DEADLOCK INDEX ANALYSIS OF MULTI-LEVEL QUEUE SCHEDULING IN OPERATING SYSTEM USING DATA MODEL APPROACH

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1 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN DEADLOCK INDEX ANALYSIS OF MULTI-LEVEL QUEUE SCHEDULING IN OPERATING SYSTEM USING DATA MODEL APPROACH D. Shukla, Shweta Ojha 2 Deptt. of Mathematc and Stattc, Dr. H.S. Gour Unverty, Sagar (M.P., 73, INDIA e-mal:dwakarhukla@radffmal.com 2 Deptt. of Computer Sc. and Applcaton, Dr. H.S. Gour Unverty, Sagar (M.P.,73, INDIA e-mal:mehwetaojha@gmal.com Abtract In the multproceor envronment the number of job arrvng to the proceor of CPU at a tme very large whch caue a long watng queue. In the proceor when any conflct are due to hared reource or overlap of ntructon or any logcal error, the deadlock tate appear where proceng of job blocked completely. A the cheduler ha jump from one job to another n order to perform the proceng work the tranton mechanm appear. Th paper preent a general tranton cenaro for the functonng of CPU cheduler n the preence of deadlock condton. A data model baed Markov chan model propoed to tudy the tranton phenomenon and a general cla of chedulng cheme degned. Some pecfc cheme are treated a t partcular cae and are compared under the etup of model through a propoed deadlock ndex meaure. Smulaton tudy performed to evaluate the comparatve mert of pecfc cheme of the cla degned wth the help of varyng value of α and d. Keyword: Proce chedulng, Markov chan model, Data model, State of ytem, Ret State, Deadlock State, Proce queue, Mult-level queue chedulng, Tranton probablty matrx, Deadlock ndex.. INTRODUCTION Operatng ytem play a major role n managng procee arrvng n the form of multple queue. Arrval of a proce random along wth ther dfferent categore and type. All thee requre chedulng algorthm to work over real tme envronment wth pecal reference to tak, control and effcency (ee Stankovc (98. The randomzaton nvolved n chedulng procedure lead to perform a probabltc tudy. Demer et al. (989 preented an analy of Far Queung algorthm wherea Cobb et al. (998 pcked up far chedulng of flaro wth the conderaton of tme hftng approach n the area of hgh-peed network. Goyal,Guo,Vn (99 dereved the Herarchcal CPU cheduler n the envronment where the multmeda operatng ytem ued. In the mlar lne, Heh and Lam (23 dcued mart cheduler for multmeda uer. A tme drven chedulng model propoed by Janon, Locke and Tokuda (98 attracted attenton of reearcher for the model formaton over functonng and procedure on operatng ytem. Katcher et al. (993 propoed an analy of fxed prorty cheduler and Davd (99 gven a ucceful contrbuton over the tudy of real tme and conventonal chedulng wth a comparatve analy. Medh (99 gven an elaborate tudy of a varety of tochatc procee and ther applcaton n varou feld. Nald (22 preented Markov chan model for undertandng the nternet traffc harng among varou operator n a compettve market. Shukla et al. (27 derved a Markov chan model for the tudy of tranton probablte n pace dvon wtche n computer network. Shukla and Jan (27 have a dcuon on the ue of Markov chan model for 93

