A Novel Genetic Algorithm for Static Task Scheduling in Distributed Systems

Transcription

1 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail 200 A Novel Genetic Algoithm fo Static Task Scheduling in Distibuted Systems Ami Masoud Rahmani and Mojtaba Rezvani Abstact The static task scheduling oblem in distibuted systems is vey imotant because of otimal usage of available machines and acceted comutation time fo scheduling algoithm. Solving this oblem using the dynamic ogamming and the back tacking needs much moe time. Theefoe, thee ae moe attemts to solve it using the heuistic methods. In this ae, a new genetic algoithm, named TDGASA, is esented which its unning time deends on the numbe of tasks in the scheduling oblem. Then, the comutation time of TDGASA to find a sub-otimal schedule is imoved by Simulated Annealing (SA). The esults show that the comutation time of the oosed algoithm deceases comaed to an existing GA-based algoithm, although, the comletion time of the final scheduled task in the system deceases a little. Index Tems Genetic algoithm, static task scheduling, distibuted systems, simulated annealing, (TDGASA) Task Deendent Genetic Algoithm using Simulated Annealing I. INTRODUCTION The comlicated tasks can not be executed on the comuting machine in an acceted inteval time. Theefoe, they must be divided into small sub-tasks. The sub-tasks can be executed eithe in the exensive multiocessos o in the distibuted systems. The latte choice is efeed due to bette atio of cost e efomance. On the othe hand, in most cases because of some constaints on multiocesso systems o the natual distibution of tasks, the only otimum choice is emloying the distibuted systems []. The distibuted system consists of some comuting machines with diffeent efomances which ae connected to each othe using the high seed inteconnections, and, ae useful fo much moe comuting alications [2]. The task scheduling oblem in the distibuted systems is known to be NP-had, since, fo allocating T tasks to H machines, the T numbe of allocation will be H and the numbe of states fo unning will be T!. One of the goals of scheduling is to detemine an assignment of tasks to comuting machines in ode to otimize the comletion time of the final task in the system. If the numbe of tasks and comuting systems ae too high, finding the otimal o sub-otimal task scheduling would be time-consuming and in some cases it consumes moe time than a andom execution of tasks. Hence, we must use the heuistic algoithms based on the oblem conditions instead of emloying the classic methods such as the back tacking and the dynamic ogamming. The heuistic algoithms event the oula eos in thei own oeation while tying to find the otimal solution. Theefoe, they aea to be aoiate fo solving oblems [3]. Thee ae moe heuistic methods fo solving the static task scheduling, some of which ae: Ootunistic Load Balancing (OLB) [], Minimum Execution Time (MET) [], Minimum Comletion Time (MCT) [], Genetic Algoithms (GAs) [-8], Simulated Annealing [], Tabu Seach []. One of the best heuistic methods is Genetic Algoithm (GA). Thee ae many eseaches unde the toics of solving the static task scheduling using GAs in the multiocesso systems [3, 8, 0,, 2] and the distibuted systems [3,,, 3, ]. In this ae, a novel GA is esented which has a good ability to solve the above oblem using the simulated annealing. In section 2, the task scheduling oblem in the distibuted systems is discussed and a mathematical model is esented. The genetic algoithm and elated wok (Basic GA) ae intoduced in section 3. In section, the oosed algoithm is intoduced. The simulation esult and the comaison between the algoithms ae esented in section and section concludes on ou findings. II. MODELING OF THE SCHEDULING PROBLEM A ogam can be consideed as a set of tasks and can be modeled as a Weighted Diected Acyclic Gah as below: T = t ; i =,..., n i is a set WDAG = (T, <, E, D) [3], whee { } of tasks, < is a atial ode defined on T which secifies oeational ecedence constaints. That is, t i < t j means that t i must be comleted befoe t j can stat execution. E is a set of diected edges. A diected edge, (i, j), between two tasks t i and t j secifies a atial ode. D is an n n matix of communication data, whee D i, j is the amount of data equied to be tansmitted fom task t i to task t j. If the distibuted system consists a set of m machines which ae connected to each othe using a fast inteconnection netwok, then, Estimated Comletion Time (ECT) would be a n m matix, whee ECT i, j shows the estimated comletion time of the task t i on the machine m j. A WDAG is shown in figue (-a) and a distibuted system consisting thee machines is shown in figue (-b). Table () illustates the ECT matix of the gah shown in figue (). DOI: 0.3/IJCTE.200.V. - -

