
• the models which will be described below make it possible to reduce the constructed matrices (and more particularly the current matrices) to matrices of which only the coefficients are dynamically variable.
• the MOD modeling module then comprises: - a static modeling sub-module ST, to build the first matrix as a function of the first data, and - a dynamic modeling sub-module DYN, to build, as a function of the second data, at minus a current matrix whose coefficients are dynamically variable.
• the ROM memory furthermore comprises a PIL module which, in cooperation with the microprocessor ⁇ P, makes it possible to apply repeatedly the first aforementioned matrix (comprising the first data) and the current matrix (comprising the second data) to the calculation module CAL.
• the product matrix obtained is stored ⁇ n memory and becomes a new first matrix. It can then be multiplied (in the MAX-PLUS algebra) to another current matrix, comprising new second data representative of new events in the network.
• window flow control of a multidimensional network admits a max-plus linear representation when the window size is constant (reference [5]).
• the Applicant is mainly interested in models which combine the adaptive control mechanism of TCP and a multidimensional network made up of several routers in series.
• the dynamics of such a controlled xnet are advantageously described at the "packet" level via iterations of matrix products in max-plus algebra.
• the present invention makes it possible to analyze instantaneous and random fluctuations in bit rate, which can be useful for estimating the quality of service offered to a connection. It also adapts well for efficient simulations of the dynamics of a TCP session operating under control, end-to-end, on a large network.
• the scalar max-plus “algebra” is a semi-ring on the real line where the addition is replaced by max (denoted ⁇ ) and multiplication by plus (denoted ®).
• the law ® is distributive with respect to the law ⁇ , which allows us to extend the usual concepts of linear algebra to this framework, and in particular the theory of matrices.
• This semi-ring is noted (R ma x f ⁇ f ®) ⁇ where R j - ⁇ x is the real line completed with minus infinity, which is the neutral element of ⁇ .
• ⁇ In a PAPS network, of the “first come, first served” type, with K queues in tandem, the n-th client arriving at station i receives a service ⁇ (n).
• this network models a single source sending packets to a single destination, through a path composed of K routers.
• the variable ⁇ ⁇ n) is the random delay caused by the transverse traffic (the other users) at the level of router i on the n-th packet. This delay does not include wait times, but only the slowdown in server speed due to the presence of cross traffic.
• the propagation delay of the n-th packet between the routers i to j is noted below d ⁇ j (n).
• the flow of the input stream is controlled by a dynamic window (n), the size of which is equal to the total number of packets sent by the source at a given instant and which have not reached the destination (or more precisely the packets which have not yet been "acquitted").
• the size of the window has a general evolution defined by the recurrence E2 given in the appendix.
• E2 the recurrence of the window.
• ACK (n) is the flow / congestion control signal giving information on the state of the system at time n and where f is a function specified below.
• f is supposed to also depend on s, which is, for the TCP models, the threshold which separates the phase of exponential growth (called “slow-start phase”) from the phase of linear growth (called “congestion-avoidance phase”).
• the recurrence relation (given in appendix by E3) defines a reference size of the window.
• the effective size is then defined as the whole part of the reference size, according to equation E3 in the appendix.
• the change in window size can be broken down into two phases which depend on ACK (n) as follows: a growth phase defined by E51 and a decrease phase defined by E52.
• ACK (n) (worth 0 or 1) is the acknowledgment signal of the n-th packet which detects a congestion state or a packet loss.
• the usual examples of the ideal window evolution policy are given by equations E61 to E67 in the appendix, in which the real ⁇ is between 0 and 1, strictly.
• the relations E61 and E62 are given respectively for exponential and linear phases.
• the value of ⁇ is set to 1/2.
• the queue at the entrance is considered below as saturated (even if the unsaturated case can be easily integrated, as will be seen below).
• the network then behaves as a closed network and its speed gives the maximum rate at which the source can send packets while keeping a stable input buffer.
• y i (n) is the date on which the n-th client leaves router i.
• the variables Mi, i belonging to ⁇ 1, ..., w * ⁇ , are given matrices of (l ⁇ ⁇ ax ).
• e is the matrix of ( ⁇ a x) of which all the elements are equal to minus infinity.
• M W * the matrix of (R ⁇ a ') defined by blocks of size kx k.
• the Applicant has shown that all the blocks are equal to the matrix e of (R ⁇ a x) 'except for the first row of blocks which is equal to M 1 # M 2 , ..., M W * .
• the Applicant has also shown that if initially the system is empty, the evolution of the date vector Z (n) is given by the max-plus linear recurrence E8.
• D is the matrix of dimension Kw * of which all the elements are equal to minus infinity except those of the form D ⁇ + ii (with i belonging to ⁇ 1, ..., k (w * - l) ⁇ ) which are all equal to 0.
• Equation E8 is, in this realization, the basis of the algebraic simulation scheme to which it was alluded above.
