A method of assigning objects to processing units

Field of the invention

0001The present invention relates to the field of data processing, and more particularly without limitation, to balancing the assignment of objects in a multi-computing environment.

Background and prior art

0002Various multi-computing architectures are known from the prior art where a plurality of processing units is coupled to form a cluster. Such architectures are used in parallel processing and also in the emerging field of blade computing.

0003Blade computing relies on blade servers, which are modular, single-board computers. An overview of blade computing is given in "<nplcit id="ncit0001" npl-type="s"><text>Architectures and Infrastructure for Blade Computing", September 2002, Sun microsystems</text></nplcit> and "<nplcit id="ncit0002" npl-type="s" url="www.sun.com/servers/entry/blade"><text>THE NEXT WAVE: BLADE SERVER COMPUTING", Sun Microsystems. (www.sun.com/servers/entry/blade</text></nplcit>).

0004A content load balancing blade is commercially available from Sun microsystems ("Sun Fire TM B10n). This blade provides traffic and content management functionalities. Content load balancing is achieved based on URLs, CGI scripts and cookies; server load balancing is achieved based on server loads, response times, and weighted round-robin algorithms.

0005<patcit id="pcit0001" dnum="US20030105903A"><text>US patent application no. 20030105903</text></patcit> shows a web edge server, which comprises a number of blade servers. A switch and an information distribution module are provided for the purpose of balancing. The information distribution module receives an information message, performs processing on the message to determine a destination, and forwards a message toward the determined destination via an internal communications network.

0006<nplcit id="ncit0003" npl-type="s"><text>Leinberger W; Karypis G; Kumar V: "Multi-Capacity Bin Packing Algorithms with Applications to Job Scheduling under Multiple Constraints (TR 99-024)</text></nplcit>" shows algorithms for job scheduling in a 'shared-everything' parallel system.

0007<nplcit id="ncit0004" npl-type="s"><text>Aggarwal G; Motwani R; ZHU A: "The load rebalancing problem</text></nplcit>" deals with the problem of rebalancing processor load. Given a possibly sub-optimal assignment of jobs to processes the purpose of load rebalancing is to reassign jobs to different processes so as to minimize the make span by moving as few jobs as possible.

0008<patcit id="pcit0002" dnum="US20020046316A1"><text>US2002/0046316 A1</text></patcit> shows a method of non-linear constraint optimization in a storage system configuration.

Summary of the invention

0009The present invention provides for a method of assigning objects to processing units of a cluster of processing units. Each one of the processing units has a certain storage capacity and load capacity. The storage capacity of a processing unit determines the maximum aggregated size of objects that can be stored by the processing unit. The load capacity of the processing unit determines the maximum processing load that the processing unit can handle. For example, the load capacity of a processing unit can be indicative of the maximum number of access operations the processing unit can provide. Access operations may comprise both read accesses (select) and write accesses (update, insert, delete) to objects stored on the processing unit. For example the load capacity can be expressed as the maximum number of access operations per time unit the processing units can handle.

0010In order to make maximum usage of the available data processing capacity provided by the cluster of processing units the distribution of the objects over the processing units needs to be balanced. This is accomplished by calculating an index for each object based on object size and object load. For example, the object load is expressed as the expected mean number of access operations per time unit to the object. The objects are sorted by index in order to provide a sequence.

0011In the following it assumed without restriction of generality that the sequence is sorted in descending order. In this instance the procedure for assigning of objects to processing units starts with the first object of the sequence. One or more of the objects of the sequence are assigned to one processing unit in sequential order until a remaining storage capacity and/or a remaining load capacity of that processing unit is too small for consecutive objects of the sequence. When this condition is fulfilled, the procedure is carried out for the next processing unit, whereby the objects that have been previously assigned to the preceding processing unit are deleted from the sequence. This way a minimum number of processing units that are required for handling a given set of objects can be determined.

0012In accordance with the invention the remaining storage capacity of a processing unit is determined by the difference between the storage capacity of the unit and the aggregated size of the objects that have been assigned to the processing unit. Likewise the remaining load capacity of a processing unit is determined by the difference between the load capacity of the unit and the aggregated loads of objects that have been assigned to the processing unit. On the basis of these definitions of the remaining storage capacity and of the remaining load capacity the minimum number of processing units is determined.