2 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail t t 2 H 0 H H 2 3 b) t 3 t t 8 a) t 3 8 Fig. a) A WDAG. b) A distibuted system consisting thee machines TABLE I: THE ECT MATRIX OF THE GRAPH SHOWN FIGURE () Machines Tasks H0 H t H3 t t t t t t 0 0 t R is a m m matix which shows the data tansfe ate between diffeent machines. If two tasks schedule on the same machine, the communication cost of tansfeing data will be zeo; othewise, it is obtained based on Equation (). Di, j CommCost( ti, t j ) = R[ H ( i), H ( j)] () D i, j is the amount of data equied to be tansmitted fom task t i to task t j and R[H(i), H(j)] is the data tansfe ate of two diffeent machines. Accoding to the outlined concets, the static task scheduling oblem in the distibuted system becomes a Π:T H maing. This maing allocates a set of tasks T to a set of machines H, whee the ecedence constaints on the tasks is satisfied and the comletion time of tasks on the machines is minimized. The oblem s answe o Scheduling Length (SL) will be given by Equation (2). Answe = min( SL = max{ Fj j = 0,..., m }) (2) F j is the comletion time of final scheduled task on machine H j including comutation time, communication time and waiting time because of ecedence constaints. Two othe aametes ae defined fo each node (task) in the gah known as b-level (the bottom level) and t-level (the to level). The b-level of a node is the length of the longest ath fom the node to a leaf node. If a node has no childen, its b-level is equal to the aveage execution time of the task on the diffeent comuting machines. The t-level of a node (task) is the length of the longest ath fom the node to a oot node in the WDAG without consideing the execution time of that task. In effect, the t-level detemines the ealiest beginning time of a task. Theefoe, if a task has no aent its t-level will be zeo. Table (2) shows the aveage Estimated Comletion Time of the tasks (AvgECT) on the diffeent machines, the b-levels and t-levels of the gah that ae shown in figue (). TABLE II: THE B-LEVELS AND T-LEVELS OF THE GRAPH SHOWN IN FIGURE () Paametes Tasks AvgECT b_level t_level t 82, 0 3, 0 0, 0 t 2, 0 38, 0 0, 0 t 3 0, 33 2, 0 3, 0 t 3,, , 33 t 08, 0, 222, 33 t 83, 83, 222, 33 33, 33, 32, 33 t III. THE GENETIC ALGORITHMS The GAs ae andom seaching methods based on the evolution selection and the natual henomena. These algoithms ae stated with a set of andom solution called initial oulation. Each membe of this oulation is called a chomosome. Each chomosome is a oblem solution which consists of the sting genes. The numbe of genes and thei values in each chomosome deend on the oblem secification. In algoithms discussed in this ae, the numbe of genes of each chomosome is equal to the numbe of the nodes (tasks) in the WDAG and the gene values demonstate the scheduling ioity of the elated task to the node (each chomosome shows a scheduling), whee the highe ioity means that task must be executed ealy. A set of chomosomes in each iteation of GA is called a geneation. The chomosomes ae evaluated by thei fitness functions. The offsing (the new geneation) is ceated by alying some oeatos on the cuent geneation. These oeatos ae a) cossove which selects two chomosomes of the cuent oulation, combines them and geneates a new offsing, and, b) mutation which changes andomly some gene values of a chomosome and ceates a new offsing. Then, the best childen and maybe thei aents ae selected by evolutionay select oeato accoding to thei fitness value(s). Thee hases of the oduction, evaluation and selection ae eeated until some condition is satisfied. Finally, a chomosome which has the best fitness value(s) is selected as a solution. A. Base Genetic Algoithm (BGA) The GA esented by Dhodhi et. al [3], named hee Base Genetic Algoithm (BGA), has fou stes as shown in figue (2). In the fist ste, the following aametes ae ead fom a database: WDAG, ECT and R. Othe aametes such as the initial oulation size (N ), the numbe of geneations (N g ), the cossove obability (X ), and the mutation obability (M ) ae ovided by the use. In the second ste, the b-level and t-level of each node in the WDAG ae calculated and then, in the fist chomosome - 2 -