• the matrices A Wn _ 1 (n) are of dimension Kw * , and as only the matrix-vector products are necessary, we can simulate the controlled transmission of n packets through the network in 2n (Kw * ) 2 operations on a single processor.
• package # 5 corresponds to the size of window 3, - which is noted 5 (3) in Figure 2A.
• packet # 5 just after the transmission of packet # 5, three packets in the network have not yet been "acknowledged".
• Figure 2A shows, the delays imposed on packets (see for example packet # 6) in internal routers can be quite complicated.
• This detection can be interpreted as giving the service rate 1 / ⁇ * of the network bottleneck and S, a round trip time RTT. Congestion is therefore detected when the average emission rate (w n / RTT) reaches the rate of the bottleneck.
• w * is the optimal window size given by the product: bandwidth x delay (reference [9]).
• the packets sent behave as if there was no interaction between them, except for the couple of packets sent at the same time when the size of the window increases by one.
• the second packet always leaves station K with a delay of ⁇ * relative to the first.
• E15 The saturation rate for TCP Tahoe with the exponential phase is given by the formula E15 and the asymptotic rate (w * infinite) is given by E16.
• the saturation flow rate is equal to 0.140084 using the formula E14.
• the saturation rate depends only on S and ⁇ * and it is given by the formulas E17 in the appendix.
• the asymptotic flows (case 1, case 2, case 3) are obtained in a fairly intuitive manner from the fluid approximation of the evolution of the size of the window.
• the speed obtained can be compared to that simulated by a simulator (for example of the NS type) by choosing an arbitrary packet size and taking a service speed of the router i corresponding to ⁇ i .
• the differences between the flow rates obtained by the NS simulation and by the above formulas can only come from differences in the mechanisms of detection of the loss by congestion, or from the fact that the integer part of W (n) in f ( as in reference [9]) is the only one considered here, while NS uses (n). Indeed, for all deterministic models with the same periodic evolution of W (n), the evolutions are exactly the same.
• the service speed is (10,5,4,2,5,4,5,5,4,5,5) Mb / s for the links 0-1, .., 9-10, 10-0.
• the NS simulator gives 152.27 packets / s.
• the flow depends on the delays only through S and ⁇ * .
• the Lyapunov exponent ⁇ (the inverse of the flow) is of the form given by the formula E20 in which ⁇ is the stationary probability of the set A.
• This model can be compared to that of reference [12], where an overall probability of loss is used to capture at the same time the time-outs (TO) due to packet losses and the triple-duplication of ACKs (TD) due to congestion.
• TO time-outs
• TD triple-duplication of ACKs
• these two mechanisms are on the contrary described separately; the loss of packets which generate the TO constitute an iid sequence (independent and identically distributed), independent of all the other elements of the network and are captured by the parameter p_; losses due to congestion are captured by the w * parameter.
• ⁇ (w * ) + p_ (l- ⁇ (w * )) ⁇ (l) where ⁇ (w * ) is the loss due to congestion and p_ (l- ⁇ (w * ) is the loss due to TO .
• the flows are equal to 0.140084 (Tahoe) and 0.172166 (Reno).
• the flows of the deterministic model seem to be higher than those of the Markov models.
• tandem queues with random services and with a fixed buffer size b for all stations are now considered.
• the service time supports are assumed to be limited.
• (n) has a deterministic evolution when (n) belongs to ⁇ l, ..., b ⁇ and a random evolution when it belongs to ⁇ b + 1, ..., b + k ⁇ .
• b is an arbitrary size (for example, half the actual size of the buffer) such that if the number of pending packets exceeds this threshold, congestion is detected.
• Time-out mechanisms can be taken into account, for example, by the condition S (n)> TO or by the condition: vk (n) - y ⁇ (n -n- ⁇ ) > ⁇ o -
• the ⁇ ⁇ n) are iid and mutually independent, with values in ⁇ 1,5,10 ⁇ with respective probabilities of 0.3, 0.4, 0.4.
• ⁇ 8 (n) is constant equal to 1 and the other services are as above.
• the basic principle of this simulator is the analysis of a controlled connection.
• the simulation of this connection begins with the acquisition of data concerning the network:
• a scheduling mechanism in a router (for example first come first out "FIFO" (or Weighed Fair Queueing) with possibly differentiations of services) can be represented in this simulation by taking into account the influence of this mechanism on the service lives ⁇ ⁇ (); once calculated as a function of the transverse traffic, the traffic of the controlled connection and the scheduling mechanism, these random durations can be injected into the simulator.
• FIFO or Weighed Fair Queueing
• the present invention finds interesting applications in the analysis of these few combinations, since all combinations can in principle be analyzed in this context.
• the invention defines a generic framework for the simulation of protocols of the TCP type on networks which may be large.
• the simulation is based on a simple processing which exploits linearity and which has a controlled complexity.

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