2 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN multlevel queue cheduler n an operatng ytem. Some other ueful contrbuton over detaled decrpton of operatng ytem are due to Slberchatz and Galvn (999, Stallng (2 and Tanenbaum and Woodhull (2. The tranton mechanm of cheduler over queue motvate to thnk over the ytem phenomenon n the form of a tochatc tudy. Nald (22, Shukla et.al. (27, Shukla and Jan (27 have hown the utlty of Markov chan model explanng the ytem properte. Dervng a motvaton from thee, a cla of chedulng cheme degned n th paper for performng an ntegrated approach of effcency comparon under the aumpton of Markov chan model and ung a deadlock ndex meaure.. DEADLOCK BASED GENERAL CLASS OF MULTI-LEVEL QUEUE SCHEDULING Suppoe a mult-level queue chedulng wth four queue Q, Q 2,Q,3,Q each havng large number of procee P j,p j ',P j ",P j "'(j=,2,3. repectvely watng for proceng. Defne Q (=,2,3, lke tate of chedulng ytem wth two other pecfc tate Q and Q. Frt four tate are related to arrval and nput of procee whle the lat two aocate wth retng and watng of cheduler. A quantum a mall pre-defned lot of tme gven for proceng, to watng procee n queue. Symbol n denote the n th quantum allotted by the cheduler to a proce for executon (n=,2,3,. Ung above, the tructure of gven cla : ( All the frt four queue Q, Q 2,Q,3,Q are allowed to accept a new proce wth ntal probablte pr,pr 2,pr 3,pr pr = = (2 Scheduler ha a random movement over all tate Q (=,2,3,,, on quantum varaton. (3 Scheduler tart proceng of any Q wth probablty pr (=,2,3,, then pck up the frt proce of that queue and allot a quantum for proceng. ( Proce reman wth proceor untl the quantum over. If t complete wthn that, then get out of Q. ( Wthn quantum, f a proce dd not complete, cheduler agn next quantum to the next proce of the ame queue and o on. The earler ncomplete proce move to next queue Q + ((+ and wat untl next quantum to be alloted for t proceng. ( State Q and Q are ued a retng the tranton ytem lke dle tate or deadlock tate. (7 Specfc condton over retng (or retrctng tranton hall be undertaken wthn ung th cla. (8 Quantum allotment procedure, wthn Q, by cheduler, contnue untl Q empty. The cheduler jump from any tate to any other tate at the end of a quantum. When Q, Q 2,Q,3,Q are empty, cheduler move toward tate Q or Q. The character of Q and Q are dfferent and to be defned under the dfferent cae of the ytem. (9 Scheduler attempt proceng n queue Q on frt come frt erve ba. Any ncomplete proce or new proce, f appear n Q, reman wth Q only untl proceed completely. 2. MARKOV CHAIN MODEL Let{x (n,n } be a Markov chan where x (n th denote the tate of the cheduler at the n quantum of tme. The tate pace for x (n {Q, Q 2,Q,3,Q,Q,Q } where cheduler X move tochatcally over thee n dfferent quantum. Predefned ntal electon probablte of tate are: 9

3 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN P[X ( =Q ]=pr P[X ( =Q 2 ]=pr 2 P[X ( =Q 3 ]=pr 3 P[X ( =Q ]=pr P[X ( =Q ]=pr P[X ( =Q ]=pr wth pr +pr 2 +pr 3 +pr +pr +pr = pr =, where pr =pr =. = CPU Q pr P P 2... P 3 new proce Q wth prorty (pr new proce Xn pr 2 P ' P 2 ' P 3 '... Q 2 wth prorty (pr 2 Scheduler pr 3 new proce Q P " P 2 " "... P 3 Q 3 wth prorty (pr 3 Fg. 2. (Sytem Dagram Q Q 2 New Proce Q Q 3 New Proce New Proce Q Fg. 2.2 (Unretrcted Tranton Dagram Let j (,j=,2,3,,, be the tranton probablte of cheduler over x tate then unt-tep tranton probablty matrx for ( n X ( n ( n [ X = Q / X = Q ], j j = P + j ; 9

4 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN X (n- X (n Q Q 2 Q 3 Q Q Q Q 2 3 Q Q Q 2 3 Q 2 3 Q 2 3 (2.2 ubject to condton =, 2 = 2, 3 =, (2.2. = = 3 = =, =, = and j. = = = The tate probablte, after frt quantum can be obtaned by a mple relatonhp: P ( ( [ X = Q ] = p X + + ( ( ( ( ( ( ( ( ( ( [ = Q ]. p[ X = Q / X = Q ] + p[ X = ]. p[ X = Q / X = ] ( ( ( ( ( ( p[ X = ]. p[ X = Q / X = ] + p[ X = ]. p[ X = Q / X = ] ( ( ( ( ( ( X = Q ]. X = Q / X = Q ] + X = Q ]. X = Q / X = Q ] 2 3 = = = = = = = pr pr 2 pr 3 pr pr pr (2.3 Smlarly, the tate probablte after the econd quantum could be obtaned by mple relatonhp: 9