3 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail 200 of the initial oulation, the gene value (ioity) of each task is set to its b-level. The genes values (ioities) of the est of the chomosomes ae the total of the genes values of the fist chomosome and the andom numbes which ae geneated in the ange of (t-level/2, -t-level/2) of the tasks. Using the Ealiest Finish Time (EFT decoding, which schedules a candidate task onto a machine on which the finish time of the task is the ealiest), the oveall comletion time of the final task in the system is chosen as a fitness function of each chomosome. Fo this eason, fist, all the genes (tasks) of each chomosome ae soted in descending ode accoding to thei values (ioities) in a eady queue. If the ecedence of the tasks in the WDAG ae not obseved in a chomosome, it is chosen as an illegal chomosome and its fitness value would be infinite. Othewise, the tasks ae selected fom the eady queue accoding to thei ioities, and scheduled to the most suitable machine on which the finish time of the task is the ealiest. Finally, the best chomosome of the fist oulation is stoed as a fist element of the Best_Schedule aay. The length of this aay is equal to N g. Ste. Read the WDAG, ECT, and R fom a database and get N, N, X and M fom the use; g Ste 2. Calculate the b-level and the t-level of each task in the WDAG; Geneate Initial Poulation ( P initial ); Pcuent P initial ; Schedules Decoding_ heuistic( Pcuent); Best _ Schedule evaluate (Schedules); Ste 3. while sto citeion not satisfied do begin P new { }; /* emty new oulation */ 3-. eeat fo N /2) times ( dad select( P, Sum_ of _ fitness); cuent mom select ( P, Sum _ of _ fitness); cuent ( dad, mom, child, child2, X Pnew Pnew csov endeeat; 3-2. fo each chomosome P do begin new mutate (chomosome, M ); endfo; 3-3. Pnew Pnew fou best chomosomesof P P ; cuent P new { } Schedules Decoding_ heuistic( Pcuent); Best _ Schedule evaluate (Schedules); endwhile; Ste. Reot the best schedule. Fig. 2 The Base Genetic Algoithm (BGA) [3] cuent In the thid ste, at long as the sto citeion, i.e. the numbe of geneations, is not satisfied, the while loo will be eeated. The thid ste consists of thee sub-stes. In the fist sub-ste, the two aent chomosomes (dad and mom) ae selected by the select function using a oulette wheel selection in a loo. A oulette wheel laces all chomosomes ); in thei oulation which evey of them has its lace big accoding to its fitness function. The chomosomes with bette fitness values will be selected moe often and have a highe obability of geneating the offsing. Then, the cossove oeato is alied to the two aents. A andom numbe between 0 and is geneated, if this numbe is equal o less than X, the aents will be selected diectly fo the new geneation; othewise, two childen ae ceated by the aents as it will be discussed late. Fo each gene a andom numbe between 0 and is geneated. If that is less than 0. then, the gene elated to the dad chomosome is coied to the fist child and the gene elated to the mom chomosome is coied to the second one. Othewise, the gene elated to the dad is coied to the second child and the gene elated to the mom is coied to the fist one. The fist sub-ste is eeated (N /2) times since in each iteation two aent chomosomes must be selected. In the second sub-ste, the mutation oeato is used to event falling all solutions in oulation into the local minima of the solved oblem and also used fo finding the new oints in the seach sace so that oulation divesity can be maintained. This oeato acts on the chomosomes which ae oduced by cossove oeato. A gene of a chomosome with a obability M is chosen by andom and its value is added to a andom numbe between the -t_level/2 and t_level/2 of that node (chomosome) in WDAG. Afte alying mutation, if the gene value is bigge than (b-level+t-level) of that node, then its value becomes (b-level+t-level). Also, if the