Patent Publication Number: US-6343076-B1

Title: ATM cell spacer

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to an ATM cell spacer. 
     A general description of this kind of facility can be found in the article by P. E. BOYER et al.: “Spacing Cells Protects and Enhances Utilization of ATM Network Links” (IEEE Network, September 1992, pages 38-49). 
     ATM cells are 53-byte information packets transmitted over high-speed physical links (bit rate of 155 or 622 Mbit/s). Each physical link supports a multiplex of cells belonging to various virtual connections. The virtual connection to which each cell pertains is identified by a pair of identifiers VPI-VCI contained in the header of the cell. Certain facilities differentiate between virtual connections according to the virtual path identifier (VPI), while other facilities differentiate between the virtual connections on the basis of the virtual channel identifiers (VCI), or of both identifiers VPI, VCI. 
     In the present description, each ATM call will be regarded as pertaining to a virtual connection identified by an identity IdCx internal to the facility provided with the spacer. This internal identity can correspond to the VPI, to the VCI, to the pair VPI-VCI, or else, more conveniently, to a specific identity individual to the facility and comprising a smaller number of bits than the VPI-VCI, so as to facilitate accesses to memory modules of reasonable size. An appropriate way of associating such identities IdCx with the ATM cells is described in French Patent Application No. 97 01222. 
     The ATM spacer is a unit whose main function is to regularize the bit rate of cells over the various connections supported by a physical link. In general, each source emitting on a virtual connection negotiates a peak bit rate with the operator. If this peak bit rate is not complied with by the source, there is a risk of congestions occurring in the network, and the operator is empowered to destroy cells on the connection. 
     In a spacer, a spacing interval T is allotted to each connection IdCx, in such a way that two consecutive cells relating to the same virtual connection are generally separated by at least the time interval T which typically corresponds to the inverse of the peak bit rate. We then speak of a real spacer. The real spacer calculates a theoretical emission time TET for each cell and then stores the cell in memory so as to emit it only at the desired time. The spacing interval T is then complied with for all the connections. In a so-called virtual spacer, a theoretical emission time TET is firstly calculated for each cell according to the same methods as before, and then the cell is stored in memory. The difference with the real spacer is that the virtual spacer emits the cells immediately in the order of the theoretical emission times. The virtual spacer does not degrade the cell delay variation (CDV). However, it does not allay the possible degradation of the bit rate by queues located upstream of the spacer. 
     The spacing function is frequently associated with the policing function which consists in eliminating cells transmitted in accordance with a virtual connection at a bit rate greater than the peak bit rate, when this excess bit rate is such that it is no longer possible to produce an output multiplex in which the cells pertaining to the connection are correctly spaced without the CDV exceeding a limit value depending on the quality of service negotiated with the operator. The policing function usually enters into the way of calculating the theoretical emission times TET of the cells. 
     A conventional way of allotting theoretical emission times to the cells and of performing the policing function is to apply the GCRA algorithm (“Generic Cell Rate Algorithm”) defined in Annex 1 of ITU-T Recommendation I.371 (see M. DE PRYCKER: “Asynchronous Transfer Mode, Solution for Broadband ISDN”, 2nd Edition, 1993, Chapter 7, paragraph 7.3.4, pages 292-293). For each virtual connection, this algorithm always satisfies the following relation: ta≦TET≦ta+τ, where ta denotes the time of arrival of the cell, at which its theoretical emission time TET is calculated, and τ denotes the CDV tolerance of the connection. 
     Cells pertaining to different virtual connections may find themselves allotted the same theoretical emission time. As a result it is necessary to provide a mechanism for resolving such conflicts. 
     A first solution, described in the document EP-A-0 438 009, consists in storing each incoming cell at an address of the cell memory corresponding to its actual time of emission. At the output of the spacer, a time counter serves as address pointer for designating the cells to be emitted. After assigning a theoretical emission time to the cell, the latter is stored at the first available address after this theoretical time, thereby avoiding conflicts. 
     A second solution, described in the document EP-A-0 498 092 (see also E. Wallmeier et al.: “The Spacing Policer, an Algorithm for Efficient Peak Bit Rate Control in ATM Networks”, Proc. of ISS&#39;92, October 1992, Vol. 2, pages 22-26), consists in associating, with each emission period, a list of cells chained by means of pointers. When an emission period is reached, the cells of the associated list are read and output one by one during this period and during the required number of succeeding periods. 
     A third solution, described in the article “A Real Time Sorter with Application to ATM Traffic Control” by J. W. Roberts et al. (Proc. of ISS&#39;95, April 1995, Vol. 1, pages 258-262), consists in utilizing a sorting technique: with the arrival of each cell, a data element made up of the cell storage address and of a sort key corresponding to its theoretical emission time is introduced into a sorting device, which at each emission period produces an element, having a minimum sort key. The cell whose address is contained in this element is emitted if the minimum key is less than or equal to the current time in the case of a real spacer, or immediately in the case of a virtual spacer. The sorting device must be capable of sorting a number N of elements equal to the maximum number of cells stored in the spacer. Moreover, it is noted that the sorting device advocated has the drawback that the number of logic circuits operating in parallel so as to perform the sorting function at a sufficient rate is proportional to N. Once the number N of elements to be sorted becomes large (a few thousand or tens of thousands as in the case of the application to an ATM cell spacer), the hardware complexity of the sorting device becomes prohibitive. 
     In the three solutions above, the spacer ignores the concept of virtual connection once a theoretical emission time has been allotted to an incoming cell. As a result, the procedure for determining a stored cell to be emitted is the choosing of a cell from a number corresponding to the maximum storage capacity of the spacer. This implies superfluous complexity from the moment that in principle the order of reception of the cells pertaining to one and the same virtual connection must be complied with on emission. 
     Should there be a risk of traffic congestion on the link equipped with the spacer, the operator sometimes has the option of increasing the spacing intervals T allotted to certain connections. However, such a modification of T acts only on the cells which have not yet been received, and not on those already written to the buffer memory of the spacer, given that the theoretical emission times calculated previously are no longer modifiable without knowing the connections concerned; yet, a sufficient number of cells may already have been written to the buffer memory for the increase in the intervals T to be ineffective in preventing congestion. The above spacers lack flexibility in this respect. 
     An ATM spacer, in which the selecting of the cell to be emitted is effected on the basis of the theoretical emission times assigned to the cells stored in the starts of FIFO lists allotted to the various virtual connections, is described in EP-A-0 710 046. This document describes a particular method of calculating the emission times in accordance with which the theoretical time of emission of a cell depends on the actual time of emission of the preceding cell pertaining to the same virtual connection. A similar method is described in the article “Multiplexing Spacer Outputs on Cell Emissions”, by G. Mercankosk et al., Proc. Infocom&#39;95—Conference on Computer Communications, 14th Annual Joint Conference of the IEEE Computer and Communications Societies, Boston, Apr. 2-6 1995, Vol. 3, pages 49-55. 
     This type of method has the drawback that, when a cell is delayed because of a conflict between cells pertaining to different connections and to which the same theoretical emission time has been allotted, the succeeding cells of the same connection are also delayed even if the conflict has disappeared. Such cases result in needless disturbance to the flow. 
     An object of the present invention is to propose an ATM spacer which is less affected by the above drawbacks. 
     SUMMARY OF THE INVENTION 
     The invention thus proposes a spacer of ATM cells transmitted according to a plurality of virtual connections, comprising: 
     a cell memory to which incoming cells are written and from which outgoing cells are read; 
     means for allocating a theoretical emission time to each cell stored in the cell memory, comprising means of recursive calculation of a theoretical emission time for each cell pertaining to a virtual connection on the basis of parameters including at least the time of arrival of said cell and a spacing interval allotted to said connection; 
     spacing control means for managing the cell memory, with the aid of an associated pointer memory, in such a way that the cell memory comprises, for each virtual connection for which it contains cells, a list of locations where said cells are stored in first-in first-out mode between a start of list and an end of list; and 
     sorting means for ordering data elements, each comprising a virtual connection identity and a sort key consisting of the theoretical time of emission of the cell contained in the start of list relating to said virtual connection, and for selecting at least one data element having a minimum sort key, the spacing control means being devised so as to command the emission of a cell contained in the start of list relating to a virtual connection identified in a data element selected by the sorting means. 