5 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Remark 2. ( 2 [ P X = Q ] = ( 2 [ P X = Q ] = ( 2 [ P X = Q ] = ( 2 [ P X = Q ] = ( 2 [ P X = Q ] = ( 2 [ P X = Q ] = 2 3 j= = j= = j= = j= = j= = ( pr ( pr ( pr ( pr ( pr ( pr j= = j j j j j j j j 2 j 3 j j j In the mlar fahon, for n quantum, the generalzed expreon (2. ( n P [ X = Q ] = ( n 2 ( n 3 ( n ( n ( n m= m= m= m= m= m= t= t= t= t= t= t= k= j= = k= j= = k= j= = k= j= = k= j= = k= j= = pr j pr pr pr pr pr j j j j j kt kt kt kt kt kt m m2 m3 m m m (2. 3. SCHEDULING SCHEME IN GENERAL CLASS By mpong retrcton and condton over way and procedure, one can generate varou chedulng cheme from the generalzed veron of cla tated n ecton.. 3. SCHEME- I: (a DefneQ andq pecfcally a Q = (watng tate D Q =W (deadlock tate 97

6 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN The deadlock tate D where the return back tranton not poble wherea the watng tate one where ytem can reach n any quantum durng proceng to a job but can alo trant back to the ame queue n any quantum. (b A new proce enter to Q, Q 2,Q 3 and Q queue. (c Tranton between W and D retrcted. (d The D aborbng tate. The dagrammatc form of th cheme n fg 3.. CPU W pr P P 2... P 3 new proce Q wth prorty (pr new proce Xn pr 2 P ' P 2 ' P 3 '... Q 2 wth prorty (pr 2 Scheduler D pr 3 P " P 2 " "... P 3 new proce Q 3 wth prorty (pr 3 The tranton dagram for Scheme-I n fg Fg. 3.. (Sytem Dagram of Scheme-I D Q 2 New Proce Q Q 3 New Proce New Proce W Fg (Tranton Dagram of Scheme-I The unt-tep tranton probablty matrx forx (n under cheme I 98

7 GESJ: Computer Scence and Telecommuncaton 2 No.(29 X (n Q Q 2 Q 3 Q W D ISSN X (n- Q 2 3 Q Q Q 2 3 W 2 3 D (3.. Defne an ndcator functon l j =, f (=,j=,2,3,, =, otherwe. The ntal probablte are P[X ( =Q ]=pr P[X ( =Q 2 ]=pr 2 P[X ( =Q 3 ]=pr 3 (3..2 P[X ( =Q ]=pr P[X ( =W]= P[X ( =D]= Remark 3.. The tate probablte, over the mpoed condton, after the frt quantum are: P[X ( =Q ]=pr l + pr 2 2 l 2 + pr 3 3 l 3 + pr l = pr l = P[X ( =Q 2 ]= pr 2l2 = P[X ( =Q 3 ]= pr 3l3 = P[X ( =Q ]= pr l (3..3 = P[X ( =W]= pr l = P[X ( =D ]= pr l = Remark 3..2 The tate probablte after the econd quantum are: 99

8 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN P[X (2 =Q ] = pr jlj jl j j= = P[X (2 =Q 2 ] = pr jlj j 2l j 2 j= = P[X (2 =Q 3 ] = pr jlj j3l j3 (3.. j= = P[X (2 =Q ] = pr jlj j l j j= = P[X (2 =W] = pr jlj jl j j= = P[X (2 =D]= = pr jlj jl j j= = Remark 3..3 For n quantum the generalzed expreon : P[X (n =Q ]=... pr jlj l ktlkt... m lm m= t= k= j= = P[X (n =Q 2 ]=... pr jlj l ktlkt... m2lm2 m= t= k= j= = P[X (n =Q 3 ]=... pr jlj l ktlkt... m3lm3 (3.. m= t= k= j= = P[X (n =Q ]=... pr jlj l ktlkt... mlm m= t= k= j= = P[X (n =W]=... pr jlj l ktlkt... mlm m= t= k= j= = P[X (n =D]=... pr jlj l ktlkt... mlm m= t= k= j= =

9 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN NUMERICAL ILLUSTRATIONS USING DATA SET CREATED WITH THE HELP OF MATHEMATICAL MODEL The bac and centfc approach for data analy related to tate tranton probablte managed by a data model wth two parameter α and d. The tand for number of queue. X (n- X (n Q Q 2 Q 3 Q Q Q Q α α +d. α +2d. α +3d. α +d. -( α +d. Q 2 α+d. α +2d. α +3d. α +d. α +d. -( α +d. Q 3 α+2d. α +3d. α +d. α +d. α +d. -( α +2d. Q α+3d. α +d. α +d. α +d. α +7d. -( α +2d. Q α+d. α +d. α +d. α +7d. α +8d. -( α +3d. Q α+d. α +d. α +7d. α +8d. α +9d. -( α +3d. Cae I wth α=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg. (α=., d=.2 Fg.2 (α=., d=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg.3 (α=., d=. Fg. (α=., d=.8