gene value is less than b-level, then its value becomes b-level of that node. Following the elitism method, in the thid sub-ste, the fou best chomosomes with the best fitness functions ae coied to the new geneation. This means at least the fou best solutions (schedules) ae coied without changes to a new oulation, and theefoe, the best found solution can suvive until the end of un. Then, the cuent geneation is elaced by the new one and afte the decoding chomosomes using the EFT, thei fitness functions ae calculated and the best chomosome will be stoed in the Best_Schedule aay. In the ste fou, afte the Ng iteation is comleted; the final stoed element in the Best_Schedule aay is the best solution fo the scheduling. IV. TDGASA: THE SUGGESTED ALGORITHM The discussed algoithm (BGA) by Dhodhi et. al [3] has used a fixed numbe of geneations (N g ) fo each WDAG with any numbe of tasks. This is a oblem in the above algoithm because if the numbe of tasks is small, thee is no need to toleate high comutation time of the algoithm, and if the numbe of tasks in WDAG is too lage, it is ossible that the numbe of geneations and the numbe of iteations ae not enough to find an otimal o sub-otimal solution. Fo tackling this oblem, we can use a new idea (algoithm) which its unning time deends on the numbe of tasks. In this new idea, two main aametes of this algoithm, i.e. N and N g ae defined as factos of tasks numbes. These two factos ae called NP_facto and Ng_facto. It is obvious that if the numbe of tasks in a WDAG is small, the comutation time will be deceased because of - 3 -

4 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail 200 lessening two above aametes. Howeve, if the numbe of tasks is lage the comutation time of the algoithm will be inceased. Fo deceasing the comutation time, the Simulated Annealing (SA) [] will be emloyed hee. To study a cetain state of a mateial, an annealing ocess is used, whee the mateial is fist melted, and then slowly cooled in a contolled way to obtain a cetain aangement of the atoms. When the temeatue is high, atoms can occasionally move to states with highe enegy, but then, as the temeatue dos, the obability of such moves is educed. In the task scheduling algoithm, the enegy of the state coesonds to its comutation time, and the temeatue becomes a contol aamete which is educed duing the execution of the algoithm. Fo deceasing the temeatue and alying the geometic cooling schedule in a oe time, a new method is used. Theefoe, a new algoithm, so-called Task Deendent Genetic Algoithm using Simulated Annealing (TDGASA) is intoduced. In TDGASA, if the convegence of the esults is ecognized afte some iteation then, some aametes of the algoithm will be changed intentionally. This haens by deceasing the numbe of cuent oulation size (N ) and X by multilying them to a value which is less than one and also, inceasing M by multilying its value to a numbe moe than one. The comutation time of a new algoithm is deceased by lessening cuent oulation and the cossove obability and thee is an attemt to event to ta with local minima by inceasing the mutation obability. Ste. Read the WDAG, ECT and R fom a database and get Cossove_Facto, Mutation_ Facto, N, N, N _ Facto, N g _ Facto, Sliding_Window, X M,, Poulation_ Facto and Comaison_ Facto, fom the use; N Numbe _ of _ tasks * N _ Facto; N g Numbe _ of _ tasks * N a) g _ Facto ; 3-. Calculate value of CD if (CD >= Comaison_Base) /* So, Annealing haens */ N N * Poulatoin _ Facto; X X * Cossove _ Facto; M M * Mutation _ Facto; Reset Sliding_Counte to zeo; endif; b) Fig 3. a) The modification in the fist ste of algoithm shown in Figue 2. b) The fouth sub-ste of ste thee is added to the algoithm shown in Figue 2. TDGASA algoithm is simila to BGA in figue (2), howeve, the fist ste is modified as shown in figue (3-a) and the fouth sub-ste of ste thee is added to the algoithm as it is shown in figue (3-b). In the fist ste, in addition to eading WDAG, ECT and R fom a database, othe aametes ae taken fom the use. Poulation_Facto, Cossove_Facto and Mutation_Facto ae the cooling schedules of the algoithm. g The suitable time fo alying these factos will be exlained late. As mentioned ealie, afte alying the cossove and mutation oeatos on the cuent geneation and oducing the new geneation and