     Upon the arrival of a cell pertaining to a virtual connection for which the cell memory contains no cell, the sorting means receive a new data element comprising the identity of said virtual connection and, as sort key, the theoretical time of emission of said cell supplied by the means of recursive calculation. Upon the emission of a first cell pertaining to a virtual connection for which the cell memory comprises a list of locations further containing at least one second cell, the sorting means receive a new data element comprising the identity of said virtual connection and, as sort key, a theoretical time of emission of said second cell equal to the theoretical time of emission of said first cell plus the spacing interval allotted to said connection. 
     There is a saving in the complexity of the spacer and a gain in its flexibility of use through the fact that the cells emitted are chosen by a sorting procedure based on the starts of list per connection rather than on all the cells stored. 
     The mode of determining the emission times limits the delays suffered by the cells owing to the conflicts with regard to the emission slots. In certain cases, even the delay suffered relative to the theoretical emission times obtained by the means of recursive calculation is reduced. 
     The sorting means advantageously comprise one or more binary-tree sorting devices of a type described in detail below. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram of a binary sort tree. 
     FIG. 2 is a schematic diagram of a sorting device usable according to the invention. 
     FIG. 3 is a schematic diagram showing the environment of each controller of the device of FIG.  2 . 
     FIGS. 4A to  4 C show a flowchart of the operation of the controller of FIG.  3 . 
     FIG. 5 shows a timing diagram of the operation of the sorting device. 
     FIGS. 6 and 7 are diagrams similar to that of FIG.  3  and showing possible variants in respect of the environment of the controllers. 
     FIG. 8 is a diagram showing a shift register usable with a sorting device according to FIG.  7 . 
     FIG. 9 shows a simplified timing diagram of the sorting device. 
     FIGS. 10A and 10B, which are to be supplemented with FIG. 4C, show a flowchart of the operation of the controller of FIG.  7 . 
     FIGS. 11A and 11B, which are to be supplemented with FIG. 4C, show a flowchart corresponding to that of FIGS. 10A,  10 B and  4 C in the particular case of the last stage of the binary tree. 
     FIG. 12 is an overall diagram of an ATM cell spacer implementing the present invention. 
     FIG. 13 shows timing diagrams of the operation of the spacer of FIG.  12 . 
     FIGS. 14 and 15 are flowcharts respectively showing the operations performed by the controller of the spacer of FIG. 12 on receiving and emitting an ATM cell. 
     FIGS. 16 and 17 are partial diagrams of variant ATM spacers implementing the present invention. 
     FIG. 18 shows timing diagrams comparable to those of FIG.  13  and referring to a variant embodiment of the spacer. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     Before describing the general structure of an ATM spacer according to the invention, embodiments of a sorting device advantageously usable in such a spacer will firstly be described with reference to FIGS. 1 to  11 . This device, which sorts data elements each including a respective sort key, comprises: 
     storage means organized according to a binary tree with 2 n −1 nodes numbered from 1 to 2 n−1 −1 which are each able to contain a data element and are distributed in n successive stages numbered from 0 to n−1, stage q comprising nodes  2   q  to  2   q+1 −1; and 
     means of control of the binary tree for dispersing the elements to be sorted within the tree in such a way as to satisfy an ordering condition according to which, for each integer i lying between 1 and 2 n−1 −1 such that node i contains an element to be sorted, each of the nodes  2   i  and  2   i +1 either contains no element to be sorted, or contains an element whose sort key is greater than or equal to, in the sense of a determined order relation, the sort key of the element contained in node i. 
     The ordering of the elements in the sort tree corresponds to what is referred to as a “heapsort” in the field of computerized sorting. In this regard, reference may be made to the work by Knuth: “The art of computer programming, Vol. 3, Sorting and searching”, Addison Wesley, 1973, pages 142-157. 
     By way of illustration, FIG. 1 shows, in the case where n=4, a sort tree comprising fifteen nodes  1 - 15  containing data elements (of which only the sort key is represented) which satisfy the ordering condition. 
     Node  1  of stage  0  is referred to as the root or vertex of the tree. The 2 n−1  nodes 2 n−1  to 2 n −1 of stage n−1 are referred to as leaves of the tree. For each node i of a stage q, the 2 n−q −1 nodes of the tree whose numbers are of the form i2 j +j′, where j and j′ are integers such that 0≦j&lt;n−q and 0≦j′&lt;2 j , are referred to as descendants of node i (here, node i is considered to be included in its descendants). Among these descendants, the sister nodes  2   i  and  2   i +1 of stage q−1 (if q&lt;n−1) are referred to as children of node i. The parent of node i (if q&gt;0) is on the other hand defined as that node of stage q−1 whose number is i/2 if i is even and (i−1)/2 if i is odd. These logic relations of parentage between the nodes of the tree are represented by arrows in FIG.  1 . 
     The order relation between the sort keys is arbitrary. In the case illustrated in FIG. 1, it is the familiar order relation between the natural integers, allowing the sorting in ascending order of the sort keys. In the case of sorting in descending order, it is clearly sufficient to invert the order relation between the keys. In FIG. 1, the nodes of the tree which are not occupied by elements to be sorted are regarded as each containing an element whose sort key is infinite, that is to say greater than any sort key of a data element to be sorted. One possibility for coding an infinite key is to reserve one bit of the data field containing the key for this purpose; the key will for example be regarded as infinite if this bit is at 1 and as finite otherwise. In other words, this bit indicates whether the node is free or occupied by a data element. 
     Once it is loaded with a set of N&lt;2 n  ordered data elements, the sorting device is capable of delivering these N elements sequentially in N cycles in the order of the sort keys. The extracting of an element from the tree in the course of a cycle consists in reading the element located at the root of the tree and in tracing back elements of its descent in such a way as to always satisfy the ordering condition. Thus, in the case represented in FIG. 1, the first cycle consists in reading the element  16  located at the root, and in moving element  24  to the root, then element  38  to node  2  and finally element  623  to node  4 . This amounts to propagating the extraction command from the root towards the leaves. 
     In some applications, it is necessary for the control means also to be capable of responding to commands for inserting a new element to be sorted into the tree. The sorting device is then capable of delivering or of receiving elements to be sorted at each cycle. It operates as a dynamic queue on the basis of the sort keys, managed according to the order relation used, and possibly representing time tags or any other type of priority index. 
     FIG. 2 shows a sorting device in which the data elements are contained in a memory  20   0 - 20   3  organized in accordance with the binary tree of FIG. 1, with n=4 stages. 
     The binary tree is controlled by a set of m distinct controllers, where m is an integer lying between 2 and the number n of stages of the tree. In the case considered in FIGS. 2 and 3, there is one controller  21   q  for each stage q of the tree, i.e. m=n=4. Each controller  21   q  comprises a bus  22   q  allowing it to access stage q. The storage means of the tree are thus divided into m=4 memory modules  20   0 - 20   3  each accessible via a respective bus  22   0 - 22   3 . In each node i there are two memory locations for respectively containing the sort key K(i) of a data element, the only key represented in FIG. 2 (K(i)=∞ when there is no element), and a reference R(i) of this element (cf. FIG.  3 ). 
     Each stage q of the tree other than stage  0  comprises, in addition to the nodes  2   q  to  2   q+1 −1,  2   q−1  locations  23  with a capacity of 1 bit, and  2   q−1  locations with a capacity of n−q+1 bits. Each location  23  contains a steering bit F(i) associated with a pair of sister nodes  2   i  and  2   i +1 of stage q, the value of which is F(i)=0 if the key contained in the left-hand sister  2   i  is less than that contained in the right-hand sister  2   i +1 (K( 2   i )&lt;K( 2   i +1)), and F(i)=1 if K( 2   i +1)≦K( 2   i ). The total number of locations  23  in the sort tree is 2 n−1 −1. 
     Each location  25  of stage q contains a differential counter Δ(i) associated with a pair of sister nodes  2   i  and  2   i +1 of stage q, the value of which is given by the difference between the number of data elements contained in the descendants of the left-hand sister  2   i  and the number of data elements contained in the descendants of the right-hand sister  2   i +1. 