0013In accordance with the invention the balancing procedure is performed again in order to further improve the quality of the balancing. For this purpose the largest gap between the aggregated sizes of objects being assigned to one of the processing units and the largest gap between the aggregated loads of objects being assigned to one of the processing units and the load capacity are determined.

0014The size gap is divided by the minimum number of processing units and the result of the division is subtracted from the maximum storage capacity to provide a size threshold level. Likewise, the load gap is divided by the number of processing units and the result of the division is subtracted from the load capacity to provide a load threshold level. When the procedure for assigning the objects to the processing units is performed again, the definition of the remaining storage capacity is the difference between the aggregated size of objects being assigned to the processing unit and the size threshold level whereas the definition of the remaining load capacity is the difference between the aggregated load of the objects being assigned to the processing unit and the load threshold level. As a result of the renewed performance of the assignment procedure, the gap can be substantially reduced.

0015In accordance with the invention the theoretical storage capacity limit is used as a size threshold. This size threshold is obtained by calculating the difference between the total of the storage capacities of the processing units and the total of the sizes of the objects and dividing the difference by the minimum number of processing units. The result of the division is subtracted from the storage capacity which provides the theoretical limit.

0016Likewise the theoretical load capacity limit is used as a load threshold. This load threshold is obtained by calculating the difference between the total of the load capacities of the processing units and the total of the loads of the objects and dividing the difference by the minimum number of processing units. The result of the division is subtracted from the load capacity which provides the theoretical load capacity limit.

0017On this basis the assignment procedure is performed again whereby the remaining storage capacity is defined as the difference between the aggregated size of the objects of the processing unit and the size threshold whereas the remaining load capacity is defined a the difference between the aggregated load of the objects of the processing units and the load threshold. Typically it will not be possible to assign all of the objects to the minimum number of processing units on this basis. If this is the case one or more iterations are performed.

0018For one iteration an excess amount of memory is divided by the minimum number of processing units. The result of the division is added to the size threshold. Likewise an excess load is divided by the minimum number of processing units. The result of the division is added to the load threshold. On the basis of the incremented size threshold and/or load threshold the assigment procedure is performed again. This process continues until all objects have been assigned to the minimum number of processing units. This way the quality of the balancing is further improved.

0019In according with a further preferred embodiment of the invention the size threshold for performing the assignment procedure is varied between the theoretical storage capacity limit and the actual storage capacity. Likewise the load threshold is varied between the theoretical load capacity limit and the actual load capacity. Preferably a new assignment procedure is performed for each permutation of the size threshold/load threshold that can be thus obtained. For each of the resulting assignments of objects to processing units a statistical measure is calculated. This statistical measure is a basis to select one of the assignments for optimal balancing.

0020In according with a further preferred embodiment of the invention the standard deviation or variance of the sum of the indices of objects assigned to a processing unit is used as a statistical measure. The assignment having the lowest overall quality measure is selected.

0021In accordance with a preferred embodiment of the invention the object sizes and object loads are normalised for the calculation of the indices. Preferably an index of an object is calculated on the basis of the sum of the normalised object size and normalised object load and the absolute difference of the normalised object size and normalised object load. Preferably the index is obtained by calculating a linear combination of the sum of the normalised object size and normalised object load and the absolute value of the difference of the normalised object size and normalised object load.

0022In accordance with the invention each one of the processing units is a blade or a blade server. One of the blades can have a program that implements the principles of the present invention in order to perform balancing. This way the number of swap-operations between the blades can be minimised.

0023In accordance with a preferred embodiment of the invention the principles of the invention are implemented in an application program running on a personal computer. The application program is provided with a list of objects and the estimated sizes and loads of the objects that need to be handled by the cluster of processing units. On the basis of the object sizes and the object loads the minimum number of processing units that are required for the processing task are determined. This information can form the basis for a corresponding investment decision of a customer.

0024Data objects, i.e. tables, arrays, lists and trees are distributed to processing units, e.g. blades, in accordance with the principles of the present invention. For example, each one of the processing units runs a data processing task to which the respective objects are assigned.