also coying the fou best chomosomes of the cuent geneation without any changes to the new one, all the chomosomes of new geneation ae decoded and the best obtained solution is stoed in the Best_Schedule aay. Theefoe, the stoed fitness value (the oveall comletion time) of each element is bette than the evious ones, so, the Best_Schedule is a descending aay. Fo alying SA method, in the fouth sub-ste, the convegence of the Best_Schedule elements is tested by a new suggestion idea. This idea uses a sliding window which its length deends on the numbe of tasks in the WDAG. The Sliding Window Length (SWL) is given by Equation (3) as below: SWL = Numbe_of_tasks * Sliding_Window (3) Sliding_Window is a coefficient of the sliding window which its suitable value is detemined late. If the beginning of sliding window is the index i of Best_Schedule, then the Convegence Degee (CD) is calculated by Equation (): SWL + i k= i Best_Schedulek CD = SWL* Best_Schedule i () Consideing the descending aay Best_Schedule, the CD is always equal o less than one. If the value of CD is nea to one, the values of the elements ae moe convegent, then alying the cooling schedules will be moe aoiate. The value of CD is comaed to a Comaison_Base; if the CD is equal o moe than that, the SA will haen and the sliding window counte will be set to zeo; othewise the next iteation of the algoithm will be done. The minimum distance between two SA events is equal to the SWL. A. Detemining the otimal aametes of TDGASA A set of simulations is done on a Pentium IV with a 2.8 MHz Intel ocesso and Gigabyte of RAM to detemine the otimal aametes of TDGASA algoithm. A set of 30 WDAG gahs consists of diffeent tasks, the deendency matix and the ECT ae geneated andomly by a witten C# ogam. All elements of matix R ae set to one. To find out the oe value of each aamete (Cossove_Facto, Mutation_Facto, Poulation_Facto, Comaison_Base, Sliding_Window), the diffeent values ae assigned to each aamete, while the values of the othe aametes emain fixed. Then, the comutation time and the oveall comletion time fo each WDAG ae calculated and accodingly, the best value fo each aamete is detemined as follow: Cossove_Facto=0., Mutation_Facto=., Poulation_Facto=0.8, Comaison_Base =0., Sliding_Window=0.2. V. SIMULATIONS AND RESULTS A set of simulations is done on a Pentium IV with a 2.8 MHz Intel ocesso and Gigabyte of RAM to comae TDGASA with BGA scheduling algoithm. A set of andom WDAG gahs consists of 00 to 200 tasks and to - -

5 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail 200 machines ae geneated andomly as shown in table (3). The matix ECT is geneated by andom and all elements of matix R ae set to one. X =0., M =0.0 ae set fo two algoithms and N =00, N g =000 ae defined fo BGA. To un the simulations of two algoithms in the nealy same condition, the initial values fo N_Facto and Ng_Facto ae set to 3 and esectively, so that by multilying thei values to the numbe of tasks (between 00 and 200), the N and N g ae attained at BGA ange value. The othe TDGASA aametes ae equal to the same values which ae obtained in section. TABLE III: THE WDAGS USED FOR THE COMPARISON OF TWO ALGORITHMS Gah numbe Numbe of tasks Numbe of machines 8 Numbe of deendencies Both of two algoithms ae un fo each gah thee times. Afte scheduling, the comutation time and the oveall comletion time (by seconds) of each algoithm ae shown in table (). Also, the aveage comutation time of TDGASA is selected as a base and the atio between the aveage comutation time of BGA and the aveage comutation time of TDGASA is calculated fo each gah. Then, by adding the obtained atios and dividing the esult by the numbe of gahs, the aveage atio is achieved. The above stes ae done fo the aveage oveall comletion time which is shown in table (). As the esults show, the comutation time of TDGASA is deceased by about 83 ecent comaed to BGA. Howeve, the aveage total comletion time is deceased a little. TABLE IV: THE RESULT OF TDGASA AND BGA SCHEDULING ALGORITHMS FOR THE GRAPHS SHOWN IN TABLE III Gah numbe Sum of atios Aveage atios Aveage comutatio n time (s) BGA Oveall comletion time (s) VI. CONCLUSIONS TDGASA Aveage Oveall comutation comletion time (s) time (s) The task scheduling oblem in the distibuted systems is known to be NP-had. Theefoe, the