     The steering bits F(i) serve to propagate the extraction or exchange commands from the root to the leaves of the tree, while the differential counters Δ(i) serve to propagate the insertion commands from the root to the leaves of the tree. 
     The means of control of the binary tree moreover comprise n−1=3 interface registers  26   1 - 26   3 , each register  26   q  serving as interface between the controller  21   q−1  of stage q−1 and the controller  21   q  of stage q. Represented moreover in the basic diagram of FIG. 2 is a register  26   0  serving as interface between the controller  21   0  of stage  0  and the environment of the sorting device. The commands sent to the sorting device are written to this register  26   0 , as are the responses supplied by the sorting device. In practice, this register  26   0  can belong to the same circuit as the controller  21   0  of the upper stage of the tree. 
     With reference to FIG. 3, each register  26   q  is made up of four locations respectively containing: 
     a command code A q  designating the nature of the command propagated from the root to the leaves of the tree; in the following account, the commands A q  will be regarded by way of example as coded on two bits as follows: A q =00 for no modification of the contents of the tree onwards of stage q, A q =01 for a command to insert a new element, A q =11 for an exchange command consisting in extracting from the tree the element having the smallest sort key at the same time as a new element is inserted therein (the straightforward extraction of the element having the smallest sort key is treated as the exchanging of this element with an element having an infinite sort key), and A q =10 for a command to reinitialize the contents of the tree onwards of stage q; 
     a sort key B q  transmitted from stage q−1 to stage q upon an insertion or exchange command, or from stage q to stage q−1 upon an exchange command; 
     a reference C q  associated with the sort key B q  and forming with the latter an inserted or exchanged data element; 
     an identification D q  composed of q−1 bits (this identification does not exist in the register  26   0 ), designating the node of stage q−1 from which the command A q  originates. More precisely, the identification D q  consists of the q−1 lowest order bits of the binary representation of the number of node i of stage q−1 from which the command A q  originates, that is to say i=1D q  to the base  2 . 
     To insert a new element into the tree, the command A 0 =01 and this new element B 0 , C 0  are written to the register  26   0 , and the command is then propagated from the root to the leaves of the tree. To make an exchange, the command A 0 =11 and the element B 0 , C 0  to be inserted into the register  26   0  (with B 0 =∞ in the case of a straightforward extraction) are written, and then the element having the smallest key is then fetched into the locations B 0  and C 0  of the register  26   0 . 
     The operations performed by each controller  21   q  are represented in the flowchart of FIGS. 4A,  4 B and  4 C. To execute these operations, each controller  21   q  is made in the form of a suitably programmed network of fast logic gates. Since the operations are essentially reads/writes, incrementations/decrementations and comparisons of binary-coded variables, this programming of the network of gates poses no problem. 
     The command A q  is firstly read from the register  26   q  (step  100 ) and then evaluated (steps  101 ) so as to identify the type of command. 
     In the case of no modification (A q= 00), the controller  21   q  simply writes the same command A q+1 =00 to the next register  26   q+1  (step  102 ). 
     In the case of a reset command (A q =10), the identification D q  of the parent is assigned to the variable s (step  103 ), and the controller  21   q  initializes the two child nodes, the binary representations of whose numbers are 1s0 and 1s1, while setting their sort key to infinity and placing the value 0 in the associated differential counter Δ(1s) (step  104 ), before propagating the command A q+1 =00 at step  102 . In the particular case of stage  0 , reset consists merely of writing K(1)=∞. 
     When the command A q  read from the register  100  refers to the insertion of a new element B q , C q  from a parent node 1D q  (A q =01), these parameters B q , C q  and D q  are read respectively by the controller  21   q  and assigned to variables k, r and s in step  105 , and then the differential counter Δ(1s) associated with the children of the identified node is assigned to the variable δ in step  106 . 
     If δ&lt;0 (comparison  107 ), the right-hand child has a larger number of descendants than the left-hand child, and among the descendants of the left-hand child there is certain to be at least one node capable of receiving the new element, so that the insertion command will be propagated to the left-hand child. The bit t is then taken equal to 0, and the variable δ incremented by one unit in step  108 . Conversely, if δ≧0, the bit t is taken equal to 1 and the variable δ decremented by one unit in step  109  so as to propagate the insertion command to the right-hand child. In step  110 , the sort key K(1st) and the reference R(1st) of the data element contained in the processed node, that is to say that to which the command is propagated, are read and assigned respectively to the variables k′ and r′. 
     If k&lt;k′ (comparison  111 ), the processed node contains a larger sort key than the data element to be inserted, so that the element w, x which will be propagated to stage q−1 is taken, in step  112 , equal to that k′, r′ read from the processed node. If k′≦k, the element to be transmitted w, x is taken, in step  113 , equal to that k, r read from the register  26   q  in step  113 , then the variables k, r respectively receive the values of the variables k′, r′. 
     If the key w of the data element to be propagated is infinite (comparison  114 ), this is because the insertion command need no longer be propagated. The processor  21   q  then gives the value 10 (reinitialization) to the variable v′ in step  115 . If the key w to be transmitted is finite, the variable v′ receives the value 01 in step  116  so as to indicate an insertion command. The processor  21   q  can subsequently fill the register  26   q−1  by writing A q+1 =v′, B q+1 =w, C q+1 =x and D q+1 =st thereto in step  117 . 
     After step  117 , the processing of the insertion command no longer requires the controller  21   q  to access its interface registers  26   q ,  26   q+1 , but merely the memory area  20 q which it is processing. In step  118 , it updates the differential counter Δ(1s) by writing thereto the new value of the variable δ. Next, in step  119 , it updates the data element of the processed node by writing thereto K(1st)=k and R(1st)=r. 
     To complete the processing of the insertion command, it then only remains for the controller  21   q  to update the value of the steering bit F(1s) associated with the processed node  1 st. The controller  21   q  first reads the sort key K(1st) of the data element contained in the sister node of the processed node, and assigns it to the variable k′. The variable f, which will be written to the location  23  containing the steering bit F(1s) in step  126 , is taken equal to 1 in step  124  (steering towards the right-hand child) if the comparisons  121 ,  122 ,  123  show that t=0 and k′≦k, or that t=1 and k≦k′. In the contrary case, we take f=0 in step  125 . 
     After step  126 , the processor  21   q  has finished processing the command A q , and can return to step  100  to process the next command originating from the register  26   q , 
     When the command read from the register  26   q  refers to the exchanging of a data element B q , C q  from a parent node  1 D q  of stage q−1 (A q =11), these parameters B q , C q  and D q  are read and assigned respectively to the variables k, r and s in step  130 , and then the value of the steering bit F(1s) associated with the two children of the identified node is assigned to the bit t in step  131 . The data K(1st), R(1st) read from the processed node  1 st are then assigned to the variables k′ and r′ in step  132 . 
     If the processed node contains a sort key greater than that of the data element read from the register  26   q  (k&lt;k′ during the comparison  133 ), the exchange command need no longer be propagated to the lower stages of the tree, so that the command v′ which will be written to the register  26   q+1  is taken equal to 00 (no modification) in step  134 . In this step  134 , the data element w′, x′, which will be returned to the register  26   q , is moreover taken equal to that k, r which has the smallest sort key. If the comparison  133  shows that k≧k′, step  134  is replaced by a step  135  in which the processor  21   q  takes w′=k′, x′=r′ and v′=11 (propagation of the exchange command). 
     The processor  21   q  then proceeds to step  136  where it writes the element w′, x′ to the locations B q  and C q  of the interface register  26   q . 
     To propagate the command, the controller  21   q  then executes step  137 , where it writes to the interface register  26   q+1 : A q+1 =v′, B q+1 =k, C q+1 =r and D q+1 =st. 
     If the propagated command is not an exchange command, that is to say if the comparison  138  shows that v′≠11, the processing of the exchange command by the controller  21   q  is terminated after the write step  137 . Otherwise, the processor  21   q  goes to step  139  where it examines whether the key k which it has transmitted to stage q−1 is infinite or not. 