Brief description of the drawings

0025In the following preferred embodiments of the invention will be described in greater detail by way of example only, by making reference to the drawings in which : <dl id="dl0001"><dt>Figure 1</dt><dd>is a schematic block diagram of a modular computer system having a cluster of blades,</dd><dt>Figure 2</dt><dd>is illustrative of a flow diagram for assigning of objects to blades and for determining the minimum number of blades,</dd><dt>Figure 3</dt><dd>is an example for tables that need to be assigned to blades,</dd><dt>Figure 4</dt><dd>shows the normalised size distribution of the tables of <figref idref="f0003">figure 3</figref>,</dd><dt>Figure 5</dt><dd>shows the loads of the tables in terms of the mean number of read accesses per second,</dd><dt>Figure 6</dt><dd>shows the normalised loads,</dd><dt>Figure 7</dt><dd>shows the normalised sizes and loads per table,</dd><dt>Figure 8</dt><dd>shows a sorted sequence of the tables,</dd><dt>Figure 9</dt><dd>shows the sorted sequence of the tables illustrating the normalised sizes and loads of each table,</dd><dt>Figures 10 to 14</dt><dd>show the assignment of tables to blade 1 of the cluster of blades</dd><dt>Figures 15 and 16</dt><dd>show the assignment of tables to blade 2,</dd><dt>Figure 17</dt><dd>shows the resulting assignment of tables to blades that is obtained on the basis of the method of <figref idref="f0002">figure 2</figref>,</dd><dt>Figure 18</dt><dd>is illustrative of the invention where the procedure of <figref idref="f0002">figure 2</figref> is performed again with lower size and load thresholds,</dd><dt>Figure 19</dt><dd>is illustrative of an alternative of a method where the load and size thresholds are varied iteratively,</dd><dt>Figure 20</dt><dd>is illustrative of an alternative where the size and load thresholds are varied in predetermined steps,</dd><dt>Figure 21</dt><dd>is illustrative of a computer system performing the assignment of objects to blades.</dd></dl>

Detailed description

0026<figref idref="f0001">Figure 1</figref> shows cluster 100 of blades B1, B2, B3, ... BN. Each one of the blades has processor 102 and memory 104. In the example considered here, all memories 104 have the same storage capacity and all blades have the same load capacity. The blades are coupled by a network 106, such as a bus system. The number N of blades of cluster 100 needs to be chosen such that a given number of M objects of varying sizes and loads can be handled.

0027For example, cluster 100 implements a so-called search engine. In this instance identical search processes run on each one of the blades. The assignment of data objects, such as index tables, to blades can be stored in a dispatcher unit (not shown on the drawing) of cluster 100. This way data objects are assigned to blades and data processing tasks running on the blades.

0028<figref idref="f0002">Figure 2</figref> shows a procedure for assigning the objects to blades and to thereby determine the minimum value for N.

0029In step 200 an sorting index is calculated for each one of the M objects. An sorting index of an object is indicative of the amount of blade resources the object requires. The sorting index serves to sort the objects in decreasing order of blade resource requirements.

0030For example the sorting index is calculated on the basis of the sum of the normalised object load and normalised object size plus the absolute value of the difference of the normalised load and size or a linear combination thereof.

0031In step 201 a sorting operation is performed in order to sort the M objects by sorting index. The corresponding object sequence is provided in step 202. In step 204 the index i for the blades is initialised to 1.

0032In step 206 processing of the object sequence starts with the first object of the sequence, i.e. the object having the largest sorting index value. The first object of the sequence is assigned to a first one of the blades, i.e. blade B1, in step 206. In step 208 the first object that has been assigned to blade B1 is deleted from the sequence.

0033In step 210 the sizes of the objects that have already been assigned to blade B1 are summed up in order to provide an aggregated object size of blades B1. Next the size of a gap G_S between the aggregated object size of blade B1 and a size threshold T_S is calculated. When the assignment procedure of <figref idref="f0002">figure 2</figref> is carried out the first time, the size threshold T_S is the storage capacity of one of the blades.

0034In step 211 the loads of the objects that have already been assigned to blade B1 are summed up in order to provide an aggregated load of blade B1. Next a gap G_L between the aggregated object loads of blade B1 and a load threshold T_L is calculated. When the assignment procedure of <figref idref="f0002">figure 2</figref> is carried out the first time, the load threshold T_L is the load capacity of one of the blades.

0035In step 212 it is determined whether there is a next object in the ordered sequence that fits into both gaps G_S and G_L. In other words, a consecutive object following the first object in the object sequence that has an object size small enough to fit into gap G_S and at the same time has an object load that is small enough to fit into G_L is searched.