heuistic algoithms which obtain nea-otimal solution in an accetable inteval time ae efeed to the back tacking and the dynamic ogamming. The genetic algoithm is one of the heuistic algoithms which have the high caability to solve the comlicated oblems like the task scheduling. In this ae, a new genetic algoithm, named TDGASA is esented which its oulation size and the numbe of geneations deends on the numbe of tasks. The comutation time of this algoithm is deceased by using simulated annealing. Thee is a tadeoff between the comutation time and the total comletion time. But with the oe using of simulated annealing, the comutation time of the algoithm deceases moe, although, the oveall comletion time is not inceased. TDGASA oved highly influential in task scheduling oblem; howeve, it can ovide a numbe of contibutions in fields such as the industial engineeing, the contol ojects, economy and etc. REFERENCES [] Tanenbaum, A. S., Moden Oeating Systems, Pentice Hall, 2. [2] Watson, D.W., Antonio, J. K., Siegel, H. Guta, J., R., and Atallah, M.J., "Static matching of odeed ogam segments to dedicated machines in a heteogeneous comuting envionment", Poceedings of the Heteogeneous Comuting Woksho, Ail, [3] Haut, R.L., Haut, S.E., Pactical genetic algoithms, John willy & Sons, 200. [] Amstong, R., Hensgen, D., and Kidd, T., "The elative efomance of vaious maing algoithms is indeendent of sizable vaiances in un-time edictions", th IEEE Heteogeneous Comuting Woksho (HCW '8), 8,. -8. [] Ali, S., Baun, T. D., Siegel, H. J., and Maciejewski, A. A., Heteogeneous comuting, in Encycloedia of Distibuted Comuting, Kluwe Academic, Nowell, MA, 200. [] Baun, T. D., Siegel, H. J. and Beck, N., "A comaison of eleven static heuistics fo maing a class of indeendent tasks onto heteogeneous distibuted systems", Jounal of Paallel and Distibuted Comuting Vol., 200,

6 Intenational Jounal of Comute Theoy and Engineeing, Vol., No., Ail 200 [] Zafaani Moatta E., Rahmani A.M., Feizi Deakhshi M.R., "Job Scheduling in Multi Pocesso Achitectue Using Genetic Algoithm", th IEEE Intenational confeence on Innovations in Infomation Technology, dubai, 200, [8] Shenassa, M. H., Mahmoodi, M., "A novel intelligent method fo task scheduling in multiocesso systems using genetic algoithm", jounal of Fanklin Institute, Elsevie, 200,. -. [] Pouhaji Kazem A. A., Rahmani A. M. and Habibi Aghdam H.,, A Modified Simulated Annealing Algoithm fo Static Scheduling in Gid Comuting, Intenational Confeence on Comute Science and Infomation Technology 2008 (ICCSIT 2008), Singaoe August 2 Setembe, 2008, [0] Rahmani A. M., Vahedi M. A., "A Novel Task Scheduling in Multiocesso Systems with Genetic Algoithm by Using Elitism Steing Method", INFOCOMP Jounal of Comute Science, Vol. (2), 2008,.8-. [] Abdeyazdan M. and Rahmani A. M., "Multiocesso Task Scheduling using a new Pioitizing Genetic Algoithm based on numbe of Task Childen", Book chate of Distibuted and Paallel Systems in Focus: Deskto Gid Comuting, Singe Velag, 2008,. 0-. [2] Lee, Y.H., Chen, C., "A Modified Genetic Algoithm fo Task Scheduling in Multiocesso Systems", the th woksho on comile techniques fo high-efomance comuting, [3] Dhodhi, M. K., Ahmad, I., Yatama, A. and Ahmad, I., "An integated technique fo task matching and scheduling onto distibuted heteogeneous comuting systems", Jounal of Paallel and Distibuted Comuting, Vol. 2, 2002, [] Radulescu, A., Gemund, A.van. "Fast and effective task scheduling in heteogeneous systems", Poceeding of Heteogeneous Comuting Woksho, [] Kikatick, S., C. D. Gelatt J., and M. P. Vecchi., "Otimization by simulated annealing", Science, Vol. 220, 83, Ami Masoud Rahmani eceived his B.S. in comute engineeing fom Ami Kabi Univesity, Tehan, in, the M.S. in comute engineeing fom Shaif Univesity of technology, Tehan, in 8 and the PhD degee in comute engineeing fom IAU Univesity, Tehan, in 200. He is an assistant ofesso in the Deatment of Comute and Mechatonics Engineeing at the IAU Univesity. He is the autho/co-autho of moe than 0 ublications in technical jounals and confeences. He seved on the ogam committees of seveal national and intenational confeences. His eseach inteests ae in the aeas of distibuted systems, ad hoc and senso wieless netwoks, scheduling algoithms and evolutionay comuting. - -