     If the comparison  139  shows that k=∞, then the exchange command is in fact a straightforward extraction command and it is necessary to update the differential counter Δ(1s) associated with the processed node. The value of this differential counter is firstly read and assigned to the variable δ in step  140 . If the controller  21   q  has processed a left-hand child (t=0 during the comparison  141 ), the variable δ is decremented by one unit in step  142 , while it is incremented by one unit in step  143 , in the contrary case. The differential counter Δ(1s) is then updated in step  144  according to the new value of the variable δ. 
     Given that the exchanging of two elements each having a finite sort key does not affect the values of the differential counters, steps  140  to  144  are not executed if the comparison  139  shows that the key transmitted k is finite. 
     The processor  21   q  then resumes the processing of the exchange command in step  145  by reading the data element B q+1 , C q+1  which the controller  21   q+1  has returned (during its step  136 ) to the register  26   q+1 , and by assigning this returned element to the variables k and r. The processing of the command subsequently terminates via steps  119  to  126  such as described above. 
     The flowchart of FIGS. 4A-4C has been presented in the case of any stage q. Of course, a few adaptations are necessary in respect of the first stage q=0 and the last stage q=n−1. Thus, for q=0, the processed node  1 st is understood to be always the root of the tree, steps  106 - 109 ,  118 ,  120 - 127 ,  131  and  139 - 144  possibly being omitted. Given that it is not necessary to provide a register  26   n  downstream of the last controller, steps  110  to  117  can be omitted as regards the last stage n−1, as can steps  102 ,  137  and  145  and also, in respect of exchange only, step  119 . 
     The temporal organization of the parallel working of the successive controllers is conditioned by the sharing of the access to the interface registers  26   q , Indicated in FIGS. 4A and 4B is the instant α q  at which the controller  21   q  has finished writing to the register  26   q+1  the command which it transmits as well as the associated parameters (after step  102 ,  117  or  137  depending on the type of command), as well as, in the case of an exchange command, the instant β q  at which the controller  21   q  has finished writing to the register  26   q  the data element B q , C q  which it returns to the controller  21   q−1  Moreover, α′ q  denotes the instant at which the controller  21   q  begins reading a new command from the register  26   q  (immediately before step  100 ), and β′ q  denotes the instant at which the controller  21   q  begins reading from the register  26   q+1  the data element returned by the controller  21   q+1  in the case of an exchange command (immediately before step  145 ). To obtain correct pipeline operation, it is sufficient to devise the controllers in such a way that, for each command, we have α q ≦α′ q+1  and β q ≦β′ q−1 . 
     To satisfy these two conditions, the controllers  21   q  can be asynchronous or synchronous. In the first case, pipeline operation is ensured with the aid of acknowledgement signals exchanged between the controllers. After having executed its step  136 , the controller  21   q  sends an acknowledgement signal to the controller  21   q−1  which then knows that it can proceed to its step  145  and to the further processing of the exchange command. Moreover, after having executed step  102  or  137  or  117 , the controller  21   q  sends an acknowledgement signal to the controller  21 q +1  which then knows that it can begin processing the command by commencing its read step  100 . 
     Synchronous operation of the controllers  21   q  will often be more convenient to implement in the case where the controllers are constructed from networks of logic gates. In this case, the organization of the pipeline is illustrated by the timing diagrams of FIG.  5 . 
     In this figure, each of the four lines illustrates the operation of the controller of one of the stages. The letters RD and WR above the line relating to stage q respectively represent a read and a write performed by the controller  21   q  from/to the register  26   q , while these same letters located below the line respectively indicate a read and a write from/to the register  26   q+1 . The arrows between stages thus represent transfers of command and of parameters by means of the pipeline registers. The hatched intervals represent the instants at which the controller  21   q  is working on the memory area  20   q  which it controls. 
     The period θ 1  indicated in FIG. 5 determines the rate at which the sorting device can receive new elements and deliver the elements having the smallest sort keys. It corresponds to the duration required by each controller in order to process the set of instructions relating to a command. It can be seen that this period θ 1  is substantially shorter than the duration of the cycle θ 2  which is necessary to re-establish the ordering rule throughout the sort tree after a new command has begun to be processed. In the example represented in FIG. 5, the first period θ 1  corresponds to the exchanging of the element located at the root of the tree with another element which is to be placed in stage  1  (that is to say, in the case of FIG.  2 , its key lies between  25  and  38 ), and the second period θ 1 , corresponds to the insertion of a new element up to stage  2  (the key is greater than or equal to that of the element introduced during the preceding exchange operation). 
     It is further noted that the response time θ 0 =β 0 −α′ 0  required by the device to return the data element having the minimum sort key to the register  26   0  corresponds to around one-third of the period θ 1 . 
     To minimize the period θ 1 , and hence maximize the rate of operation of the sorting device, it is beneficial to homogeneously intersperse the processing operations performed by the controllers within the intervals separating the instants at which they access their interface registers. This can be achieved by moving the processing of certain instructions of the flowchart of FIGS. 4A to  4 C. If, for example, before the instants β′ q  there are timespans  146  (FIG. 5) in which the controller q must wait for the controller  21   q+1  to have finished executing its series of instructions  130 - 136  before reading the result thereof from the register  26   q+1 , at least some of this timespan can be filled by executing other instructions, and this will make it possible to save time elsewhere. Thus, for example, in the case of FIGS. 4A-4C, the reading  120  of the sort key of the sister of the processed node could be performed before step  145  in an exchange operation and after step  118  in an insertion operation. This type of optimization depends largely on the choices of architecture which are made for programming the logic gate networks. 
     In the above description, the case was considered in which each of the controllers is associated with a single stage of the binary tree, access to which is reserved therefor, thus affording the device the best speed performance. The complexity of the device, measured as the number of logic circuits (controllers  21   q ) necessary for its operation, is then n, that is to say the logarithm of the maximum number of elements to be sorted. 
     This complexity can be reduced, at the cost of a corresponding decrease in the speed of the device, by associating several consecutive stages of the tree with some at least each of the controllers (i.e. m&lt;n), instead of just a single stage. The number of stages per controller is not necessarily identical for all the controllers. In particular, if the controller associated with stage  0  at least also carries out other functions in connection with the environment of the sort tree, provision may be made for this controller to manage a smaller number of stages than the others. 
     In the case in which a controller is associated with several stages of the tree, the propagation of a command along these stages is processed sequentially by this controller. 
     As FIG. 6 shows in the case of a controller  21   q,p  associated with stages q to q+p−1 of the tree, only the interface registers  26   q ,  26   q+p  between the stages associated with different controllers constitute pipeline registers in respect of the parallel operation of the successive controllers. The other registers  26   q+1 , . . . ,  26   q+p−1  are accessible only by the controller  21   q,p . They may form part of the logic circuit constituting this controller  21   q,p , or else form part of the memory module reserved for this controller and comprising stages q to q+p−1. 
     It will be noted that it is possible to dispense with the differential counters Δ(i) in the stages of the binary tree which are associated with the m-th controller. Let us assume that this latter controller is associated with the p stages n−p to n−1 (1≦p&lt;n−1). When an insertion command A n−p =01 is read from the pipeline register  26   n−p  the parent from which this command originates is the node  1 D n−p  identified in this register. If, for each of the 2 n−p−1  possible parents, the last controller keeps up to date a respective list of free leaves forming part of the descendance of this parent node, then the last controller can process the insertion command by propagating it sequentially from stage n−1 towards stage n−p starting from a free leaf belonging to the list associated with the parent node identified in the field D n−p  of the pipeline register. In each of these lists, each of the leaves can be simply designated by p bits which, together with the n−p−1 bits of the identification D n−p  identify the leaf unambiguously. A simple way of keeping this list consists in organizing it in last-in first-out (LIFO) mode. The last controller can also propagate the insertion command from stage n−p towards stage n−1, given that the p bits designating a free leaf on the basis of an identified parent can be used at each stage to steer the propagation of the insertion command. 
     In the final analysis, the sorting device of the type illustrated by FIGS. 2 to  6  can be constructed by providing just 2 n−p−1 −1 differential counters Δ(i) respectively associated with the pairs of nodes  2   i  and  2   i +1 of the tree for i ranging from 1 to 2 n−p−1 −1. 