0036The next consecutive object in the sequence that fulfils this condition is assigned to blade B1 in step 214 and deleted from the sequence in step 216 before the control goes back to step 210.

0037If there is no such object that fulfils the condition of step 212, step 218 is carried out. In step 218 it is determined whether all objects have already been assigned to blades. In other words, in step 218 it is checked whether the sequence is empty. If this is not the case the index i is incremented in step 220 and the control goes back to step 206 in order to assign remaining objects of the sequence to the next blade B2.

0038If the contrary is the case the index i is the minimum number N of blades that are required to handle the M objects, i.e. i =N. This number is output in step 220. The minimum number N of blades that are required to handle the M objects can be a basis for an investment decision for purchasing of a corresponding number of blades. The assignment of objects to blades is output in step 224 in order to visualise the quality of the object size balancing.

0039<figref idref="f0003">Figure 3</figref> shows an example of objects to be assigned to blades. In the example considered here the objects are a number of 20 different tables having various sizes between 50MB and 3,566MB as indicated in <figref idref="f0003">figure 3</figref>. For example, table 1 has a size of 3,250MB, table 2 has 250MB, table 3 has 750MB, etc. The table sizes can be actual table sizes or average table sizes that have been obtained by monitoring a real-life data processing system. Alternatively the table sizes are estimates for the purpose of planning cluster 100 (cf. <figref idref="f0001">figure 1</figref>).

0040<figref idref="f0004">Figure 4</figref> shows the normalised table sizes of the tables of <figref idref="f0003">figure 3</figref>. The normalised size of a table is obtained by dividing the table size by the maximum storage capacity of one of the blades.

0041<figref idref="f0005">Figure 5</figref> shows the loads of the tables. In the preferred embodiment considered here the mean number of access operations (selects) per second that are performed or expected to be performed with respect to a table is used as a load indicator. In the example considered here the load as expressed by the number of read accesses per second to a table varies between five read accesses per second (table 6) and 950 read accesses per second (table 8). The table loads given in <figref idref="f0005">figure 5</figref> can be actual table loads or average table loads that have been obtained by monitoring a real-life data processing system. Alternatively the table loads are estimates or simulation results for the purpose of planning cluster 100.

0042<figref idref="f0006">Figure 6</figref> shows the normalised table loads. The normalised table load of a given table is obtained by dividing the number of read accesses per second of that table by the load capacity of one of the blades.

0043In the preferred embodiment considered here the storage capacity of a blade is 4,096MB. Hence a normalised table size of one indicates that the table has the absolute maximum size that can be handled by a given blade hardware.

0044The load capacity of a blade is the maximum possible access load that can be handled by a core engine running on one of the blades in the example considered here. This maximum value can be determined by benchmarks, by experiment or simulation. The load capacity depends on various parameters such as hardware and software characteristics and network bandwidth if a network is used to perform the table accesses. In the preferred embodiment considered here, the load capacity of one of the blades is 1,000 read accesses per second. For the purpose of explanation only read accesses are considered here. However, other typical data processing tasks, such as accesses that involve changes to the data, can also be taken into consideration for determining load capacity and table loads.

0045<figref idref="f0007">Figure 7</figref> shows a diagram illustrating the various normalised table sizes and table loads. As apparent from <figref idref="f0007">figure 7</figref> there are tables that require only a minimum amount of blade resources, especially table 13, that has a small table size and a low table load. On the other hand there are tables that require a large amount of blade resources as they have both large table size and high table load. The distribution of tables to blades aims to balance the usage of the respective blade resources with respect to both size and load. The two constraints, i.e. size and load, are combined into a common sorting index that provides an objective measure for the amount of blade resources a given table requires.