10 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Cae II wth α=.2 P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg. 2. (α=.2, d=.2 Fg. 2.2 (α=.2, d=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg. 2.3 (α=.2, d=. Fg. 2. (α=.2, d=.8 Cae II wth α=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg. 3. (α=., d=.2 Fg. 3.2 (α=., d=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg. 3.3 (α=., d=. Fg. 3. (α=., d=.8 2

11 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Cae II wth α=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg.. (α=.,d=.2 Fg..2 (α=.,d=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg..3 (α=.,d=. Fg.. (α=.,d=.8 Cae II wth α=.8 P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg.. (α=.8, d=.2 Fg..2 (α=.8, d=. P[X(n=Q ] Q Q P[X(n=Q ] Q Q Fg..3 (α=.8, d=. Fg.. (α=.8, d=.8 3

12 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN WAITING INDEX ANALYSIS For the tate Q =D, a deadlock ndex [I (n ] defned below: [I (n ] c = P[x (n =Q ] / [P[x (n =Q ] + P[x (n =Q ]] (. where c denote dfferent chedulng cheme [c= I, II, III, IV]. The (. a relatve meaure of cheduler probablty toward the chance of beng on the deadlock tate. The Q (=W lke an dle tate where cheduler reache n mot of the tme when no proce n the queue left or otherwe and Q (=D an aborbng tate where deadlock of the tranton ytem occur. The deadlock ndex meaure the ntenty of chance toward deadlock tranton by the cheduler under pecfed value of α and d. A pecal, f P[x (n =Q ]= then [I (n ] c = whch how the chedulng cheme hghly uffer from deadlock. If P[x (n =Q ]= then [I (n ] c = whch reveal the hgh effcency of the cheme becaue the cheme ndependent of the ( n deadlock fear. Therefore, I and P[x (n =Q ]= P[x (n =Q ]=/2 provde ndex [I (n ] c ( [ ] 2 n =/2. The I c / hown n fg.. [ ] c ( [ ] n the lower zone of ndex whle / 2 I the upper zone a < c Lower zone Upper zone ½ Deadlock Index [I (n ] c Fg.. The lower zone reflect for better operaton and effcency of chedulng cheme.. Calculaton of Index CondtonI (Alpha=., d=.2 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CASE CondtonII (Alpha=., d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] II n= n= n= n= n= n= n= CondtonIII (Alpha=., d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] III n= n= n= n= n= n= n= CondtonIV (Alpha=., d=.8 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] IV n= n= n= n= n= n= n=

13 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN CondtonI (Alpha=.2, d=.2 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CASE 2 CondtonII (Alpha=.2, d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] II n= n= n= n= n= n= n= CondtonIII (Alpha=.2, d=. CondtonIV (Alpha=.2, d=.8 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] III n= n= n= n= n= n= n= quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] IV n= n= n= n= n= n= n= CondtonI (Alpha=., d=.2 CASE 3 CondtonII (Alpha=., d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] II n= n= n= n= n= n= n= CondtonIII (Alpha=., d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n=.2.. n= n= n= n= n= n= CondtonIV (Alpha=., d=.8 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] II n= n= n= n= n= n= n=

14 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN CASE CondtonI (Alpha=., d=.2 CondtonII (Alpha=., d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CondtonIII (Alpha=., d=. CondtonIV (Alpha=., d=.8 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CASE CondtonI (Alpha=.8, d=.2 CondtonII (Alpha=.8, d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CondtonIII (Alpha=.8, d=. quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n= CondtonIV (Alpha=.8, d=.8 quantum P[x (n =Q ] P[x (n =Q ] P[I (n ] I n= n= n= n= n= n= n=

15 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Index Graph for Cae I condton- condton-2 condton-3 condton- Index Graph for Cae II condton- condton-2 condton-3 condton- Index Graph for Cae III condton- condton-2 condton-3 condton- 7