     FIGS. 7 to  11  illustrate another embodiment of a sorting device. 
     To facilitate the account, the case will again be considered in which each controller  21   q  is associated with a single stage q of the binary tree (m=n). However, it will be understood that, as before, the architecture of this sorting device is easily transposable to the case in which at least one of the controllers is associated with several stages (m&lt;n). 
     Unlike the exemplary embodiment described earlier, that of FIGS. 7 to  11  does not use differential counters to propagate the insertion commands from the root to the leaves of the tree. Each memory module  20   q  corresponding to a stage q of the tree thus comprises nodes  2   q  to  2   q+1 −1 and the locations  23  for receiving the steering bits F( 2   q−1 ) to F( 2   q−1 ), but no locations  25  for receiving differential counters, as FIG. 7 shows. 
     Each interface register  26   q  comprises, in addition to the four locations containing the parameters A q , B q , C q  and D q  defined earlier, an additional location which receives a bit E q  which designates, during the propagation of an insertion command from a node  1 D q  of stage q−1, the child node of stage q to which this command is propagated. Thus, if E q =0, the insertion command is propagated to the left-hand child  1 D q   0 , while, if E q =1, the insertion command is propagated to the right-hand child  1 D q 1. 
     In the register  26   q , the identification D q  of the parent node and the bit E q  designating the child node consist of the q highest order bits of the contents G p  of a leaf designation field of n−1 bits. The contents G q  of this leaf designation field designate, during the propagation of an insertion command, one of the free leaves of the binary tree towards which this command is propagated. The binary representation of this free leaf is 1G q . Given that the leaf designated is free, the inserted element will definitely be able to find its place on the path from the root of the tree to this designated free leaf, on condition that no other insertion command to this same leaf is currently propagating downstream of the binary tree. 
     To fulfil this condition, the leaf designation field of the interface register  26   1  between stages  0  and  1  receives its value G 1  from the controller  21   n−1  associated with the last stage of the tree. The controller  21   n−1  keeps a first list of free leaves, for example by means of a shift register  30  such as that shown diagrammatically in FIG.  8 . This register contains a number n′ of locations of n−1 bits, and performs a shift operation at each command period θ 1 . Any leaf towards which an insertion command may perhaps be propagating within the binary tree forms part of this first list of n′ free leaves. So long as the command A n−1 read by the last controller from the interface register  26   n−1  is not an insertion command (A n−1 ≠01) the shift register  30  is looped back on itself as shown by FIG. 8, so that it delivers the same leaf designation every n′ periods θ 1 . This designation G 1 , which is then known to be different from each of those of the leaves towards which insertion commands may perhaps be propagating within the tree, is written to the corresponding field of the interface register  26   1 . If by contrast an insertion command A n−1 =01 reaches the last stage of the tree, then a new free leaf P, extracted by the last controller from a second list of free leaves in a manner which will be explained later, is introduced into the shift register  30  and into the interface register  26   1 . 
     To explain this manner of operation, FIG. 9 enlists the timing diagrams of FIG. 5, in a simplified form, in the case in which the device processes in consecutive fashion commands for inserting new elements into the tree. In this FIG. 9, each arrow tip designates an instant α′ q  at which a controller  21   q  begins to process an insertion command. Thus, at the instants α′ 0 , the controller  21   0  receives the pertinent commands and parameters A 0 , B 0 , C 0  from the environment of the device, and at the instants α′ q  with q≧1, the controller  21   q  receives the commands and parameters A q , B q , C q  and G q  in the register  26   q  and commences the corresponding processing operations. In the exemplary temporal organization represented in FIG. 9, each insertion command for which the last controller  21   n−1  has written the corresponding designation G 1  of a free leaf to the register  26   1  reaches this last controller in the register  26   n−1  after two periods θ 1 . Consequently, in this example, it is sufficient to take n′=2 locations in the shift register  30 . 
     In this same example (see also FIG.  1 ), FIG. 8 shows the n′=2 leaves  9  and  13  (designated by 001 and 101 respectively since the binary representations of the numbers  9  and  13  are  1001 and  1101 ) contained in the list kept in the register  30 . The leaf  9  has therefore been designated in the field G 1  during the penultimate command. If this command refers to the insertion of a new element and culminates at leaf  9  (that is to say A n−1 =01 in the current period of operation of the last processor), the leaf  9  is deleted from the list and from the register  30  and is replaced by a new leaf ( 10 ,  11  or  15  in the case of FIG. 1) designated by P. Otherwise, said penultimate command either does not refer to an insertion, or refers to the insertion of a data element which has found its place upstream of stage n−1, so that the leaf  9  is retained in the register  30  and is again designated in the field G 1  for the next command. 
     In practice, the number n′ shall always be less than the number n of stages in the binary tree. Given that this embodiment of the sorting device implies that at each instant the binary tree has at least n′ free leaves, the maximum number of data elements which the device is capable of sorting is reduced, as compared with the device described earlier, by an amount which is always less than  2 n′, so that the sorting capacity of the device is not significantly affected when the number of stages is not too small. If, for example, the device comprises n=12 stages with n′=4, it can sort up to N=4095elements in the case where differential counters are used, and up to N=4088 elements in the case where lists of free leaves are used, the difference between these two values of N not being significant. 
     FIGS. 10A and 10B, which should be supplemented with FIG. 4C, show a flowchart similar to that of FIGS. 4A to  4 C (the same numerical references have been employed to designate similar steps), and detail the operations performed by a controller  21   q  of the type represented in FIG. 7, with q&lt;n−1, during the processing of a command. 
     As compared with the flowchart of FIGS. 4A,  4 B and  4 C, that of FIGS. 10A,  10 B and  4 C has been simplified by deleting all the operations referring to the differential counters. In steps  105  and  117  executed in the processing of an insertion command, the whole of the leaf designation field G q  or G q+1  is read or written from/to the interface register  26   q  or  26   q+1 , rather than just the identification of the parent node D q  or D q+1 . A simplification of the structure of the controllers and a reduction in the memory space which each of them must respectively be capable of accessing are obtained, as compared with the previous example. 
     FIGS. 11A and 11B, which should be supplemented with FIG. 4C, show the operations performed by the last controller in relation to stage n−1 of the tree. Step  150 ,  151  or  152 , executed between the instants β n−1  and α n−1  corresponds to the writing, to the leaf designation field of register  26   1 , of the n−1 lowest order bits G 1 =T(i) of the number of the leaf of rank i (0≦i&lt;n′) in the list of free leaves corresponding to the contents of the shift register  30  illustrated in FIG.  8 . The processing of each of the commands in relation to the last stage n−1 terminates in all cases by an incrementation, modulo n′, of counter i in step  153 , this corresponding to a shift operation in the register  30 . 
     The controller  21   n−1  also keeps a second list of free leaves, which it manages for example in last-in first-out (LIFO) mode. The first leaf of this second list is designated by a pointer P with n−1 bits stored in a register of the last controller or in its memory area  20   n−1  The binary representation of the number of this first leaf is 1P. Each leaf of the second list contains a data element whose sort key is infinite, and the portion of memory corresponding to the associated reference is for example used to store a continuation pointer equal to the designation on n−1 bits of the next leaf in the second list (the portion corresponding to the key could also be used if one bit is reserved to identify the infinite keys). 
     When an insertion command reaches the controller of the last stage in the interface register  26   −1  (A n−1 =01), the free leaf designated by G n−1  must be filled so as to contain the new data element. Consequently, steps  110  to  117  of the flowchart of FIGS. 10A and 10B are unnecessary. The reading step  105  is followed by a step  155  in which the controller  21   n−1  reads from the variable h the continuation pointer R(1P) contained in the memory portion corresponding to the reference of the element contained in the first free leaf of the second list (step  155 ). In the next step  156 , the controller  26   n−1  updates the two lists of free leaves. It removes the free leaf designated by G n−1  from the first list and replaces it, in the area T(i), by the pointer P of the first leaf of the second list; it then replaces this value P by that of the pointer read in step  155 . The processor  21   n− 1 finishes processing the insertion command by going to the aforementioned step  150  and then to steps  119  to  126  of FIG.  4 C and to step  153 . 