0046The following definition of the sorting index is used for the purposes of explanation only and without restriction of generality:<maths id="math0001"><math display="block"><mi>Sorting index</mi><mo mathvariant="normal">=</mo><mi mathvariant="normal">W</mi><mo>⁢</mo><mn mathvariant="normal">1</mn><mo mathvariant="normal">*</mo><mfenced><mi>size</mi><mo mathvariant="normal">+</mo><mi>load</mi></mfenced><mo mathvariant="normal">+</mo><mi mathvariant="normal">W</mi><mo>⁢</mo><mn mathvariant="normal">2</mn><mo mathvariant="normal">*</mo><mi>absolute value</mi><mo>⁢</mo><mfenced><mi>size</mi><mo mathvariant="normal">-</mo><mi>load</mi></mfenced><mo mathvariant="normal">,</mo></math><img file="EP1533699B1_D0001.tif" /></maths> where size is the table size, load is the table load W1 is a weighting factor for (size + load) and W2 is a weighting factor for the absolute value of the difference of size and load.

0047For the purposes of the following example the weighting factors W1 and W2 are set to one without restriction of generality.

0048In this case the above expression evaluates as follows: <ul id="ul0001" list-style="none" compact="compact"><li>If size > load: sorting index = 2 * size</li><li>If size = load: sorting index = 2 * size = 2 * load</li><li>If size < load: sorting index = 2 * load.</li></ul>

0049<figref idref="f0008">Figure 8</figref> shows a sorted sequence in descending order of the sorting indices of the tables. The table that has the largest sorting index value and thus requires the largest amount of blade resources is table 8, whereas the table having the smallest sorting index value and which does require the lowest amount of blade resources is table 13 as apparent from <figref idref="f0008">figure 8</figref>.

0050<figref idref="f0009">Figure 9</figref> shows the sorted sequence of <figref idref="f0008">figure 8</figref> illustrating the normalised table sizes and table loads of the individual tables.

0051<figref idref="f0010">Figure 10</figref> illustrates the first iteration for assigning tables to blades based on the ordered sequence as shown in <figref idref="f0008">figure 8</figref> and <figref idref="f0009">9</figref>. It is assumed that each one of the blades has a storage capacity that corresponds to a normalised size threshold T_S = 1 and a load capacity that corresponds to a normalised load threshold T_L.

0052The assignment procedure starts with the first table of the sorted sequence, i.e. table 8. Table 8 is assigned to blade 1 as illustrated in <figref idref="f0010">figure 10</figref>. This results in a normalised gap G_S of unused storage capacity G_S = 0,6948 and a gap G_L of unused load capacity G_L = 0,05.

0053Next consecutive tables in the ordered sequence are searched that have table sizes and table loads that fit into the respective gaps G_S and G_L. These are tables 6 and 13. As table 6 precedes table 13 in the ordered sequence, it is assigned to blade 1 as illustrated in <figref idref="f0011">figure 11</figref>.

0054Next the aggregated table size and the aggregated table load of blade 1 is updated as illustrated in <figref idref="f0012">figure 12</figref>. This results in a updated normalised gap G_S = 0,6362 and an updated normalised gap G_L = 0,045 as illustrated in <figref idref="f0013">Fig. 13</figref>. Now tables of the ordered sequence that are consecutive to table 8 that fit into both gaps G_S and G_L are searched.

0055The only table that fulfils both conditions is table 13 which is thus assigned to blade 1 as illustrated in <figref idref="f0013">figure 13</figref>. The result is shown in <figref idref="f0014">figure 14</figref>. The updated normalised gap G_S is 0,6167 and the updated normalised gap G_L is 0,03. No table within the ordered sequence satisfies both constraints.

0056As there remain unassigned tables in the sequence an additional blade 2 is required as illustrated in <figref idref="f0015">figure 15</figref>. By definition the first table of the remaining ordered sequence, i.e. table 20 is assigned to blade 2. This results in normalised gaps G_S = 0,1294 and G_L = 0,5600. The only table that satisfies both constraints is table 12 which is thus moved onto blade 2 as illustrated in <figref idref="f0015">figure 15</figref>.

0057<figref idref="f0016">Figure 16</figref> illustrates the result of this assignment. The updated normalised gap G_S is 0,0024 and the updated normalised gap G_L is 0,4500. None of the tables of the remaining ordered sequence satisfies these constraints such that an additional blade 3 is required etc. This procedure is carried out until the ordered sequence is empty, i.e. after all tables have been assigned to one blade. The resulting assignment of blades and the resulting minimum number of blades is illustrated in <figref idref="f0017">figure 17</figref>. In the example considered here the minimum number N of blades that is required for handling of all of the tables is N = 10.