16 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Index Graph for Cae IV,8,,, condton- condton-2 condton-3 condton- Index Graph for Cae V,8,,,2 condton- condton-2 condton-3 condton By fg., the deadlock for cheme-iii contantly lower than any other cheme over the ncreang quantum. Th how uperorty of th cheme over I, II and IV. The ame remark obtaned wth Equal tranton probablty matrx. Therefore, n term of deadlock ndex vewpont, the cheme-iii n lower zone n quantum up to n=7 and o uperor and recommendable over other. 8

17 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN CONCULDING REMARKS The general cla of mult-level queue chedulng contan four cheme, a member, whch are compared ung a Markov chan model. Every cheme ha term, condton and retrcton over the general cla. Markov chan model condered n Secton 2. a common platform to compare the properte of thee cheme. Scheme-I uffer a hgh chance for ytem reachng to deadlock tate. Unequal tranton probablte are lke a benefcal approach for cheme-i. In Scheme-II, the chance for deadlock lttle lower than other cheme and unequal tranton element matrx provde better reult. Scheme-III havng lowet amount of deadlock probablty for cheduler and unequal cae effcent over equal. Lat cheme-iv bear moderately hgh deadlock probablty than cheme-iii. Moreover th one alo better for unequal tranton element. Deadlock ndex analy alo upport the above fact. Thee ndce are n lower zone for cheme-iii contantly over all even quantum. Scheme-IV ha pooret deadlock ndex, howng the low performance n term of ndex meaure. Overall, n the etup of Markov chan model and under deadlock ndex a a performance meaure, cheme-iii better then cheme-i, II, IV. The unequal value element of tranton probablty matrx provde betterment over equal n all the mulated group. Deadlock ndex proved a a trong meaure of performance evaluaton ung Markov chan model etup, whle comparng dfferent chedulng cheme. REFERENCES. Cobb, J. Gouda, M. and EL-Naha, A. (June, 998: Tme-Shft Far Schedulng of Flaro n Hgh-Speed Network, IEEE/ACM Tranacton of Networkng, pp Davd B. Goub, (99: Operatng Sytem Support for Coextence of Real-Tme and Conventonal Schedulng, Carneqe Mellon Unverty, PHburg W. PA. 3. Demer, A., Kehar, S. and Shenker, S (989: Analy and Smulaton of a Far Queung Algorthm, Proceedng of SIGCOMM, pp.-2.. Goyal, P. Guo., X. and Vn, H.M.(Oct., 99: A Heranchcal CPU Schedular for Multmeda Operatng Sytem, In Proceedng of the Second Sympoum on Operatng Sytem Degn and Imjplementaton (OSDI 9, Secattle, WA, pp Heh, J. and Lam, M.S. (May 23: A SMART Scheduler for Multmeda Applcaton, ACM Tranacton on Computer Sytem (TOCS, vol. 2(2, pp Janon, D. Locke, C.D. and Tokuda, H. (December, 98: A Tme Drver Schedulng Model for Real-Tme Operaton Sytem, IEEE Real-Tme Sympoum, pp Katcher (Oct., 993: Engneerng and Analy of Fxed Prorty Scheduler, IEEE Tranacton of Software Engneerng, pp Medh, J. (99: Stochatc procee, Ed., Wley Lmted (Fourth Reprnt, New Delh. 9. Nald, M. (22: Internet acce traffc harng n a mult-uer envronment, Computer Network, Vol. 38, pp Slberchatz, A., Galvn, P. (999: Operatng ytem concept, Ed., John Wley and Son (Aa, Inc.. Shukla, D. and Jan, Saurabh. (27: A Markov chan model for mult-level queue cheduler n operatng ytem, Proceedng of the Internatonal Conference on Mathematc and Computer Scence, ICMCS-7, pp

18 GESJ: Computer Scence and Telecommuncaton 2 No.(29 ISSN Shukla, D. Gadewar, S. Pathak, R.K. (27: A Stochatc model for pace-dvon wtche n computer network, Appled mathematc and Computaton (Elever Journal, Vol. 8, Iue 2, pp Stankovc, J.A. (June 98: Smulaton of three Adaptve, Decentralzed controlled, Tak chedulng algorthm, Computer Network, vol. 8, No. 3, pp Stallng, W. (2:Operatng ytem, Ed., Pearon Eduacton,Sngopore,Indan Edton, New Delh.. Tanenbaum, A. and Woodhull, A.S. (2: Operatng ytem, Ed. 8, Prentce Hall of Inda, New Delh. Artcle receved: 2--8