     To process an exchange command (A n−1 =11), the controller of the last stage firstly executes steps  130  to  136  discussed previously. Step  137  is not necessary and is replaced by the aforementioned step  151 . If the sort key k=B n−1  proposed in exchange from stage n−2 is larger than that K(1st) read from the processed leaf (v′=11 during comparison  138 ), this key k is compared with infinity in step  139 . If this key k is finite, the processing of the exchange command terminates via steps  119  to  126  of FIG.  4 C and via step  153 . Otherwise, the command refers to a straightforward extraction and frees a previously occupied leaf. In step  157 , this leaf is updated by writing thereto an infinite sort key and, by way of reference, the value P of the pointer of the first leaf of the second list. The associated steering bit F(1s) receives the value complementary to that read in step  131 . Before passing to the final step  153 , the controller  26   n−1  finishes processing the extraction command in step  158  by updating the pointer P of the first leaf of the second list with the binary designation st of the freed leaf. 
     On initialization of the device according to FIGS. 7 to  11 , the two lists of free leaves are for example initialized as follows: T(i)=i, to the base  2 , for 0≦i&lt;n′; P=n′, to the base  2 ; and R( 1   i )=i+1, to the base  2 , for n′≦i&lt;2 n−1 . 
     In the exemplary implementation illustrated by FIGS. 8,  11 A and  11 B, the last controller  21   n−1  keeps the “first list” and the “second list” by means of a shift register  30  and an LIFO stack. It will be noted that other logic organizations of comparable complexity could be adopted. For example, the controller  21   n−1  could keep a logic queue managed in first-in first-out (FIFO) mode, containing the numbers of the free leaves, while being assured that this FIFO queue always contains at least n′ free leaf numbers. Under these conditions, the “first list” consists of the last n′ locations of the queue, and the “second list” of the preceding locations of the queue. 
     In the sorting devices described above, the order relation according to which the keys are sorted, that is to say compared with one another in steps  111 ,  122 ,  123  and  133 , corresponds to the ascending order of the natural integers. It will be understood that any order relation for which comparisons are easily made by means of simple logic circuits could be used to sort the elements in such a device. 
     If, for example, each sort key K(i) is a time tag defining a future instant at which it will be required to fetch the corresponding reference R(i) for the data element, the sorting device can serve as time-out device for controlling the temporal ordering of procedure. The key of the element located at the root of the tree is then compared with the current instant so as to exchange or extract this element if the current instant is attained. 
     If, in this application, the values of time are coded on L bits by a cyclic counter varying from 0 to 2 L −1, the order relation between two L-bit keys k and k′ can be: k≦k′ if and only if 0≦(k′−k) (mod  2   L )&lt;2 L−1 . Stated otherwise, it is sufficient, in step  122  for example, to calculate the difference k′−k on L bits (that is to say ignoring the highest order carry), and to examine whether the bit of order 2 L−1  of this difference is 0 (k≦k′) or 1 (k&gt;k′). The chronological order of the keys is then complied with provided that no key designates an instant more than 2 L−1  earlier or more than 2 L−1 −1 later than the current instant, an easy condition to fulfil by choosing a sufficiently large number L. 
     An application of the sorting devices described above will now be described in an ATM cell spacer. 
     In the spacer of FIG. 12, the policing function is carried out by a module  40  on the basis of the current time and of the identity IdCx of the connection to which each incoming cell pertains. The theoretical emission time TET calculated recursively for each cell is delivered by this module  40  to the spacing controller  41  together with the spacing interval T associated with the connection to which this cell pertains. On the basis of this information and the connection identities IdCx, the spacing controller  41  supervises the management of the cell memory  42  to which −the incoming cells are written and from which the outgoing cells are read, and also manages a pointer memory  43  and the sorting device  44 . 
     NCX denotes the number of virtual connections, numbered from IdCx=1 to IdCx=NCX, which the spacer is capable of processing, and NCE denotes the number of cells which the memory  42  is capable of containing, in predefined locations Ch_cell( 1 ) to Ch_cell(NCE). 
     In the exemplary embodiment represented, the cell memory  42  and the pointer memory  43  consist of two distinct memory modules, the first of which is managed by a unit  46  under the control of the controller  41 . However, it will be understood that other embodiments are possible. In particular, the memories  42  and  43  could be implemented within a single memory module in which accesses would be commanded by the controller  41 . Thus, a two-megabyte RAM memory module makes it possible for example to store up to NCE=32,000 cells pertaining to NCX=4096 different virtual connections together with the pointers necessary for managing the cell memory. 
     FIG. 13 shows a cell-clock signal CKC on the basis of which a sequencer  47  of the spacer supplies the necessary clocking signals to the module  40 , to the spacing controller  41 , to the sorting device  44  and to the manager  46  of the cell memory (FIG.  12 ). The period of this clock signal is 2.7 μs in the case of a 155-Mbit/s link. At each period of this signal CKC, the spacer must be capable of receiving a cell written to the memory  42  (third line of FIG.  13 ), and of emitting a cell read from the memory  42  (fourth line of FIG.  13 ). In the exemplary clocking represented in FIG. 13, each cell period is divided into two successive phases of like duration, the first for receiving any incoming cell and the second for emitting any outgoing cell. 
     In the first phase of each cell period, the spacing controller  41  supplies the manager  46  with a start address a in the cell memory  42 , starting from which this manager commands the writing of the 53 bytes of the incoming cell. In the second phase, the start address a supplied by the controller  41  enables the manager  46  to command the reading of the 53 bytes stored starting from the address a in the memory  42  so as to deliver the outgoing cell. For the purposes of the present account, the address a will be regarded as corresponding to the number of that location Ch_cell(a) of the memory  42  (1≦a≦NCE) to which the cell is written or from which it is read, and that, by convention, a=0 tells the manager  46  that it must not command access to the memory  42  in the relevant phase (no incoming cell, or no cell to be emitted, during the cell period). 
     The cell memory  42  is organized in such a way as to contain, for each virtual connection for which it contains cells, a list of locations at which these cells are arrayed in first-in first-out (FIFO) mode. These lists are managed by the controller  41  by means of the pointer memory  43 . 
     The pointers of the memory  43  comprise a free location pointer Ptr_free, NCX start of list pointers Ptr_start(IdCx) for 1≦IdCx≦NCX, NCX end of list pointers Ptr_end(IdCx) for 1≦IdCx≦NCX, and NCE continuation pointers Ptr_cont(i) for 1≦i≦NCE, respectively associated with the locations Ch_cell( 1 ) to Ch_cell(NCE). Each identity IdCx of a virtual connection for which the memory  42  does not contain any cell at a given instant has its end of list pointer Ptr_end(IdCx) at zero at this instant, indicating an empty list (this is the case for IdCx=2 in the example represented in FIG.  12 ). Otherwise, the number i of the location Ch_cell(i) wherein is stored the cell received least recently according to the connection IdCx is equal to the start of list pointer Ptr_start(IdCx), and the number of that wherein is stored the cell received most recently according to the connection IdCx is equal to the end of list pointer Ptr_end(IdCx). The FIFO list relating to a connection IdCx is chained by means of the continuation pointers: the continuation pointer Ptr_cont(i) associated with a location Ch_cell(i) which is not an end of list designates the location Ch_cell (Ptr_cont(i)) which follows thereon in its list. If the location Ch_cell(i) is an end of list, then we set Ptr_cont(i)=0. In the example of FIG. 12, the list relating to IdCx=1 is Ch_cell(NCE−1), Ch_cell( 1 ) and Ch_cell( 3 ), and that relating to IdCx=NCX reduces to the location Ch_cell( 6 ). The locations of the memory  42  which are not occupied by cells to be emitted form an LIFO list of free locations, the first of which is designated by the pointer Ptr_free and the succeeding ones by the successive continuation pointers. In the example of FIG. 12, the list of free locations is, in output order, Ch_cell( 5 ), Ch_cell(NCE) and Ch_cell( 2 ). 
     The root of the sort tree of the spacer of FIG. 12 is accessible by the spacing controller  41 , which carries out the processing operations of the controller  21   0  associated with stage  0  (FIGS. 2 to  11 ). The data element K( 1 ), R( 1 ) located at the root of the tree can then be stored in the pointer memory  43  as represented, or else in a special register of the controller  41 . The controller  41  exchanges the commands and parameters with stages  1  to n−1 of the sorting device  44  by way of the interface register  26   1  which, in the example considered, is in accordance with that described with reference to FIG.  7 . 