0058In order to further improve the quality of the balancing the method of <figref idref="f0018">figure 18</figref> can be carried out on the basis of the result provided by the method of <figref idref="f0002">figure 2</figref>. In step 800 the largest remaining gaps, G_S and G_L are determined as illustrated in <figref idref="f0017">figure 17</figref>. In the example considered in <figref idref="f0017">figure 17</figref> the largest remaining gap G_S is on blade 1 and the largest remaining gap G_L is on blade 10.

0059In step 802 the largest remaining gap G_S is divided by N which yields delta 1 and the largest remaining gap G_L is divided by N which yields delta 2.

0060In step 804 the size threshold T_S is reduced by delta 1 and the load threshold T_L is reduced by delta 2. In step 806 the method of <figref idref="f0002">figure 2</figref> is performed again with the reduced thresholds as determined in step 804. In case the sorting indices and the original object sequence obtained from the method of <figref idref="f0002">figure 2</figref> by performing steps 200 to 202 have been saved, these steps can be skipped in order to start processing of the method of <figref idref="f0002">figure 2</figref> in step 204. The result is a further improved balancing.

0061<figref idref="f0019">Figure 19</figref> shows an alternative approach for refining the balancing. In step 900 delta 3 is calculated by calculating the difference of the sum of the storage capacity of the blades and the sum of the object sizes of all objects to be assigned to the blades and by dividing the difference by the minimum number of blades N. In step 902 delta 4 is calculated by calculating the difference of the sum of the load capacities of the blades and the sum of the object loads of all objects to be assigned to the blades and by dividing the difference by the minimum number of blades N..In the example considered here no normalized values are used in steps 900 and 902.

0062In step 904 the size threshold T_S is reduced by the normalised value of delta 3. The normalised value of delta 3 is obtained by dividing delta 3 by the storage capacity of one of the blades.

0063Likewise the load threshold T_L is updated in step 906 by the normalised delta 4. Normalisation of delta 4 is performed by dividing delta 4 by the load capacity of one of the blades.

0064The reduced size threshold T_S and the reduced load threshold T_L correspond to the theoretical limit of blade resources that are required for handling of the given objects. As the object granularity is finite the theoretical threshold limits will be surpassed in most cases:

0065In order to refine the balancing the method of <figref idref="f0002">figure 2</figref> is performed again (step 908) on the basis of the size threshold T_S obtained from step 904 and the reduced load threshold T_L obtained from step 906 with the modification that the number of blades for the renewed performance of the method of <figref idref="f0002">figure 2</figref> is limited by the minimum number of blades N that has been determined previously. In other words, the assignment procedure of <figref idref="f0002">figure 2</figref> stops when the minimum number N of blades has been used up; this may have the consequence that there will be an excess amount of memory and/or load requirement for the last blade of the minimum number N of blades considered for the assignment procedure that surpasses the respective thresholds T_S and/or T_L. Again steps 200 to 202 of the method of <figref idref="f0002">figure 2</figref> can be skipped in case the sorting indices and the sorted sequence has been stored when the method of <figref idref="f0002">figure 2</figref> was performed the first time. In step 910 it is determined whether there is such an excess amount of memory requirement and/or load requirement for the last blade N, i.e. blade 10. If this is not the case the resulting assignment of objects to blades is output in step 912.

0066If the contrary is the case step 914 is carried out in order to calculate the values of delta 5 and/or delta 6. Delta 5 is obtained by dividing the excess amount of memory, if any, by the number of blades N. Likewise delta 6 is obtained by dividing the excess load requirement, if any, by the number of blades N.

0067On this basis the size and/load thresholds are incremented in step 916. From there the control goes back to step 908.

0068Steps 908 to 916 are carried out repeatedly until there is no longer an excess amount of memory and/or load requirement that cannot be provided by the given number N of blades.

0069<figref idref="f0020">Figure 20</figref> shows a further alternative for refinement of the balancing. First steps 900 and 902 of the method of <figref idref="f0019">figure 19</figref> are carried out in order to obtain delta 3 and delta 4. The gaps delta3 and delta4 are now scanned by stepwise variation of the respective size and load thresholds in order to identify a more balanced assignment of objects to blades. For this purpose delta 3 and delta 4 are divided into equidistant intervals having step sizes delta 7 and delta 8, respectively, as shown in step 1000.The number of increments for performing the respective scans can be predefined or is user selectable.