     Each data element supplied to the sorting device  44  consists, in respect of the sort key K(i), of the theoretical time of emission of a cell stored in a location of the memory  42  constituting a start of list, and in respect of the reference R(i), of the identity IdCx of the virtual connection to which this cell pertains. The key K(i) is therefore a time tag which can be defined, as explained earlier, by a cyclic counter of L bits. A counter of L=16 bits for example, plus one bit to distinguish the infinite keys, is suitable for the application to an ATM spacer. The references R(i) can be on 12 bits for NCX=4096 connections. 
     If the spacer is a real spacer, the controller  41  compares the key K( 1 ) present at the root of the tree with the current instant ta, and supplies a=Ptr_start(R( 1 )) to the manager  46  if K( 1 )≦ta so that the cell with the smallest theoretical emission time out of those cells located in starts of lists is emitted. In the case of a virtual spacer, the controller  41  acts in the same way, but without comparison with the current instant: a cell is emitted at each period as soon as K( 1 )&lt;∞. 
     Upon the arrival of a cell pertaining to a connection IdCx whose list of locations is empty (Ptr_end(IdCx)=0), this cell is stored at the location Ch_cell(Ptr_free), the list of free locations is updated, and the controller  41  commands the insertion into the sort tree of a data element whose reference corresponds to this IdCx and whose sort key is the TET calculated by the module  40  for this cell. 
     The arrival of a cell pertaining to a connection IdCx whose list of locations is not empty does not modify the contents of the sort tree, and requires only storage at the location Ch_cell(Ptr_free), and an updating of the list of free locations and of the list associated with the connection IdCx. 
     The emission of a cell pertaining to a connection IdCx whose list of locations contains this one cell entails the straightforward extraction of the corresponding element of the sort tree, which amounts to an exchange with an element having infinite key. 
     The emission of a cell pertaining to a connection IdCx whose list of locations contains one or more cells after this one entails an exchange between the corresponding element of the tree and a new element whose reference corresponds to this IdCx and whose sort key is the theoretical emission time assigned to the cell stored in second position in the list, that is to say at the location Ch_cell(Ptr_cont(Ptr_start(IdCx))). 
     In this latter case, the theoretical emission time forming the key of the new element can be that supplied by the module  40  in respect of the cell stored in the new start of list. It is then useful to store the TET times supplied by the module  40  as and when the cells arrive. However, it is preferable for the controller  41  to recalculate a theoretical emission time for the cell when it supplies the new data element to the sorting device  44 . 
     To this end, the memory  43  contains an array in which are stored the values TT(IdCx) of the spacing intervals T allotted to the various virtual connections IdCx, which values the controller  41  receives from the module  40  when cells arrive according to the connections concerned. When K( 1 )≦ta, the real spacer emits the cell stored in Ch_cell(Ptr_start(R( 1 ))), and commands the exchanging of the element K( 1 ), R( 1 ) located at the root of the sort tree with a new element K( 1 )+TT(R( 1 )), R( 1 ). Stated otherwise, the theoretical time of emission of the cell stored in the new start of list is taken equal to that of the cell emitted plus the time interval TT(IdCx) allotted to the relevant connection. 
     This way of proceeding has two advantages. The first is that if the module  40  assigns, to two consecutive cells pertaining to a connection IdCx, theoretical emission times TET which are more than TT(IdCx) apart on account of their respective arrival times and if the second of these two cells is already written to the memory  42  when the first is emitted, then the theoretical time of emission of the second cell can be advanced relative to that calculated by the module  40  as can the theoretical times of emission of succeeding cells of the connection without impairing the required spacing properties. This avoids needlessly delaying some cells. 
     The second advantage is that the spacing intervals allotted to some connections can be modified dynamically and immediately. When the clogging of the link gives rise to the risk of congestion, the facility can for example increase the spacing interval for some virtual connections. This increase takes effect immediately, including in respect of the cells of this connection contained in the memory  42  which will therefore not be emitted in accordance with their initially calculated TETs. A delay in the application of preventive measures is thus avoided, which delay could lead to the congestion not being avoided. Of course, permission to increase the spacing interval for a connection must be agreed with the source when this connection is established, given that, for the same CDV tolerance and the same behaviour of the source, it increases the probability that cells will be destroyed by the policing function. 
     FIG. 14 shows the operations performed by the controller  41  in the first phase of each cell period, during the time intervals  200  indicated in the second line of FIG.  13 . 
     The first step  201  consists in determining whether an incoming cell reaches the spacer during the cell period in question, and if appropriate in ascertaining the identity IdCx of the connection to which this cell pertains together with the theoretical emission time TET and the spacing interval T supplied for this cell by the module  40 . 
     If no incoming cell is received, the address a=0 is supplied to the manager  46  of the cell memory in step  202 , and then the controller  41  writes a no modification of the contents of the binary tree command (A 1 =00) to the interface register  26   1  in step  203 . 
     If an incoming cell is present, the free location pointer Ptr_free is read from the pointer memory  43  in step  204 , and is assigned to the address a which is supplied to the manager  46  in step  202 . If a=0 (no cell received or more free location in the memory  42 ), the manager  46  does not write to the memory  42  in the current cell period, and the spacing controller  41  executes the aforementioned step  203  so that the contents of the binary tree remain unchanged. Otherwise, the controller  41  goes to the pointer reading step  205 . 
     In step  205 , the number Ptr_cont(a) of the second location of the list of free locations, the number Ptr_start(IdCx) of the start of list relating to the connection IdCx and the pointer Ptr_end(IdCx) of this list are assigned to the variables b, c and d respectively. In step  206 , the array TT of spacing intervals is updated for the connection IdCx according to the value T received from the module  40 , the address a is written to the memory  43  as the pointer to the end of the list of locations which relates to the connection  35  IdCx, the continuation pointer Ptr_cont(a) associated with this location is set to zero to indicate that henceforth we have an end of list, and the free location pointer Ptr_free is updated with the variable b. 
     If the list of locations relating to the connection IdCx was not empty (that is to say if d≠0 during comparison  207 ), no modification of the contents of the sort tree is necessary as explained earlier, so that the spacing controller  41  executes the aforementioned step  203  after having updated the continuation pointer associated with the preceding end of list with the old free location pointer in step  208 : Ptr_cont(d)=a. 
     If the comparison  207  shows that d=0, the controller  41  completes the updating of the list pointers in step  209  by writing Ptr_start (IdCx)=a. It then proceeds to insert the new data element TET, IdCx into the sort tree. The operations which it performs therefor correspond to those performed by the controller  26   0  of stage  0  of the binary tree, that is to say to steps  110  to  119  of the flowchart of FIGS. 10A,  10 B and  4 C. In step  21   0 , the controller  41  assigns to the variables k and r the sort key K( 1 ) and the reference R( 1 ) of the data element read at the root of the tree, and then it compares the key k with the theoretical emission time TET received from the module  40  in step  201  (comparison  211 ). If TET&gt;k, the insertion command must be propagated to stage  1  of the sort tree, so that the controller  41  writes A 1 =01, B 1 =TET and C 1 =IdCx to the pipeline register  26   1  in step  212 , the leaf designation field of the register  26   1  receiving the number of a free leaf G 1  from the last controller  21   n−1  of the sorting device  44 , as indicated in FIG.  12 . 
     If the comparison  211  shows that TET&lt;k, then the new data element TET, IdCx needs to be written at the root of the tree, this being performed in step  216 . Prior to this, the controller  41  propagates a reset command A 1 =10 in the pipeline register  26   1  in step  214  if the sort key k previously located at the root of the tree is infinite (comparison  213 ). Otherwise, the controller  41  writes to the register  26   1  an insertion command (A 1 =01) for the element B 1 =k, C 1 =r previously located at the root in step  215 . 
     As far as the synchronization of the controller  41  with those of the sorting device  44  is concerned, FIG. 14 shows that the instant α 0  corresponding to that which was relevant with reference to FIGS. 5 and 9 occurs after the step  203 ,  212 ,  214  or  215  of writing by the controller  41  to the pipeline register  26   1 . Commencing from this instant α 0 , the controller  21   1  of stage  1  can begin processing the command (instant α′ 1  indicated in FIG.  13 ). 
     FIG. 15 shows the operations performed by the controller  41  in the second phase of each cell period, during the time intervals  300  indicated in the second line of FIG.  13 . 
     The first step  301  consists in reading the sort key K( 1 ) and the reference R( 1 ) of the data element located at the root of the tree, and in assigning them to the variables k and r respectively. The next comparison  302  serves to decide whether a cell is or is not to be emitted. In the case of a real spacer, this step  302  consists in comparing the sort key k with the current time ta. In the case of a virtual spacer, it consists simply in examining whether the key k is finite or infinite. If k&gt;ta (in the case of a real spacer), the controller  41  performs no operation in the second phase of the cell period, except for writing a no modification of the contents of the binary tree command A 1 =00 to the pipeline register  26   1  (step  303 ). 
     If from step  302  it ensues that a cell is to be emitted, the number of the location at the start of list in relation to the connection r, as well as the continuation pointer associated with this location are read from the memory  43  and assigned to the variables a and b respectively in step  304 . The address a can then be supplied to the manager  46  in step  305  so that it emits the cell stored at this address (fourth line of FIG.  13 ). If the list of locations relating to the connection r=R( 1 ) identified in the element located at the root of the tree contained only a single cell, then the variable b is at 0. This is detected by the comparison  306 . In this case, the end of list pointer Ptr_end(r) is set to zero in step  307  to indicate that this list no longer contains any cell, and in step  308  an infinite value is assigned to the theoretical emission time TET which will constitute the sort key of the new element to be exchanged in the binary tree. 
     If b≠0 in step  306 , the list of locations contains several cells, and the variable b is written in step  309  as the start pointer for this list, and, in step  311 , the cell stored in the location Ch_cell(b) receives a new theoretical emission time TET equal to the key k=K( 1 ) read in step  301 , to which is added a variable T taken equal to the spacing interval TT(r) of the relevant connection, read in step  310 . The command (A 1 =11) for exchanging the element K( 1 ), R( 1 ) located at the root of the tree with the new element B 1 =TET, C 1 =r is written to the pipeline register  26   1  in step  312 . 
     The instant α 0  commencing from which the controller  21   1  of the sorting device  44  can begin to process the command is located after step  312  (or step  303 ), as FIG. 15 shows. The spacing controller  41  must wait for the instant β′ 0 ≦β 1  (see FIG. 13) before fetching into the register  26   1  the element returned from stage  1  of the sort tree. In the example illustrated by FIG. 15, the controller  41  updates the list of free locations in the interval [α 0 ,β′ 0 ): in step  313  it reads the free location pointer Ptr_free and assigns it to the variable c; next, in step  314 , it writes Ptr_cont(a)=c and Ptr_free=a to the memory  43 . 
     Once the controller of stage  1  of the tree has returned the element having the smallest key to the register  26   1 , this element is read by the controller  41  in step  315 , and then written to the root of the tree in step  316 . 
     FIG. 16 shows a variant of an ATM cell spacer capable of taking into account priority indices assigned to the virtual connections. This priority index, which is assumed to take its values between 1 and U, is denoted u. The spacer of FIG. 16 comprises U sorting devices  44   (u)  each having a pipeline register  26   1   (u)  between its stage  0  and its stage  1 . The operation of each sorting device  44   (u)  is the same as that described earlier. The root of each binary tree is assumed to be contained in the pointer memory  43  (the remainder of whose contents is not represented in FIG. 16) and to be managed by the spacing controller  41 . The operation of the cell memory  42  and of its manager  46  is the same as previously in respect of the writing and reading of cells at the addresses a supplied by the controller  41 . 
     Each of the sorting devices  44   (u)  processes data elements whose references R (u)  (i) designate identities of virtual connections IdCx having the same priority index u. Among these elements, the device  44   (u)  selects at its root (in the memory  43  in the example represented) an element whose key K (u)  ( 1 ) is minimal. The spacing controller is then devised so as to command the emission of the cell contained in the start of list relating to the connection identified in that of the data elements located in the roots of the trees which exhibits the smallest sort key. In the event of equality between several minimum sort keys K (u)  ( 1 ), the spacing controller  41  picks the connection which has the largest priority index amongst the ex aequos. 
     This management of the priority indices does not significantly complicate the spacing controller  41 . As far as the operations performed on receiving a cell are concerned, the flowchart of FIG. 14 is unchanged, steps  210  to  216  being performed in regard to the sort tree  44   (u)  which corresponds to the priority index u received by the controller  41  at the same time as the connection identity IdCx. 
     As far as the operations performed in the second phase of each cell period are concerned (FIG.  15 ), the steps  301 ,  302  for reading the element located at the root of the tree and for comparing the key of this element with the current time are performed in succession in descending order of priority indices until, for an index u, step  302  shows that the current time has been reached. In this case, steps  304  to  316  are executed without change, writing  312  and reading  315  being performed to/from the register  26   1   (u) , and writing  316  to the root of the sort tree concerned. 
     In the example of FIG. 16, the U sorting devices are distinct. It is noted that these various sorting devices could share their control means, namely their controllers  21   q  and their pipeline registers  26   q . FIG. 17 illustrates such an implementation in the particular case where U=2. 
     In the embodiment of FIG. 17, the U=2 sort trees share the interface registers  26   q  and the stage controllers  21   q . Only their storage stages  20   q   (1) ,  20   q   (2)  (q≧0) are differentiated. The two stages  0  are contained within the pointer memory  43 . For each stage q≧1, the corresponding stages  20   q   (1) ,  20   q   (2)  of the two trees are formed by two distinct areas of the memory managed by the controller  21   q , which are differentiated on the basis of an additional address bit consisting for example of the binary priority index then forming the highest order bit of the field D q  of the pipeline registers. 
     FIG. 18 illustrates the operation of a variant embodiment of the spacer which can be used when the bit rate of the link is not too high (for example for a 155 Mbit/s link). In this variant, the sorting device comprises two controllers, one  21   0,n−p  associated with stages  0  to n−p−1 of the binary tree, and the other  21   n−p,p  associated with stages n−p to n−1 of the binary tree. In this sorting device, the extraction or exchange commands are propagated from stage  0  to stage n−1 as described earlier, while the insertion commands are propagated from stage n−1 towards stage  0 . Consequently, it is unnecessary to provide either differential counters or locations in the interface registers to receive a free leaf designation G q . 
     Each cell period is divided into two phases I and II which correspond for example to the phase of writing any cell to the cell memory and to the phase of reading any cell from the cell memory as indicated in FIG.  18 . At the beginning of the first phase I, the spacing controller examines whether there is cause to insert an element into the sort tree and to exchange or extract an element of this tree. If appropriate, the first controller  21   0,n−p  then begins processing the exchange command from stage  0  to stage n−p−1, and the second controller  21   n−p,p  begins processing the insertion command by propagating it from stage n−1 to stage n−p. To ascertain which leaf to propagate the insertion command from, the controller  21   n−p,p  keeps a list designating all the free leaves of stage n−1, one of them being selected (by an LIFO procedure for example) to serve as start point for the insertion command. 
     In the second phase II, the insertion command is, if necessary, propagated from stage n−p−1 to stage  0  by the controller  21   0,n−p , while the controller  21   n−p,p  propagates, if necessary, the exchange command from stage n−p to stage n−1. 
     The interface register  26   n−p  then serves as pipeline register between the two controllers of the sort tree. Any exchanging of parameters between the two controllers between phases I and II can for example be done by splitting this pipeline register into two (one register for the upward direction and one register for the downward direction), or else by exchanging the parameters in one direction and then in the other in succession. 
     The embodiment illustrated by FIG. 18 can for example be used in the case of a 155 Mbit/s link supporting up to N=4096 virtual connections. The sort tree can then be dimensioned with n=12 and p=8, the first controller  21   0,n−p  supervising stages  0  to  3  possibly being merged with the spacing controller which manages the cell pointers.