0070It is to be noted that the number of increments for scanning G_S and for scanning G_L does not need to be the same. Preferably the scans are performed independently from each other such that the total number of assignments that is considered is the number of increments for the G_S scan multiplied by the number of increments for the G_L scan.

0071In step 1002 the size and load thresholds are set to the respective theoretical minima that are required to provide sufficient blade resources for handling of the given number of objects. On this basis the method of <figref idref="f0002">figure 2</figref> is performed again in step 1004. In step 1006 a statistical measure is calculated as a quality measure for the balancing of the assignment of objects to blades obtained as a result of step 1006, if any. For example, the standard deviation of the aggregated sorting index values of objects assigned to each one of the blades is calculated. In other words, for each blade the total of the sorting index values of the objects that have been assigned to the blade is calculated. This provides one total sorting index value per blade. Next the standard deviation is calculated for the total sorting index values.

0072In step 1008 at least one of the thresholds T_S or T_L is incremented by the normalised value of delta 7 or the normalised value of delta 8, respectively. Next step 1004 is carried out again on the basis of the incremented size and load thresholds. Steps 1004 to 1008 are carried out repeatedly until the respective scans through G_S and G_L have been completed and the corresponding assignments of objects to blades have been obtained. In step 1010 one of the assignments is selected based on the statistical measures. For example, the assignment having the lowest standard deviation is selected.

0073It is to be noted that this procedure is limited by the minimum number of blades N. For assignments that do not fit on this given minimum number of blades N no statistical measure needs to be calculated as these assignments are not considered further in the procedure.

0074<figref idref="f0021">Figure 21</figref> shows a computer 108 that has processor 110 for running program 112. Program 112 has module 113 for calculating a sorting index value for each object to be assigned to a blade. Further program 112 has module 114 for sorting of the objects by sorting index value and module 116 for assigning of objects to blades.

0075Further computer 108 has storage 118 for storing a table listing the objects, object sizes, and object loads of objects to be assigned to blades, storage 120 for storage of a storage capacity value of the blades, storage 121 for storage of a load capacity value of the blades, and storage 122 for storing of the number of blades. Further computer 108 has interface 124 for coupling to workstation 126.

0076In operation the table with the object names/numbers, object sizes and object loads is entered via interface 124 and stored in storage 118. Further a storage capacity value for the storage capacity of each individual blade is entered via interface 124 and stored in storage 120. Likewise a load capacity value for the load capacity of each individual blade is entered via interface 124 and stored in storage 121.

0077Next program 112 is invoked. Program 112 calculates a sorting index for each object contained in the table stored in storage 118 on the basis of the normalised object size and object load. The resulting indices are entered into the table stored in storage 118 by module 113. Next module 114 sorts the table of storage 118 by decreasing storage index to provide a sequence of objects (cf. the sequence of <figref idref="f0008">figure 8</figref>). Next module 116 performs the method of <figref idref="f0002">figure 2</figref> in order to determine the minimum number of required blades.

0078This minimum number is stored in storage 122 and is output via user interface 124. This number can be a basis for a users investment decision for purchasing the number of blades to realise the data processing system being capable of handling the objects as listed in the table.

0079In addition, module 116 can perform the methods of <figref idref="f0018">figure 18</figref>, <figref idref="f0019">19</figref> and/or 20 for refining of the balancing.

0080Alternatively, computer 108 is one of the blades. In this instance computer 108 can dynamically change the assignment of objects to blades when the object size changes. This way frequent swapping operations can be avoided. In other words, the creation of "hot spots" is prevented by balancing the load.

List of Reference Numerals

0081<dl id="dl0002"><dt>100</dt><dd>cluster</dd><dt>102</dt><dd>processor</dd><dt>104</dt><dd>memory</dd><dt>106</dt><dd>network</dd><dt>108</dt><dd>computer</dd><dt>110</dt><dd>processor</dd><dt>112</dt><dd>Program</dd><dt>113</dt><dd>module</dd><dt>114</dt><dd>module</dd><dt>116</dt><dd>module</dd><dt>118</dt><dd>storage</dd><dt>120</dt><dd>storage</dd><dt>121</dt><dd>storage</dd><dt>122</dt><dd>storage</dd><dt>124</dt><dd>interface</dd><dt>126</dt><dd>workstation</dd></dl>